With the rapid rise of social media and Internet culture, memes have become a popular medium for expressing emotional tendencies. This has sparked growing interest in Meme Emotion Understanding (MEU), which aims to classify the emotional intent behind memes by leveraging their multimodal contents. While existing efforts have achieved promising results, two major challenges remain: (1) a lack of fine-grained multimodal fusion strategies, and (2) insufficient mining of memes' implicit meanings and background knowledge. To address these challenges, we propose MemoDetector, a novel framework for advancing MEU. First, we introduce a four-step textual enhancement module that utilizes the rich knowledge and reasoning capabilities of Multimodal Large Language Models (MLLMs) to progressively infer and extract implicit and contextual insights from memes. These enhanced texts significantly enrich the original meme contents and provide valuable guidance for downstream classification. Next, we design a dual-stage modal fusion strategy: the first stage performs shallow fusion on raw meme image and text, while the second stage deeply integrates the enhanced visual and textual features. This hierarchical fusion enables the model to better capture nuanced cross-modal emotional cues. Experiments on two datasets, MET-MEME and MOOD, demonstrate that our method consistently outperforms state-of-the-art baselines. Specifically, MemoDetector improves F1 scores by 4.3% on MET-MEME and 3.4% on MOOD. Further ablation studies and in-depth analyses validate the effectiveness and robustness of our approach, highlighting its strong potential for advancing MEU.

This manuscript introduces a novel preassigned-time distributed optimization protocol for resource allocation in multiagent systems, addressing both local convex set constraints and global equality constraints. The protocol operates through two sequential phases: initially, each agent’s state is deterministically driven into its feasible set within a prespecified time; subsequently, global equality constraints are continuously maintained while progressively converging to the optimal solution, achieving exact optimization within the total preassigned time. Distinct from conventional finite-time, fixed-time, or predefined-time distributed algorithms, our framework innovatively employs a state-based generator mechanism. A key advantage is the settling time’s invariance to both initial conditions and system parameters, enabling precise offline determination of convergence timelines and offering substantial practical benefits for real-time implementations. Numerical experiments validate the theoretical soundness and practical efficacy of the proposed methodology in resource-constrained distributed coordination scenarios.

Large language models (LLMs) have demonstrated significant utility in a wide range of applications; however, their deployment is plagued by security vulnerabilities, notably jailbreak attacks. These attacks manipulate LLMs to generate harmful or unethical content by crafting adversarial prompts. While much of the current research on jailbreak attacks has focused on single-turn interactions, it has largely overlooked the impact of historical dialogues on model behavior. Although recent studies have explored multi-turn jailbreak attacks, they generally assume that the attacker can only manipulate the user prompt. In contrast, we highlight that an attacker can also control the model’s previous outputs. To this end, we introduce DIA, a new paradigm that leverages fabricated dialogue history to enhance jailbreak effectiveness. DIA operates in a black-box setting, requiring only access to the chat API or knowledge of the LLM’s chat template. We propose two methods for constructing adversarial historical dialogues: one adapts gray-box prefilling attacks, and the other exploits deferred responses. Our experiments demonstrate that DIA achieves state-of-the-art attack success rates on recent LLMs, including Llama-3.1 and GPT-4o. Additionally, we show that DIA can bypass 6 different defense mechanisms, highlighting its robustness.

In the control problems of multi-agent systems, collision avoidance is a fundamental safety requirement. One effective approach to ensure safety involves combining control barrier functions (CBFs) with quadratic programming (QP), where nominal control inputs are incorporated into QPs to achieve desired control objectives. Additionally, it is crucial to study the control performance of multi-agent systems to balance these objectives with control efforts. This work demonstrates that the performance index is closely related to the hyperparameters in the CBF-based QP controller, and the Bayesian optimization algorithm is used to optimize and improve performance. Firstly, a safe control approach is developed and a unified performance enhancement framework is established to optimize the performance index. Hyperparameters are then explored and categorized, introducing the concept of feasible hyperparameters to describe the attainability of control objectives. Subsequently, the constrained Bayesian optimization algorithm is employed to identify a set of feasible and optimal hyperparameters in a data-driven manner, even when the functional expressions of performance and constraints are unknown. Finally, experiments are conducted to demonstrate the feasibility of the proposed methods in multi-agent systems. Note to Practitioners—Both safety and optimality are of great importance in the control systems. The design and development of controllers for multi-agent systems are currently undergoing significant evolution. Academic researchers and industrial practitioners are actively refining controller designs to perform better in a variety of collaborative tasks. With practical applications in mind, there is a growing demand for control techniques capable of ensuring a safe operating environment while maintaining efficiency in energy consumption. Therefore, this paper aims to furnish practitioners and researchers with a safe control framework, facilitating the refinement of optimal control solutions for efficient collaboration among multiple agents.

Fault-tolerant control (FTC) is an effective control method designed to maintain a faulty system within an acceptable risk level while ensuring its safety. However, handling both uncertainties and faults in a system remains challenging. In this article, we propose two probabilistic model-based adaptive FTC methods for faulty nonlinear systems with unknown dynamics. We study Gaussian process (GP) regression in two cases: 1) an offline learning-based control method and 2) an event-triggered online data-driven modeling method, to learn unknown system dynamics. Considering the computational complexity of GP regression in practical applications, we discuss the case of computational delays in real-time predictions. Moreover, we develop four theoretical criteria to ensure the probabilistic stability of closed-loop systems. Finally, numerical simulations validate the effectiveness of proposed control methods and demonstrate their competitiveness compared to existing approaches.

This paper provides theoretical analysis of the fixed-time multi-almost-periodicity in switched fuzzy neural networks, employing multi-controller strategies and a state-dependent switching mechanism. Utilizing the Ascoli-Arzela theorem, the properties of$M$-matrix, Lyapunov functions method, and some inequality techniques, we establish some sufficient conditions to ascertain that the number of exponentially stable almost-periodic solutions can be up to$4^{n}$, where$n$is the number of neurons. Furthermore, we design various controllers to achieve the fixed-time stability for various almost-periodic solutions located in the positive invariant sets. Then, the settling time for the switched fuzzy networks to achieve multi-almost-periodicity is estimated. It is noteworthy to state that this paper considers fixed-time multiperiodicity and fixed-time multistability as special cases of fixed-time multi-almost-periodicity. Two numerical examples are presented to demonstrate the theoretical results.

This article deals with linear equations of the form $Ax = b$ . By reformulating the original problem as an unconstrained optimization problem, we first provide a gradient-based distributed continuous-time algorithm over weight-balanced directed graphs, in which each agent only knows partial rows of the augmented matrix $(A\; b)$ . The algorithm is also applicable to time-varying networks. By estimating a right-eigenvector corresponding to 0 eigenvalue of the out-Laplacian matrix in finite time, we further propose a distributed algorithm over weight-unbalanced communication networks. It is proved that each solution of the designed algorithms converges exponentially to an equilibrium point. Moreover, the convergence rate is given out clearly. For linear equations without solution, these algorithms are used to obtain a least-squares solution in approximate sense. These theoretical results are illustrated by four numerical examples.

This article concentrates on solving the k -winners-take-all (k WTA) problem with large-scale inputs in a distributed setting. We propose a multiagent system with a relatively simple structure, in which each agent is equipped with a 1-D system and interacts with others via binary consensus protocols. That is, only the signs of the relative state information between neighbors are required. By virtue of differential inclusion theory, we prove that the system converges from arbitrary initial states. In addition, we derive the convergence rate as O(1/t) . Furthermore, in comparison to the existing models, we introduce a novel comparison filter to eliminate the resolution ratio requirement on the input signal, that is, the difference between the k th and (k+1) th largest inputs must be larger than a positive threshold. As a result, the proposed distributed k WTA model is capable of solving the k WTA problem, even when more than two elements of the input signal share the same value. Finally, we validate the effectiveness of the theoretical results through two simulation examples.

A novel aperiodic event-triggered control is adopted to address the synchronization issue of T-S fuzzy neural networks with time delay. This control strategy refers to the execution of control tasks in a control system based on real-time events, rather than following a fixed time interval. It allows for more flexible and faster responses to real-time events, and can reduce the computational load, energy consumption, and system costs. At first, a linear event-triggered control mechanism is formulated, in which its triggering condition includes an exponential term. Subsequently, the synchronization criteria based on linear matrix inequalities (LMIs) are deduced under the formulated event-triggered control. In addition, a novel approach that employs the reduction to absurdity technique is proposed to address the nonexistence of Zeno behavior. Eventually, the proposed theory's efficacy is demonstrated by employing an example and an accompanying simulation.

This article addresses the consensus tracking control of multiagent systems (MASs) via a quadratic programming (QP) optimization framework, where the control Lyapunov function (CLF) condition serves as a constraint. The optimal controllers, derived through the QP solver, not only ensure the tracking control objective but also minimize the cost functions of agents. To enhance energy efficiency, discontinuous control methods, such as intermittent control strategy and event-triggered mechanism, are employed in the control framework. The CLF-based QP controllers are only updated at specific time instants, in order to reduce the frequency of QP problem-solving. In addition to considering optimization, the proposed methods are extended to uncertain MASs to enhance robustness, where the uncertainty is modeled by Gaussian process regression. In the end, simulation results are provided to demonstrate the feasibility of the theoretical analysis.

This article focuses on the robust$\mathcal {H}_{\infty }$synchronization of two types of coupled reaction–diffusion neural networks with multiple state and spatial diffusion couplings by utilizing pinning adaptive control strategies. First, based on the Lyapunov functional combined with inequality techniques, several sufficient conditions are formulated to ensure$\mathcal {H}_{\infty }$synchronization for these two networks with parameter uncertainties. Moreover, node-based pinning adaptive control strategies are devised to address the robust$\mathcal {H}_{\infty }$synchronization problem. In addition, some criteria of$\mathcal {H}_{\infty }$synchronization for these two networks under parameter uncertainties are developed via edge-based pinning adaptive controllers. Finally, two numerical examples are presented to verify our results.

This paper addresses the multistability of switched fuzzy neural networks with a general class of activation functions under state-dependent switching. The existence, stability, and attraction basins of equilibria are analyzed via state-space decomposition based on Brouwer fixed point theorem and M-matrix properties. It is shown that there exist$5^{k_{1}}3^{k_{2}}$equilibria, and$3^{k_{1}}2^{k_{2}}$of them are locally exponentially stable under four sets of sufficient conditions for an$n$-neuron switched network, where$k_{1}$and$k_{2}$are nonnegative integers such that$0< k_{1}+k_{2}\leq n$. The results reveal that the switched fuzzy neural networks have much more equilibria than conventional fuzzy neural networks. Four numerical examples with simulation results are discussed to substantiate the theoretical results.

This article presents theoretical results on the multistability of fuzzy neural networks with rectified linear units and a state-dependent switching rule. Because of the boundlessness of state activation and multifariousness of state-dependent switching, such fuzzy neural networks exhibit very rich and complex dynamics. We show that there are up to$3^{n}-2^{n}-1$stable equilibria in an$n$-neuron switched fuzzy neural network, substantially more than recurrent neural networks without switching. Based on the properties of positive invariant set, we derive seven sets of sufficient conditions to ensure the multistability of switched fuzzy neural networks with rectified linear units. We elaborate on three numerical examples to illustrate the theoretical results and a potential application in associative memories.

In this article, a distributed adaptive continuous-time optimization algorithm based on the Laplacian-gradient method and adaptive control is designed for resource allocation problem with the resource constraint and the local convex set constraints. In order to deal with local convex sets, a distance-based exact penalty function method is adopted to reformulate the resource allocation problem instead of the widely used projection operator method. By using the nonsmooth analysis and set-valued LaSalle invariance principle, it is proven that the proposed algorithm is capable of solving the nonsmooth resource allocation problem. Finally, two simulation examples are presented to substantiate the theoretical results.

This article focuses on developing distributed optimization strategies for a class of machine learning problems over a directed network of computing agents. In these problems, the global objective function is an addition function, which is composed of local objective functions. Such local objective functions are convex and only endowed by the corresponding computing agent. A second-order Nesterov accelerated dynamical system with time-varying damping coefficient is developed to address such problems. To effectively deal with the constraints in the problems, the projected primal-dual method is carried out in the Nesterov accelerated system. By means of the cocoercive maximal monotone operator, it is shown that the trajectories of the Nesterov accelerated dynamical system can reach consensus at the optimal solution, provided that the damping coefficient and gains meet technical conditions. In the end, the validation of the theoretical results is demonstrated by the email classification problem and the logistic regression problem in machine learning.

This article presents theoretical results on the multistability of switched neural networks with Gaussian activation functions under state-dependent switching. It is shown herein that the number and location of the equilibrium points of the switched neural networks can be characterized by making use of the geometrical properties of Gaussian functions and local linearization based on the Brouwer fixed-point theorem. Four sets of sufficient conditions are derived to ascertain the existence of$7^{p_{1}}5^{p_{2}}3^{p_{3}}$equilibrium points, and$4^{p_{1}}3^{p_{2}}2^{p_{3}}$of them are locally stable, wherein$p_{1}$,$p_{2}$, and$p_{3}$are nonnegative integers satisfying$0\leq p_{1}+p_{2}+p_{3}\leq n$and$n$is the number of neurons. It implies that there exist up to$7^{n}$equilibria, and up to$4^{n}$of them are locally stable when$p_{1}=n$. It also implies that properly selecting$p_{1}$,$p_{2}$, and$p_{3}$can engender a desirable number of stable equilibria. Two numerical examples are elaborated to substantiate the theoretical results.

In this paper, we address the finite-time and fixed-time synchronization of a general class of switched neural networks (SNNs) with time delays subject to stochastic disturbances. Considering two types of switching in this class of SNNs: 1) intra-SNN state-dependent switching and 2) inter-SNN Markovian switching, we develop three control laws and derive three sets of sufficient conditions for both finite-time and fixed-time synchronization of SNNs subject to stochastic disturbances. We make two remarks on the effects of control-law parameters on synchronization settling time. Moreover, we derive several upper bounds of synchronization settling time and evaluate their pros and cons. Finally, we elaborate on two numerical examples to illustrate the viability of the theoretical results.

This article is devoted to analyzing the finite-time and fixed-time synchronization of coupled memristive neural networks with time delays. The synchronization is leaderless rather than leader-follower as the tracking targets are uncertain. By designing a proper controller and using the Lyapunov method, several sufficient conditions are obtained to achieve the finite-time and fixed-time synchronization of coupled memristive neural networks by introducing a class of special auxiliary matrices. Moreover, the settling times can be estimated for finite-time synchronization that depends on the initial values as well as fixed-time synchronization that is uniformly bounded for any initial values. Finally, two examples are presented to substantiate the effectiveness of the theoretical results.

This article investigates the synchronization problem of multiple memristive neural networks (MMNNs) in the case of switching communication topologies and parameter mismatch. First, the distributed event-triggered control under continuous sampling conditions is studied. Then, a periodic event-triggered control (PETC) model is proposed to substantially reduce control consumption. Using the Lyapunov method, the properties of M -matrix, and some inequalities, the sufficient criteria of synchronous control are derived. The results can be used in the analysis of other multiagent nonlinear systems. A norm-based threshold function is given to determine the update time of the controller, and it is proved that the trigger condition excludes the Zeno behavior. Subject to parameter mismatch, a quasisynchronous control strategy is proposed, which can be extended to complete synchronization provided that the system mismatch or disturbance disappears. It is worth mentioning that this article introduces the signal function into the controller, so that the theoretical error can be limited to an arbitrarily small range. Furthermore, this new controller is used in the PETC strategy which automatically avoids the Zeno behavior. Finally, one example is given to illustrate our results.

In this article, we investigate a class of memristive neural networks (MNNs) with time-varying delays and leakage delays via sliding mode control (SMC) with and without control disturbance. SMC is used to ensure MNNs' stability. According to the characteristics of the MNNs, we consider the following three models: the first is the MNNs with time-varying delays, the second is the MNNs with time-varying delays and the control disturbance, and the third is the MNNs with time-varying delays, leakage delays, and the control disturbance. We quote some assumptions and lemmas to ensure that our main results are true. The sliding surface, the corresponding sliding mode controller, and the Lyapunov functions are constructed in different models to ensure MNNs' stability. Finally, some examples and simulations verify the validity of our main results by solving linear matrix inequality (LMI), and the conclusions and analysis of the results are given.

This article presents new theoretical results on global exponential synchronization of nonlinear coupled delayed memristive neural networks with reaction-diffusion terms and Dirichlet boundary conditions. First, a state-dependent memristive neural network model is introduced in terms of coupled partial differential equations. Next, two control schemes are introduced: distributed state feedback pinning control and distributed impulsive pinning control. A salient feature of these two pinning control schemes is that only partial information on the neighbors of pinned nodes is needed. By utilizing the Lyapunov stability theorem and Divergence theorem, sufficient criteria are derived to ascertain the global exponential synchronization of coupled neural networks via the two pining control schemes. Finally, two illustrative examples are elaborated to substantiate the theoretical results and demonstrate the advantages and disadvantages of the two control schemes.

This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function. Sufficient criteria are provided for ascertaining the stability of recurrent neural networks with various numbers of equilibria, such as a unique equilibrium, finite, and countably infinite numbers of equilibria. Multiple exponential stability criteria of equilibria are derived, and the attraction basins of equilibria are estimated. Furthermore, criteria for complete stability and instability of equilibria are derived for recurrent neural networks without time delay. In contrast to the existing stability results with a finite number of equilibria, the new criteria, herein, are applicable for both finite and countably infinite numbers of equilibria. Two illustrative examples with finite and countably infinite numbers of equilibria are elaborated to substantiate the results.

This article focuses on the observer-based quasi-synchronization problem of delayed dynamical networks with parameter mismatch under impulsive effect. First, since the state of each node is unknown in the real situation, the state estimation strategy is proposed to estimate the state of each node, so as to design an appropriate synchronization controller. Then, the corresponding controller is constructed to synchronize the slave nodes with their leader node. In this article, we take the impulsive effect into consideration, which means that an impulsive signal will be applied to the system every so often. Due to the existence of parameter mismatch and time-varying delay, by constructing an appropriate Lyapunouv function, we will eventually obtain a differential equation with constant and time-varying delay terms. Then, we analyze its trajectory by introducing the Cauchy matrix and prove its boundedness by contradiction. Finally, a numerical simulation is presented to illustrate the validness of obtained results.

This article presents a simple and intuitive solution for multilabel image classification, which achieves the competitive performance on the popular COCO and PASCAL VOC benchmarks. The main idea is to capture how humans perform this task: we recognize both labels (i.e., objects and attributes) and the correlation of labels at the same time. Here, label recognition is performed by a standard ConvNet pipeline, whereas label correlation modeling is done by projecting both labels and image features extracted by the ConvNet to a common latent vector space. Specifically, we carefully design the loss function to ensure that: 1) labels and features that co-appear frequently are close to each other in the latent space and 2) conversely, labels/features that do not appear together are far apart. This information is then combined with the original ConvNet outputs to form the final prediction. The whole model is trained end-to-end, with no additional supervised information other than the image-level supervised information. Experiments show that the proposed method consistently outperforms previous approaches on COCO and PASCAL VOC in terms of mAP, macro/micro precision, recall, and$F$-measure. Further, our model is highly efficient at test time, with only a small number of additional weights compared to the base model for direct label recognition.

This paper presents a complete solution for the hardware design of a memristor-based long short-term memory (MLSTM) network. Throughout the design process, we fully consider the external and internal structures of the long short-term memory (LSTM), both of which are efficiently implemented by memristor crossbars. In the specific design of the internal structure, the parameter sharing mechanism is used between the LSTM cells to minimize the hardware design scale. In particular, we designed a circuit that requires only one memristor crossbar for each unit in the LSTM cell. The activation function, including sigmoid and tanh (hyperbolic tangent function), involved in each unit is approximated by a piecewise function, which is designed with the corresponding hardware. To verify the effectiveness of the system we designed, we test it on IMDB and SemEval datasets. Considering the huge impact of the dimensions of the input data on the scale of the hardware design, we use word2vector instead of one-hot encoding for the input data encoding. With the parameter sharing mechanism, the transformed vectors are input in different periods, so only 65 memristive crossbars are needed in the entire system to complete the sentiment analysis of the input text. The experimental results verify the effectiveness of our proposed MLSTM system.

This paper presents new theoretical results on the multistability of switched recurrent neural networks with radial basis functions and state-dependent switching. By partitioning state space, applying Brouwer fixed-point theorem and constructing a Lyapunov function, the number of the equilibria and their locations are estimated and their stability/instability are analyzed under some reasonable assumptions on the decomposition of index set and switching threshold. It is shown that the switching threshold plays an important role in increasing the number of stable equilibria and different multistability results can be obtained under different ranges of switching threshold. The results suggest that switched recurrent neural networks would be superior to conventional ones in terms of increased storage capacity when used as associative memories. Two examples are discussed in detail to substantiate the effectiveness of the theoretical analysis.

In this paper, we investigate the global synchronization control problem for memristive neural networks (MNNs) with time-varying delay. A novel event-triggered controller is introduced with the linear diffusive term and discontinuous sign term. In order to greatly reduce the computation cost of the controller under certain event-triggering condition, two event-based control schemes are proposed with static event-triggering condition and dynamic event-triggering condition. Some sufficient conditions are derived by these control schemes to ensure the response MNN to be synchronized with the driving one. Furthermore, under certain event-triggering conditions, a positive lower bound is achieved for the interexecution time to guarantee that Zeno behavior cannot be executed. Finally, numerical simulations are provided to substantiate the effectiveness of the proposed theoretical results.

This paper is concerned with the multistability of switched neural networks with piecewise linear activation functions under state-dependent switching. Under some reasonable assumptions on the switching threshold and activation functions, by using the state-space decomposition method, contraction mapping theorem, and strictly diagonally dominant matrix theory, we can characterize the number of equilibria as well as analyze the stability/instability of the equilibria. More interesting, we can find that the switching threshold plays an important role for stable equilibria in the unsaturation regions of activation functions, and the number of stable equilibria of an n-neuron switched neural network with state-dependent parameters increases to 3nfrom 2nin the conventional one. Furthermore, for two-neuron switched neural networks, the precise attraction basin of each stable equilibrium point can be figured out, and its boundary is composed of the stable manifolds of unstable equilibrium points and the switching lines. Two simulation examples are discussed in detail to substantiate the effectiveness of the theoretical analysis.

In this paper, new results on the global synchronization of multiple recurrent neural networks (NNs) with time delays via impulsive interactions are presented. Impulsive interaction means that a number of NNs communicate with each other at impulse instants only, while they are independent at the remaining time. The communication topology among NNs is not required to be always connected and can switch ON and OFF at different impulse instants. By using the concept of sequential connectivity and the properties of stochastic matrices, a set of sufficient conditions depending on time delays is derived to ascertain global synchronization of multiple continuous-time recurrent NNs. In addition, a counterpart on the global synchronization of multiple discrete-time NNs is also discussed. Finally, two examples are presented to illustrate the results.

This paper presents theoretical results on the global exponential synchronization of multiple memristive neural networks with time delays. A novel coupling scheme is introduced, in a general topological structure described by a directed or undirected graph, with a linear diffusive term and discontinuous sign term. Several criteria are derived based on the Lyapunov stability theory to ascertain the global exponential stability of synchronization manifold in the coupling scheme. Simulation results for several examples are given to substantiate the effectiveness of the theoretical results.

This paper is concerned with the global exponential synchronization of two memristor-based recurrent neural networks (MRNNs) with time delays via static or dynamic coupling. First, four coupling rules (i.e., static state coupling, static output coupling, dynamic state coupling, and dynamic output coupling) are designed for the exponential synchronization of drive-response pair of MRNNs. Then, several global exponential synchronization criteria are derived by constructing suitable Lyapunov-Krasovskii functionals based on the Lyapunov stability theory. Compared with existing results on synchronization of MRNNs, the conditions herein are easy to be verified. Moreover, the designed dynamic state coupling and output coupling rules have good anti-interference capacity. Finally, two illustrative examples are presented to substantiate the effectiveness and characteristics of the presented theoretical results.

This paper is concerned with the global robust synchronization of multiple memristive neural networks (MMNNs) with nonidentical uncertain parameters. A coupling scheme is introduced, in a general topological structure described by a direct or undirect graph, with a linear diffusive term and a discontinuous sign term. First, a set of sufficient conditions are derived based on the Lyapunov stability theory for ascertaining global robust synchronization of coupled MMNNs. Second, a pinning adaptive coupling method is proposed to ensure global synchronization without knowing the bound of parameter uncertainties. Two illustrative examples are discussed to substantiate the theoretical results.

This paper presents new theoretical results on the invariance and attractivity of memristor-based cellular neural networks (MCNNs) with time-varying delays. First, sufficient conditions to assure the boundedness and global attractivity of the networks are derived. Using state-space decomposition and some analytic techniques, it is shown that the number of equilibria located in the saturation regions of the piecewise-linear activation functions of an n-neuron MCNN with time-varying delays increases significantly from 2(n) to 2(2n2)+n) (2(2n2) times) compared with that without a memristor. In addition, sufficient conditions for the invariance and local or global attractivity of equilibria or attractive sets in any designated region are derived. Finally, two illustrative examples are given to elaborate the characteristics of the results in detail.

This paper presents new theoretical results on the passivity and passification of a class of memristor-based recurrent neural networks (MRNNs) with time-varying delays. The casual assumptions on the boundedness and Lipschitz continuity of neuronal activation functions are relaxed. By constructing appropriate Lyapunov-Krasovskii functionals and using the characteristic function technique, passivity conditions are cast in the form of linear matrix inequalities (LMIs), which can be checked numerically using an LMI toolbox. Based on these conditions, two procedures for designing passification controllers are proposed, which guarantee that MRNNs with time-varying delays are passive. Finally, two illustrative examples are presented to show the characteristics of the main results in detail.