Most researches on brain-inspired emotional circuits are grounded in memristors. Memcapacitors offer better static power consumption than memristors and exhibit dynamic characteristics that align well with biological neurons. In this article, we propose a memcapacitive circuit design for emotion modulation and congruency with schemas, anchored in the emotion classification model. The proposed circuit is rooted in the theories of schema memory and brain emotion, comprising essential components, such as sensory neuron modules, emotion neuron modules, and emotion-sensation association neuron modules. These modules emulate the functions of the hippocampus, amygdala, primary sensory cortex, and ventromedial prefrontal cortex in the brain. The circuit can receive sensory stimulation across five different frequencies, including visual, auditory, tactile, gustatory, and olfactory stimuli. Besides realizing multiemotional associative memories encompassing surprise, happiness, fear, anger, disgust, and sadness, this work also implements primary schema memory and can be applied to smart home control in Internet of Things based on prior knowledge, showcasing its versatility in practical and interdisciplinary contexts.

Association is not a singular associative process, different emotional states affect associative responses. Most memristor-based multilateral associative circuits aim to optimize associative patterns, neglecting the combination of emotional states and bidirectional association. Based on the emotional association mechanism of brain, a memristor-based circuit for two-dimensional emotional recall and bidirectional associative relationships is proposed. The circuit model continuously modifies the storage and recall processes of emotional memory, persistently adjusting two-dimensional emotions and revealing their impact on bidirectional association and self-regulation. The circuit consists of the temporal lobe cortex module, amygdala module, hippocampus module, prefrontal cortex module and hypothalamus module. Emotional recall is achieved through the temporal lobe cortex module, amygdala module and hippocampus module. Two-dimensional emotions and emotional regulation are realized by the prefrontal cortex module. Emotional state responses are realized by the hypothalamus module. Ultimately, this circuit is applied to machine fault prediction, providing a new reference for bionic intelligent robot in the application of Internet of Things (IoT).

From the perspective of time, the generation of emotion has not only emotional generalization but also emotional differentiation. Most studies of emotional systems only consider the present tense, and the past and future tenses are not considered. In this article, based on the bionic multiloop emotion learning model, a memristor-based feature recall neural network circuit with temporal differentiation of emotion is proposed. The circuit is composed of thalamus module, insular cortex module, anterior cingulate cortex module, sensory cortex module, amygdala module, and feature recall module. Feature recall module and emotion learning circuit are used to combine feature associative memory with emotion generation. Temporal differentiation of emotions is realized. The multiloop affective learning circuit also takes into account the activation patterns of different brain regions in response to positive and negative stimuli. The feasibility of the above circuits is verified by PSpice simulation software. The feature recall neural network circuit with temporal differentiation of emotion provides further reference for the bionic robot to realize inference prediction function.

Conditioning and associative memory play an important role in the learning process of biological brain, and many neural network circuits have been designed to reproduce the relevant classical experiments. However, these circuits are mainly devoted to the realization of various phenomena in the acquisition process, such as reacquisition, generalization, differentiation, and blocking. A Pavlov associative memory circuit based on memristor is designed in this article. The circuit realizes latent inhibition effect and a variety of biological forgetting features. The correctness of implementing these functions described above is demonstrated by simulation results in Pspice. This circuit can realize the influence of external environment changes on the learning and forgetting states of organisms. It offers valuable insights for modeling biological intelligence and simulating the learning function of human associative memory. Particularly, associative memory and transient forgetting can be applied to industrial intelligent grasping robots.

In the field of biocomputing and neural networks, deoxyribonucleic acid (DNA) strand displacement (DSD) technology performs well in computation, programming, and information processing. In this article, the multiplication gate, addition gate, and threshold gate based on DSD are used to cascade into a single DNA neuron. Multiple DNA neurons can be cascaded to form different neural networks. The DNA neural networks are designed to implement seven classical conditioned reflexes from Pavlovian associative memory experiments. A classical conditioned reflex is a combination of a conditioned stimulus (CS) and another un CS with a reward or punishment. So that the individual develops a conditioned reflex that is similar to an unconditioned reflex in the use of CS alone. The seven classical conditioned reflexes include acquisition and forgetting, interstimulus interval effect, blocking, conditioned inhibition, overshadowing, generation, and differentiation. The simulations are verified by the software visual DSD. This article provides a direction for the integration of biology and psychology.

Most memristor-based neural network circuits consider only a single pattern of overshadowing or emotion, but the relationship between overshadowing and emotion is ignored. In this article, a memristor-based neural network circuit of associative memory with overshadowing and emotion congruent effect is designed, and overshadowing under multiple emotions is taken into account. The designed circuit mainly consists of an emotion module, a memory module, an inhibition module, and a feedback module. The generation and recovery of different emotions are realized by the emotion module. The functions of overshadowing under different emotions and recovery from overshadowing are achieved by the inhibition module and the memory module. Finally, the blocking caused by long-term overshadowing is implemented by the feedback module. The proposed circuit can be applied to bionic emotional robots and offers some references for brain-like systems.

Different emotional states have different impacts on the emotional system. To mitigate these impacts, the emotional system will maintain the stability of the system through various adjustment methods, such as emotional self-regulation. However, there is no hardware circuit to realize the regulation of the emotional system in different emotional states. In this article, based on the brain emotion theory of the limbic system, a memristor-based emotion regulation circuit is proposed. The circuit is composed of the thalamus module, sensory cortex module, amygdala module, and orbitofrontal cortex module. It can not only produce corresponding emotions according to different stimuli but also output and regulate the current emotional state. The function of emotion generation and emotion output is realized through the thalamus module, sensory cortex module, and amygdala module. Emotional self-regulation, emotional generalization, mood disorder and mood disorder regulation are realized through the combined action of the amygdala module and the orbitofrontal cortex module. Finally, the emotion regulation circuit composed of the memristor is applied to the fault robot monitoring, which provides a reference for the bionic intelligent robot in the actual industrial application scenario.

Signaling activity in the cerebral cortex is corrected by inhibition and blocking to make neural response processes more precise and efficient, inhibition and blocking are positive neural processes. In this article, a memristor-based conditioned inhibition neural network circuit with blocking generalization and differentiation is proposed. The designed circuit consists of the voltage control module, synapse neuron module, inhibition module, blocking module, and generalization module. Through the cooperative action of the neuronal associative learning and the inhibition module, the neutral conditioned stimulus is transformed into a conditioned stimulus with inhibitory properties to achieve conditioned inhibition. The influence of unconditioned stimulus on synaptic weight is considered during associative learning, and unblocking is realized by using the blocking module. Based on the blocking module and the generalization module, blocking, generalization, and differentiation are combined to realize blocking generalization and differentiation. The PSPICE simulation verifies the feasibility of the above functions. Conditioned inhibition neural network circuit with blocking generalization and differentiation provides a reference for the further development of brain-like technology.

Most associative memory neural networks are realized by memristor, but memcapacitor which can simulate the biological behavior of neuron preferably has better characteristics than memristor to realize the pavlov associative memory neural networks. This article introduces a novel neural network paradigm with memcapacitors, encompassing thirteen classical conditional reflection functions. These include pivotal aspects such as learning, forgetting, time interval conditioning, latent inhibition, time delay conditioning, facilitation, blocking, secondary conditioning, and fear learning, meticulously validated through simulation results. The proposed architecture interconnects nine analogous neuron modules through diverse synapses, culminating in a meticulously designed circuit. This memcapacitor biomimetic circuit not only achieves the implementation of thirteen classical conditional reflections but also boasts scalability, offering versatility in its application. Particularly noteworthy is its potential application in marine debris collection robots, showcasing adaptability in working intricate oceanic traffic conditions.

Most memristor-based neural network circuits consider only a single pattern of classical conditioning (CC) or operant conditioning (OC), but the simultaneous occurrence of CC and OC during actual animal training is ignored. In this paper, a memristor-based neural network circuit of operant conditioning with bridging and conditional reinforcement is designed. CC and OC can occur simultaneously and multiple CC and OC functions are considered. The designed circuit mainly consists of memory module, delay module, prefrontal cortex module, experience module and generalization module. Bridging in OC is implemented by the delay module and the prefrontal cortex module. Conditional reinforcement in OC is realized by the memory module and the prefrontal cortex module. Finally, the generalization of OC is achieved through the generalization module and the experience module. The proposed circuit may inform the study of smarter brain-like systems.

Picture Archiving and Communication System (PACS) is an important technology for the transmission of medical images and related information. Using the PACS technology, medical images can be transmitted and shared over local area networks, wide area networks. However, ensuring transmission security continues to be crucial challenges in the field of modern medicine. In this paper, a hyperbolic memristor model with different hysteresis loops for different input signals is proposed, which has both locally active and passive properties under different parameters. Based on the memristor model, a four-neuron Hopfield neural network (HNN) is introduced, incorporating a memristor as a replacement for one of the synaptic weights, while subjecting one of the four neurons to electromagnetic radiation. The effects of the memristor parameters and coupling weights on neural network are studied, which reveals the existence of coexistence behavior in neural network. In addition, an equivalent circuit of HNN is implemented to demonstrate the accuracy of the dynamical analysis. Finally, a medical image encryption approach with bi-directional dynamic permutation and multi-directional dynamic diffusion process is proposed. The experimental findings demonstrate that the encryption scheme has strong robustness, which can be applied in PACS to enhance the security of medical images during transmission.

This article investigates the predefined-time synchronization of a group of fuzzy recurrent neural networks (FRNNs) under a leaderless communication topology. An effective control strategy is proposed based on a time-dependent exponential function as the scaling function. Sufficient criteria for guaranteeing the predefined-time synchronization of multiple FRNNs are derived under the digraph with strong connectivity and the digraph containing spanning trees, respectively. Unlike commonly used state-dependent sign function or time-dependent power function in existing works, the scaling function in this article is new and selected as the time-dependent exponential function. Moreover, the communication topology in this article is assumed to be leaderless, which is distinct from the master–slave or leader–following topologies previously investigated for predefined-time synchronization. Numerical examples are provided to illustrate the correctness of results.

The 1-D and 2-D emotion models realized by hardware circuits have been studied. However, 3-D emotional model which is most suitable for human emotion has not been considered. In this article, a bionic circuit of 3-D emotional space model is proposed, which can generate brain-like emotions according to the information of visual, speech, and text. The designed memristor circuits are based on the brain emotion theory of limbic system, including thalamus, sensory cortex, orbitofrontal cortex, cingulate gyrus, amygdala, and other circuit modules. Moreover, the perceptual brain and rational brain in the memristor circuits are also considered. The 3-D model in this article is a PAD emotional space model composed of three dimensions: 1) pleasure (P); 2) arousal (A); and 3) dominance (D). Many emotions can be expressed by using the PAD emotional model. In addition, the PAD emotional model composed of memristor circuits is applied to mood congruity, which considers the relationship between emotion and learning. The PAD emotion designed by memristor circuits may provide a reference for bionic robot to realize human–computer emotional companionship.

In this article, a general memristor model emulator based on the hyperbolic function is proposed. Based on the mathematical model of hyperbolic function memristor, a general circuit model emulator is designed. The general circuit can realize memristor models of different hyperbolic functions by controlling the state of switches in the circuit. The advantage of the emulator is that it can realize three different mathematical models of hyperbolic function and be easily integrated. The circuit of the hyperbolic function memristor model conforms to three basic characteristics of the mem-element, so it can be regarded as a memristor element. Finally, the model of charge-controlled memristor based on hyperbolic function is derived. The universal memristor model proposed in this article enriches the research of constructing memristor components with existing components and provides a reference for future research on mem-element emulators.

Currently, the research in memristor-based associative memory neural networks pays more attention to classical conditioning and lays less attention to operant conditioning. Moreover, a single reinforcing stimulus is applied in the most studies of operant conditioning. In this paper, a memristor-based duple-stimulus operant conditioning circuit is designed. The circuit utilizes duple stimuli which include two stimuli and realizes the effect of stimuli with two intensities on operant conditioning. In addition, the circuit is applied to a memristor-based neural network circuit of duple-reward and duple-punishment operant conditioning with time delay. The application circuit realizes duple-reward and duple-punishment operant conditioning with time delay on the basis of duple-stimulus operant conditioning circuit. Meanwhile, the factors that affect operant conditioning such as satiety and the immediacy of stimuli are implemented in the circuit. Different delays for duple-reward module and duple-punishment module are designed. The application circuit is closer to the practical application and is more consistent with biological characteristics. It provides more references for neural networks of operant conditioning with further development.

The reinforcement and extinction in conditioned reflex have been studied extensively, but memristor-based generalization and differentiation circuits under different emotional conditions are rarely studied. Therefore, a memristor-based generalization and differentiation circuit under positive and negative emotional conditions is presented in this paper. The circuit includes emotion module, synapse module, voltage selection module and output module. The emotion module is divided into positive emotion and negative emotion modules. Different emotions have different effects on the synapse module, which in turn affects the output module. The memristor-based circuit proposed in this paper can not only realize the process of generalization and differentiation under the influence of different emotions, but also realize the function of secondary differentiation. The results presented in this paper can be verified in PSPICE. By analyzing the effects of different emotions on differentiation and generalization, this paper provides some references for future researches in the field of generalization and differentiation.

In this article, the synchronization of multiple fractional-order neural networks with unbounded time-varying delays (FNNUDs) is investigated. By introducing a pinning linear control, sufficient conditions are provided for achieving the synchronization of multiple FNNUDs via an extended Halanay inequality. Moreover, a new effective adaptive control which applies to the fractional differential equations with unbounded time-varying delays is designed, under which sufficient criteria are presented to ensure the synchronization of multiple FNNUDs. The introduced control in this article is also workable in traditional integer-order neural networks. Finally, the validity of obtained results is demonstrated by a numerical example.

Most of the classical conditioning laws implemented by existing circuits are involved in learning and forgetting between only three neurons, and the problems between multiple neurons are not considered. In this article, a multimode generalization and differentiation circuit for the Pavlov associative memory is proposed based on memristors. The designed circuit is mainly composed of voltage control modules, synaptic neuron modules, and inhibition modules. The secondary differentiation is accomplished through the process of associative learning and forgetting among multiple neurons. The process of multiple generalization and differentiation is realized based on the nonvolatility and thresholding properties of memristors. The extinction inhibition and differentiation inhibition in forgetting is considered through the inhibition modules. The Pavlov associative memory neural network with multimodal generalization and differentiation may provide a reference for the further development of brain-like intelligence.

The stability analysis of recurrent neural networks (RNNs) with multiple equilibria has received extensive interest since it is a prerequisite for successful applications of RNNs. With the increasing theoretical results on this topic, it is desirable to review the results for a systematical understanding of the state of the art. This article provides an overview of the stability results of RNNs with multiple equilibria including complete stability and multistability. First, preliminaries on the complete stability and multistability analysis of RNNs are introduced. Second, the complete stability results of RNNs are summarized. Third, the multistability results of various RNNs are reviewed in detail. Finally, future directions in these interesting topics are suggested.

This paper addresses the synchronization of multiple fractional-order recurrent neural networks (RNNs) with time-varying delays under event-triggered communications. Based on the assumption of the existence of strong connectivity or a spanning tree in the communication digraph, two sets of sufficient conditions are derived for achieving event-triggered synchronization. Moreover, an additional condition is derived to preclude Zeno behaviors. As a generalization of existing results, the criteria herein are also applicable to the event-triggered synchronization of multiple integer-order RNNs with or without delays. Two numerical examples are elaborated to illustrate the new results.

This article focuses on the cluster synchronization of multiple fractional-order recurrent neural networks (FNNs) with time-varying delays. Sufficient criteria are deduced for realizing cluster synchronization of multiple FNNs via a pinning control by applying an extended Halanay inequality applicable for time-delayed fractional-order differential equations. Moreover, an adaptive control applicable for the synchronization of fractional-order systems with time-varying delays is proposed, under which sufficient criteria are derived for realizing cluster synchronization of multiple FNNs with time-varying delays. Finally, two examples are presented to illustrate the effectiveness of the theoretical results.

The Halanay inequality is widely used in various time-delayed dynamical systems analyses and its vectorial form has become available recently. In this article, the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms. It is shown that the fractional-order vectorial Halanay-type inequalities hold under the derived conditions in the form of$M$-matrices. In addition, the time-invariant inequalities are applied to analyzing the stability and synchronization of fractional-order systems with two numerical examples to substantiate the theoretical results.

Most memristor-based associative memory neural networks are focused on classical conditioning and ignored operant conditioning. In this paper, a memristor-based neural network of operant conditioning accorded with biological feature is designed. The designed circuit includes a voltage control module, an operant module and synapse modules. It realizes learning, forgetting, long-term memory, reinforcement and punishment functions based on variable synapse structure and double self-protection measure. Meanwhile, the four factors that affect operant conditioning such as contingency, immediacy, magnitude and deprivation are discussed and implemented. The simulation results in PSPICE show that the circuit can be used to simulate actual conditioned reflex and complicated applications. The memristor-based neural network circuit of operant conditioning provides more references for further development of neural networks.

In this article, we analyze the projective synchronization of fractional-order neural networks with mixed time delays. By introducing an extended Halanay inequality that is applicable for the case of fractional differential equations with arbitrary initial time and multiple types of delays, sufficient criteria are deduced for ensuring the projective synchronization of fractional-order neural networks with both discrete time-varying delays and distributed delays. Furthermore, sufficient criteria are presented for ensuring the projective synchronization in the Mittag-Leffler sense if there is no delay in fractional-order neural networks. The results derived herein include complete synchronization, anti-synchronization, and stabilization of fractional-order neural networks as particular cases. Moreover, the testable criteria in this article are a meaningful extension of projective synchronization of neural networks with mixed time delays from integer-order to fractional-order ones. A numerical simulation with four cases is provided to verify the validity of the obtained results.

Over the past decades, the synchronization of complex networks with directed topologies has received considerable attention owing to its extensive applications in the realistic world. Design of proportional-integral-derivative (PID) control protocols for achieving synchronization with directed networks is known to be a challenging task. The purpose of this paper is to establish a connection between the PID control protocols and synchronization of complex dynamical networks with directed topologies. Based on the classical complex network model, we investigate global synchronization with PD controller of a balanced strongly connected directed network and global synchronization with PI controller of a strongly connected directed network, and a directed network containing a spanning tree, respectively. Several sets of sufficient conditions are established under which the network reaches global synchronization. The simulation examples are presented to verify the efficiency of the theoretical results.

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 paper addresses the problem of complete stability of delayed recurrent neural networks with a general class of piecewise linear activation functions. By applying an appropriate partition of the state space and iterating the defined bounding functions, some sufficient conditions are obtained to ensure that an n-neuron neural network is completely stable with exactly Πi=1n(2Ki-1) equilibrium points, among which Πi=1nKiequilibrium points are locally exponentially stable and the others are unstable, where Ki(i = 1, .. . ,n) are non-negative integers which depend jointly on activation functions and parameters of neural networks. The results of this paper include the existing works on the stability analysis of recurrent neural networks with piecewise linear functions as special cases and hence can be considered as the improvement and extension of the existing stability results in the literature. A numerical example is provided to illustrate the derived theoretical results.

This article is devoted to the cluster synchronization issue of coupled fractional-order neural networks. By introducing the stability theory of fractional-order differential systems and the framework of Filippov regularization, some sufficient conditions are derived for ascertaining the asymptotic and finite-time cluster synchronization of coupled fractional-order neural networks, respectively. In addition, the upper bound of the settling time for finite-time cluster synchronization is estimated. Compared with the existing works, the results herein are applicable for fractional-order systems, which could be regarded as an extension of integer-order ones. A numerical example with different cases is presented to illustrate the validity of theoretical results.

This paper presents new theoretical results on the global synchronization of coupled fractional-order recurrent neural networks. Under the assumptions that the coupled fractional-order recurrent neural networks are sequentially connected in form of a single spanning tree or multiple spanning trees, two sets of sufficient conditions are derived for ascertaining the global synchronization by using the properties of Mittag-Leffler function and stochastic matrices. Compared with existing works, the results herein are applicable for fractional-order systems, which could be viewed as an extension of integer-order ones. Two numerical examples are presented to illustrate the effectiveness and characteristics of the theoretical results.

In this paper, we analyze stability of incremental exponential stability for switched nonlinear systems with time delay. The continuous contraction theory is generalized to introduce a new type of switching laws. On this basis, the incremental exponential stability is established for both stable and unstable subsystems within the overall switched nonlinear systems with time delay. Computer simulations are presented to validate the theoretical findings.

This paper is concerned with the coexistence of multiple equilibrium points and dynamical behaviors of recurrent neural networks with nonmonotonic activation functions and unbounded time-varying delays. Based on a state space partition by using the geometrical properties of the activation functions, it is revealed that an -neuron neural network can exhibit equilibrium points with . In particular, several sufficient criteria are proposed to ascertain the asymptotical stability of equilibrium points for recurrent neural networks. These theoretical results cover both monostability and multistability. Furthermore, the attraction basins of asymptotically stable equilibrium points are estimated. It is shown that the attraction basins of the stable equilibrium points can be larger than their originally partitioned subsets. Finally, the results are illustrated by using the simulation results of four examples.

This letter studies the multistability analysis of delayed recurrent neural networks with Mexican hat activation function. Some sufficient conditions are obtained to ensure that an [Formula: see text]-dimensional recurrent neural network can have [Formula: see text] equilibrium points with [Formula: see text], and [Formula: see text] of them are locally exponentially stable. Furthermore, the attraction basins of these stable equilibrium points are estimated. We show that the attraction basins of these stable equilibrium points can be larger than their originally partitioned subsets. The results of this letter improve and extend the existing stability results in the literature. Finally, a numerical example containing different cases is given to illustrate the theoretical results.

In this paper, coexistence and stability of multiple equilibrium points of fractional-order recurrent neural networks are addressed. Several sufficient conditions are derived for ascertaining the existence of Πi=1n(2Ki+ 1) equilibrium points (Ki≥ 0) and the local Mittage - Leffler stability Πi=1n(Ki+ 1) equilibrium points of them by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. In contrast with many existing results, the derived results cover both mono-stability and multistability, and the activation functions herein could be nonmonotonic and nonlinear in any open interval. In addition, three numerical examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.

This paper presents new theoretical results on the multistability analysis of a class of recurrent neural networks with nonmonotonic activation functions and mixed time delays. Several sufficient conditions are derived for ascertaining the existence of 3nequilibrium points and the exponential stability of 2nequilibrium points via state space partition by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. Compared with existing results, the conditions herein are much more computable with one order less linear matrix inequalities. Furthermore, the attraction basins of these exponentially stable equilibrium points are estimated. It is revealed that the attraction basins of the 2nequilibrium points can be larger than their originally partitioned subspaces. Three numerical examples are elaborated with typical nonmonotonic activation functions to substantiate the efficacy and characteristics of the theoretical results.