This study aims to introduce a user-controlled chaotic fuzzy cellular neural network (FCNN) model that incorporates the effects of stochastic (external) disturbances and proportional delay. Theoretically, synchronization analysis is a considerably more effective approach to exploring the dynamical characteristics of the FCNN model with and without external control input. FCNN models with suitable control input help to possess the dynamical characteristics of traditional FCNN but with the potential to handle stochastic disturbances and other uncertainties. Besides, this study focuses on achieving synchronization within a prescribed-time synchronization (PTS). In this regard, a quantified intermittent control (QIC) scheme is proposed, which is a considerably simple but effective control for nonlinear models with stochastic disturbances. Along with QIC, the synchronization of uncontrolled (drive)-controlled (response) FCNN models can be guaranteed by employing the Lyapunov stability theory, Ito's calculus, and some inequalities. Mathematically, sufficient conditions that guarantee the global asymptotically stability of the error model will ensure the synchronization of the drive-response FCNN model. In terms of application, the drive-response model can be used as a cryptosystem (pseudorandom generator) that helps to encrypt the information from the sender side and to decrypt the information from the receiver side. Due to the chaos and randomness in the solutions, the proposed encryption/decryption algorithm is more effective and resistive than existing algorithms.

This article aims to model and investigate the dynamical properties of a grid-connected permanent magnet synchronous motor (PMSM) in wind energy conversion systems (WECSs). Considering the dc-link capacitor in voltage equations of PMSM can cause hyperchaotic solution behavior, whereas the conventional PMSM model exhibits chaotic solutions. In addition, disturbances are inevitable in WECS hence in this study the aerodynamics of PMSM is considered as stochastic disturbances that can degrade the performance of the WECSs. As a result, grid-connected PMSM is modeled as stochastic differential equations with nonlinear characteristics. Due to nonlinearity, investigating the stability properties of PMSM with dc-link is economically expensive. In this regard, an equivalent Takagi–Sugeno (T–S) fuzzy model can be derived to mimic the dynamical characteristics of the stochastic PMSM model with the help of fuzzy membership grades. Overall this study focuses on designing a suitable control algorithm that guarantees the global stable performance of T–S-based linear hyperchaotic PMSM model involving stochastic disturbances. Among various controllers, an event-triggered-based sampled-data control scheme with continuous-type network transmission delay is considered to be effective for the proposed model with disturbances. Theoretically, the Lyapunov stability theory is employed to derive sufficient stability conditions in terms of solvable linear matrix inequalities. Technically, the numerical simulations are performed with the experimental range of parameter values to validate the effectiveness of the proposed theoretical frameworks.

This article aims to explore the dynamics involved in the intricate realm of chaotic synchronization in the Hindmarsh–Rose (H–R) neuronal model, which is known for its resemblance to the brain's information-processing components. Distinct from the existing studies related to the H–R neuronal model, this research focuses on addressing nonlinearities of membrane potential through a Takagi–Sugeno (T–S) fuzzy approach. A sampled-data-based controller scheme that can resolve the stabilization issues inherent to the H–R neuronal model is proposed. Compared with many existing control schemes, sampled-data control has several advantages, which include easy digital implementation and robustness against transmission delays. This research utilizes the zero-order holder technique to handle discrete-time control actions in a continuous-time T–S fuzzy model. Furthermore, synchronization analysis pertaining to the T–S fuzzy-based H–R model with user-designed control inputs is conducted to understand and overcome the associated spiking, chaotic, and bursting behaviors. Closed-loop dynamics of the resulting model with and without control input, namely, the error model, are analyzed by employing the Lyapunov stability theory and integral inequalities. Specifically, a suitable Lyapunov Krasovskii functional is formulated and solved using the linear matrix inequalities technique to guarantee the global asymptotically stability of the error model. The developed theoretical framework is validated using numerical simulations, and the corresponding outcomes are graphically illustrated and discussed.

This study aims to investigate the synchronization of user-controlled and uncontrolled neural networks (NNs) that exhibit chaotic solutions. The idea behind focusing on synchronization problems is to design the user-desired NNs by emulating the dynamical properties of traditional NNs rather than redefining them. Besides, instead of conventional NNs, this study considers NNs with significant factors such as time-dependent delays and uncertainties in the neural coefficients. In addition, information transmission over transmission may experience stochastic disturbances and network transmission. These factors will result in a stochastic differential NN model. Analyzing the NNs without these factors may be incompatible during the implementation. Theoretically, the model with stochastic disturbances can be considered a stochastic differential model, and the stability conditions are derived by employing Itô's formula and appropriate integral inequalities. To achieve synchronization, the sampled-data-based control scheme is proposed because it is more effective while information is being transmitted over networks. In contrast to the existing studies, this study contributes in terms of handling stochastic disturbances, effects of time-varying delays, and uncertainties in the system parameters via looped-type Lyapunov functional. Besides this, in the application view, delayed NNs are employed as a cryptosystem that helps to secure the transmission between the sender and the receiver, which is explored by illustrating the statistical measures evaluated for the standard images. From the simulation results, the proposed control and derived sufficient conditions can provide better synchronization and the proposed delayed NNs give a better cryptosystem.

The aim of this study is to focus on proposing the theoretical framework for investigating the stability properties of permanent magnet synchronous motors (PMSMs) considering the stochastic disturbances and parameter uncertainties in the fractional domain. To do this, the aerodynamics of PMSM is chosen as stochastic disturbances, followed by the inherent parameter uncertainties in voltage equations. In addition, for the proposed nonlinear PMSM model, an equivalent linear submodels holding same dynamical properties of PMSM are derived through Takagi–Sugeno (T–S) fuzzy approach. Besides, the derivative of white noise is considered with Hurst parameter known as fractional Brownian motion (FBM) and it holds the properties of conventional Brownian motion when Hurst parameter is chosen as 0.5. The Lyapunov stability theory is employed to derive the sufficient stability conditions that guarantee the global stable performance of the proposed fuzzy-based PMSM model. In this regard, instead of traditional Ito’s differential formula, the study utilizes Ito’s fractional differential formula to obtain the sufficient conditions. To validate the proposed approach, numerical experiments are performed by considering the experimental range of parameter values and the outcomes are illustrated through time-series, and phase-portraits.

Neural networks (NNs) play a significant role in the machine learning and deep learning domains that include pattern recognition, computer-vision and so on. However, understanding the theoretical properties of neural networks will helps to deliver the user-desired performance in such practical applications. In the literature, the fundamental analysis of a NN, such as stability analysis, parameter sensitivity analysis can be performed by modeling the neuronal activities as differential equations. Through differential equations, the rate at which information is transmitted can be experimented along with various significant factors, such as time-delays during data transmission, switching parameters with respect to time, random disturbances caused by interruption of data blocks. The present study focuses on fundamental analysis of neuronal activities through differential model. Besides, the factors, such as time-delays, exogenous disturbances, and Markovian-jumping parameter (MJP) that has an ability to degrade the stable performance of the neuronal model is incorporated in the model. Distinct to the previous studies in stochastic neural networks, the study address the synchronization problem of stochastic neural networks (SNNs) with fractional-derivative of Brownian motion and event-triggered control scheme. Theoretically, due to nonlinearties, the Lyapunov stability theory is employed to derive the sufficient stability conditions that ensure the stable performance of SNNs. In this regard, looped-Lyapunov functional candidate is considered and corresponding linear matrix inequalitys (LMIs) are derived. Technically, a model of two neurons, three neurons, and four neurons are considered with the given factors to validate the proposed theoretical conditions and controller performance and their results are picturised.

The main objective of this study is to focus on dynamical analysis of full-scale direct-driven permanent-magnet-synchronous-generator-based wind energy conversion systems (WECSs) configured with back-to-back voltage source converters. The mathematical methods are employed to discuss the properties WECSs in a theoretical manner, which are proven to be cost effective. It can be seen that the considered model contains the nonlinearities in terms of currents and rotational speed of the shaft that results in nonlinearities. The Takagi–Sugeno fuzzy approach is considered to be an effective tool to approximate the nonlinear model into local linear submodels without compromising the system characteristics. In general, WECSs are networked to each other, the event-triggered-based control (ETC) is considered to be an appropriate control regarding the reduction of packet loss and the ability to ensure the stable performance of the WECSs in an effective manner. The main advantage of utilizing the ETC is that it will activate the controllers with a user-designed event-triggering condition that helps to restrict the unnecessary network transmissions and reduce the leakages. By the virtue of the fuzzy Lyapunov function, intensive attention is focused on deriving the theoretical-based sufficient conditions in terms of solvable linear matrix inequalities, which ensure the global stability of the closed-loop model based on the Lyapunov stability theory. Detailed numerical simulations are performed with an experimental range of system parameters that illustrate the effectiveness of the proposed ETC scheme.

The main aim of this article is to design the observer-based event-triggered (ET) fuzzy integral sliding mode control (ETFISMC) for the generalized Takagi-Sugeno (T-S) fuzzy system which is formulated from a nonlinear system through blending the membership grades altogether. Distinct to the existing controller schemes, the proposed fuzzy integral sliding mode control (FISMC) scheme contains the ET condition which needs to be satisfied for the activation of the controller. Besides that, the network-induced communication constraints are considered into the derivation of sufficient conditions, and then the corresponding stabilization issue is attenuated in the sense of H∞control performance. In addition, the appropriate Lyapunov-Krasovskii functional (LKF) candidate is constructed and evaluated through convex matrix inequality approach that ensures the stable H∞performance of the closed-loop system in terms of solvable linear matrix inequalities (LMIs). Further, instead of considering the general problem for the validation of the proposed result, the stabilization problem of nonlinear chaotic permanent magnet synchronous generator (PMSG) model is taken into account for the validation of the proposed sufficient conditions. The purpose of considering the PMSG model is because of its significance in the wind energy conversion systems.

This paper is mainly concerned with the synchronization problem of reaction-diffusion neural networks (RDNNs) with delays and its direct application in image secure communications. An adaptive control is designed without a sign function in which the controller gain matrix is a function of time. The synchronization criteria are established for an error model derived from master-slave models through solving the set of linear matrix inequalities derived by constructing the suitable novel Lyapunov-Krasovskii functional candidate, Green's formula, and Wirtinger's inequality. If the proposed sufficient conditions are satisfied, then the global asymptotic synchronization of the error model is guaranteed. The numerical illustrations are provided to demonstrate the validity of the derived synchronization criteria. In addition, the role of system parameters is picturized through the chaotic nature of RDNNs and those unprecedented solutions is utilized to promote better security of image transactions. As is evident, the enhancement of image encryption algorithm is designed with two levels, namely, image watermarking and diffusion process. The contributions of this paper are discussed as concluding remarks.

The main concern of this paper is to design the efficient sampled-data controller scheme that resolves the stabilization issue of a surface-mounted permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS). Distinct to the existing controller schemes on WECS, the present scheme contains both continuous (plant) and discrete (control) type of signals which outperforms the traditional scheme with continuous or discrete signals. Besides that the fundamental analysis of the closed-loop system under the designed controllers explore the dynamical characteristics of the considered PMSG-based WECS. The stability and stabilization of the proposed closed-loop system have guaranteed through the Lyapunov stability theory and solvable linear matrix inequalities (LMIs). In detail, first, the nonlinear PMSG model has equivalently expressed into linear submodels via the Takagi-Sugeno (T-S) fuzzy approach based on suitable membership rules. Second, the sufficient conditions have been derived as LMIs that ensure the stability and stabilization of the formulated T-S fuzzy PMSG-based WECS. Finally, the effectiveness of the designed controller as well as the consistency of sufficient conditions has demonstrated through numerical evaluations of the closed-loop system.

This paper aims to address the stabilization problem of permanent magnet synchronous motor (PMSM) based wind energy conversion system (WECS) through a novel adaptive fractional fuzzy integral sliding mode control scheme in contrast to the traditional integer order control schemes. The main objective of modeling the fractional order control for nonlinear PMSM is to enhance the convergence rate which is effectively better when compared to integer order control schemes. In addition, this paper intensively investigates the performance of fractional order controllers in both PMSM and surface-mounted PMSM-based WECS through analyzing the global stability of closed-loop system based on Lyapunov stability theory. In this regard, the nonlinear PMSM model is transformed into equivalent linear submodels through an effective Takagi-Sugeno fuzzy membership rules. Then, a novel automated (adaptive) controller is designed along with fractional sliding surface, which involves an integral term to control the considered PMSM. In general, adaptive controllers are much more effective than manual controllers. Further, the sufficient conditions are derived in terms of linear matrix inequalities via constructing the novel fractional fuzzy Lyapunov functional with quadratic terms, which guarantees the global stabilization of PMSM-based WECS. Overall performance and effectiveness of the proposed theoretical results are demonstrated through numerical simulations.

In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

This brief is mainly concerned with a series of dynamical analyses of the Hindmarsh-Rose (HR) neuron with state-dependent time delays. The dynamical analyses focus on stability, Hopf bifurcation, as well as chaos and chaos control. Through the stability and bifurcation analysis, we determine that increasing the external current causes the excitable HR neuron to exhibit periodic or chaotic bursting/spiking behaviors and emit subcritical Hopf bifurcation. Furthermore, by choosing a fixed external current and varying the time delay, the stability of the HR neuron is affected. We analyze the chaotic behaviors of the HR neuron under a fixed external current through time series, bifurcation diagram, Lyapunov exponents, and Lyapunov dimension. We also analyze the synchronization of the chaotic time-delayed HR neuron through nonlinear control. Based on an appropriate Lyapunov-Krasovskii functional with triple integral terms, a nonlinear feedback control scheme is designed to achieve synchronization between the uncontrolled and controlled models. The proposed synchronization criteria are derived in terms of linear matrix inequalities to achieve the global asymptotical stability of the considered error model under the designed control scheme. Finally, numerical simulations pertaining to stability, Hopf bifurcation, periodic, chaotic, and synchronized models are provided to demonstrate the effectiveness of the derived theoretical results.