Exponential Synchronization of Memristive Chaotic Recurrent Neural Networks Via Alternate Output Feedback Control

This paper considers the global exponential synchronization problem of two memristive chaotic recurrent neural networks with time‐varying delays using periodically alternate output feedback control. First, the periodically alternate output feedback control rule is designed for the global exponential synchronization of two memristive chaotic recurrent neural networks. Then, according to the Lyapunov stability theory, we construct an appropriate Lyapunov‐Krasovskii functional to derive several new sufficient conditions guaranteeing exponential synchronization of two memristive chaotic recurrent neural networks under periodically alternate output feedback control. Compared with existing results on synchronization conditions on the basis of linear matrix inequalities of memristive chaotic recurrent neural networks, the derived results complement, extend earlier related results, and are also easy to validate in this paper. An illustrative example is provided to illustrate the effectiveness of the synchronization criteria.     

随机混沌时滞神经网络的指数同步

研究受随机扰动且具有时变时滞神经网络的指数同步. 根据Lyapunov稳定性理论结合线性矩阵不等式技巧, 通过构造含时滞的状态反馈控制器, 使得受到随机扰动的驱动系统和响应系统达到指数同步, 给出了随机时滞神经网络指数同步的新判据, 最后通过仿真验证了所用方法的有效性.     

Exponential Stabilization of Stochastic Memristive Recurrent Neural Networks Under Periodically Intermittent State Feedback Control

In this paper, the exponential stabilization problem is investigated for a class of memristive time‐varying delayed neural networks with stochastic disturbance via periodically intermittent state feedback control. First, a periodically intermittent state feedback control rule is designed for the exponential stabilization of stochastic memristive time‐varying delayed neural networks. Then, by adopting appropriate Lyapunov‐Krasovskii functionals in light of the Lyapunov stability theory, some novel stabilization criteria are obtained to guarantee exponential stabilization of stochastic memristive time‐varying delayed neural networks via periodically intermittent state feedback control. Compared with existing results on stabilization of stochastic memristive time‐varying delayed neural networks, the obtained stabilization criteria in this paper are not difficult to verify. Finally, an illustrative example is given to illustrate the validity of the obtained results.     

Lag Synchronization of Unknown Chaotic Delayed Yang–Yang-Type Fuzzy Neural Networks With Noise Perturbation Based on Adaptive Control and Parameter Identification

This paper considers the lag synchronization (LS) issue of unknown coupled chaotic delayed Yang–Yang-type fuzzy neural networks (YYFCNN) with noise perturbation. Separate research work has been published on the stability of fuzzy neural network and LS issue of unknown coupled chaotic neural networks, as well as its application in secure communication. However, there have not been any studies that integrate the two. Motivated by the achievements from both fields, we explored the benefits of integrating fuzzy logic theories into the study of LS problems and applied the findings to secure communication. Based on adaptive feedback control techniques and suitable parameter identification, several sufficient conditions are developed to guarantee the LS of coupled chaotic delayed YYFCNN with or without noise perturbation. The problem studied in this paper is more general in many aspects. Various problems studied extensively in the literature can be treated as special cases of the findings of this paper, such as complete synchronization (CS), effect of fuzzy logic, and noise perturbation. This paper presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed adaptive scheme. This research also demonstrates the effectiveness of application of the proposed adaptive feedback scheme in secure communication by comparing chaotic masking with fuzziness with some previous studies. Chaotic signal with fuzziness is more complex, which makes unmasking more difficult due to the added fuzzy logic.      

Robust synchronization in an array of fuzzy delayed cellular neural networks with stochastically hybrid coupling

In this paper, the robust synchronization control problem of an array of fuzzy cellular neural networks with uncertain stochastically coupling is investigated, which involves constant coupling, discrete time-varying delay coupling and distributed time-varying delay coupling. By using adaptive feedback control scheme and exploiting some stochastic analysis techniques, several sufficient conditions are developed to ensure the synchronization of stochastically hybrid coupled fuzzy neural networks with all admissible uncertainties in mean square. Finally, a numerical example illustrated by scale-free complex networks is provided to show the effectiveness and the applicability of the proposed method.     

基于自适应事件触发牵制控制的多时滞随机耦合神经网络簇同步

本文通过自适应事件触发牵制控制策略,研究了多时滞的随机耦合神经网络在均方意义下以指数速率进行簇同步的问题.在耦合神经网络中,同一簇中的节点只需与相应的孤立节点同步,而对于不同簇中节点之间的同步状态没有要求.首先,本文提出了一种事件触发牵制控制方法来解决耦合神经网络中节点数量众多、通讯复杂的问题.该方法不仅能减少耦合神经网络中控制器的数量,还可以减少控制信号的传输次数、减轻网络传输压力.然后根据M矩阵方法,建立了随机耦合神经网络均方指数稳定的充分条件.同时,利用自适应控制策略,给出了反馈增益的更新规律.最后,通过一个数值例子验证了所提出的自适应事件触发牵制控制策略的有效性和适用性.     

Master‐slave synchronization for coupled neural networks with Markovian switching topologies and stochastic perturbation

In this paper, the master‐slave synchronization for coupled neural networks with Markovian jumping topology and stochastic perturbation is discussed. Based on a graph theory, the ergodic property of the Markovian chain, and the strong law of the large numbers for local martingales, several sufficient conditions are established to ensure the almost sure exponential synchronization or asymptotic synchronization in mean square for coupled neural networks with Markovian jumping topology. By the pinning control method, the chaotic synchronization between the master system and the slave systems with stochastic disturbance is achieved. The effectiveness of the results is finally illustrated by a numerical example.     

Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms

The global exponential synchronization for a class of fuzzy cellular neural networks with delays and reaction-diffusion terms is discussed. Some new sufficient conditions are obtained by using the Lyapunov functional method, many real parameters and inequality techniques. The result is also easy to check and plays an important role in the design and application of globally exponentially synchronization. Finally, an example is given to verify our results.     

Exponential synchronization of stochastic chaotic neural networks with mixed time delays and Markovian switching

This paper studies the exponential synchronization problem for a class of stochastic perturbed chaotic neural networks with both Markovian jump parameters and mixed time delays. The mixed delays consist of discrete and distributed time-varying delays. At first, based on a Halanay-type inequality for stochastic differential equations, by virtue of drive-response concept and time-delay feedback control techniques, a delay-dependent sufficient condition is proposed to guarantee the exponential synchronization of two identical Markovian jumping chaotic-delayed neural networks with stochastic perturbation. Then, by utilizing the Jensen integral inequality and a novel Lemma, another delay-dependent criterion is established to achieve the globally stochastic robust synchronization. With some parameters being fixed in advance, these conditions can be solved numerically by employing the Matlab software. Finally, a numerical example with their simulations is provided to illustrate the effectiveness of the presented synchronization scheme.     

Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control

In this paper, lag synchronization for a class of delayed fuzzy cellular networks is investigated. By utilizing inequality technique, Lyapunov functional theory and the analysis method, some new and useful criteria of lag synchronization for the addressed networks are derived in terms of p-norm under a periodically intermittent controller. Finally, an example with simulation is given to show the effectiveness of the obtained results.     

Stability Analysis of Stochastic Fuzzy Cellular Neural Networks With Time-Varying Delays and Reaction-Diffusion Terms

In this paper, a class of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms is investigated. By using Lyapunov–Krasovskii functional and stochastic analysis approaches, new and less conservative delay-derivative-dependent stability criteria are presented to guarantee the neural networks to be globally exponentially stable in the mean square for all admissible stochastic perturbations. Numerical simulations are carried out to illustrate the main results.     

On the exponential synchronization of stochastic impulsive chaotic delayed neural networks

In this paper, the exponential synchronization of stochastic impulsive chaotic delayed neural networks is investigated. Based on the Lyapunov function method, time-varying delay feedback control technique and the efficient modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical chaotic delayed neural networks with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Comparing with the existing works that consider single perturbation (stochastic or impulsive one), the proposed method can provide a more general framework for the synchronization of multi-perturbation chaotic systems, which is favorable for practical application in secure communication. Finally, numerical simulations verify the effectiveness of the proposed method.     

Exponential p-Synchronization of Non-autonomous Cohen–Grossberg Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control

The problem of \(p\) -synchronization for a class of stochastic non-autonomous reaction-diffusion Cohen–Grossberg networks with mixed delays by using periodically intermittent feedback control is investigated in this paper. Some exponential synchronization criteria based on \(p\) -norm are obtained by utilizing some analysis methods. These proofs indirectly generalized the Halanay inequality and facilitated the proof processing of the existing works. Finally, an illustrative example is given to show the effectiveness of the theoretical results.     

Exponential synchronization of Cohen-Grossberg neural networks via periodically intermittent control

In this paper, a class of Cohen-Grossberg neural networks with time-varying delays are studied by designing a periodically intermittent controller. Some novel and effective exponential synchronization criteria are derived by applying some analysis techniques. These results generalize a few previous known results and remove some restrictions on control width and time-delays. Finally, a chaotic Cohen-Grossberg neural network is represented to show the effectiveness and feasibility of our results.     

Synchronization of Complex Networks with Coupled and Self‐Feedback Delays Via Aperiodically Intermittent Strategy

In this paper, we concern the exponential synchronization problem for hybrid‐coupled delayed dynamical networks via aperiodically intermittent control. Different from previous works, the delayed coupling term considered here contains the transmission delay and self‐feedback delay, and the intermittent control can be aperiodic. By utilizing a different technique compared with some previous results, several useful criteria are derived analytically to realise exponential synchronization for a class of coupled complex network. As a special case, some sufficient conditions ensuring the exponential synchronization for a class of coupled neural network are obtained. Finally, a numerical example is given to demonstrate the validness of the proposed scheme.     

Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks

This paper is devoted to investigating delay-dependent robust exponential stability for a class of Markovian jump impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks (IRDCGNNs) with mixed time delays and uncertainties. The jumping parameters, determined by a continuous-time, discrete-state Markov chain, are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing a Lyapunov–Krasovskii functional, and using poincarè inequality and the mathematical induction method, several novel sufficient criteria ensuring the delay-dependent exponential stability of IRDCGNNs with Markovian jumping parameters are established. Our results include reaction-diffusion effects. Finally, a Numerical example is provided to show the efficiency of the proposed results.     

Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays

In this paper, we establish a method to study the mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. By using the properties of M-cone and inequality technique, we obtain some sufficient conditions ensuring mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range. Two examples are also discussed to illustrate the efficiency of the obtained results.     

Synchronization of complex networks with coupling delays via adaptive pinning intermittent control

The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.     

Robust stability of delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales

In this paper, the global robust exponential stability of equilibrium solution to delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales is studied. Using topological degree theory, M-matrix method, Lyapunov functional and inequality skills, we establish some sufficient conditions for the existence, uniqueness and global robust exponential stability of equilibrium solution to delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales. One example is given to illustrate the effectiveness of our results.     

Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters

In this paper, we investigate the robust exponential stability for stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jump parameters. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain sufficient conditions for the exponential stability of the equilibrium solution. The obtained stability criteria can be easily checked by linear matrix inequality (LMI) techniques. Finally numerical examples are provided to illustrate the obtained theoretical result.