Passivity Analysis of Coupled Stochastic Neural Networks with Multiweights

In this paper, we devote to the investigation of passivity in two types of coupled stochastic neural networks (CSNNs) with multiweights and incompatible input and output dimensions. First, some new definitions of passivity are proposed for stochastic systems that may have incompatible input and output dimensions. By utilizing stochastic analysis techniques and Lyapunov functional method, several sufficient conditions are respectively developed for ensuring that CSNNs without and with multiple delay couplings can realize passivity. Besides, the synchronization criteria for CSNNs with multiweights are established by employing the results of output-strictly passivity. Finally, two simulation examples are given to illustrate the validity of the theoretical results.

Global Stability of a Lotka-Volterra Competition-Diffusion-Advection System with Different Positive Diffusion Distributions

In this paper, the problem of a Lotka–Volterra competition–diffusion–advection system between two competing biological organisms in a spatially heterogeneous environments is investigated. When two biological organisms are competing for different fundamental resources, and their advection and diffusion strategies follow different positive diffusion distributions, the functions of specific competition ability are variable. By virtue of the Lyapunov functional method, we discuss the global stability of a non-homogeneous steady-state. Furthermore, the global stability result is also obtained when one of the two organisms has no diffusion ability and is not affected by advection.

Outer Synchronization of Drive-Response Complex-Valued Complex Networks via Intermittent Pinning Control

This paper is concerned with the outer exponential synchronization of the drive-response complex dynamical networks subject to time-varying delays. The dynamics of nodes is complex valued, the interactions among of the nodes are directed, and the two coupling matrices in the drive system and the response system are also different. The intermittent pinning control is proposed to achieve outer exponential synchronization in the aperiodical way. Some novel sufficient conditions are derived to guarantee outer exponential synchronization of the considered complex-valued complex networks by using the Lyapunov functional method. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed control protocols.

Periodic solution for inertial neural networks with variable parameters

<abstract><p>We discuss periodic solution problems and asymptotic stability for inertial neural networks with $ D- $operator and variable parameters. Based on Mawhin's continuation theorem and Lyapunov functional method, some new sufficient conditions on the existence and asymptotic stability of periodic solutions are established. Finally, a numerical example verifies the effectiveness of the obtained results.</p></abstract>

Periodic solution for neutral-type inertial neural networks with time-varying delays

In this paper the problems of the existence and stability of periodic solutions of neutral-type inertial neural networks with time-varying delays are discussed by applying Mawhin’s continuation theorem and Lyapunov functional method. Finally, two numerical examples are given to illustrate our theoretical results.

Nonlinear dynamics of full-range CNNs with time-varying delays and variable coefficients

In the article, the dynamical behaviours of the full-range cellular neural networks (FRCNNs) with variable coefficients and time-varying delays are considered. Firstly, the improved model of the FRCNNs is proposed, and the existence and uniqueness of the solution are studied by means of differential inclusions and set-valued analysis. Secondly, by using the Hardy inequality, the matrix analysis, and the Lyapunov functional method, we get some criteria for achieving the globally exponential stability (GES). Finally, some examples are provided to verify the correctness of the theoretical results.

Exponential Synchronization for Neutral-Type Neural Network with Stochastic Perturbation and Markovian Jumping Parameters

The problem of exponential synchronization for neutral-type neural network with stochastic perturbation and Markovian switching parameters is considered in this article. Based on Lyapunov functional method and the theory of stochastic process, the exponential synchronism of the neural network is analyzed. By designing an adaptive state feedback controller, the exponential synchronization criterion of the neural network is obtained which can be represented as linear matrix inequality. Furthermore, the update rule for the adaptive controller is obtained. Finally, a simulation example is proposed to explain the availability of the results and method obtained in this article.