Existence of solutions to Caputo fractional differential inclusions of 1<α<2 with initial and impulsive boundary conditions

This paper is concerned with the existence of solutions to the Caputo fractional differential inclusion of 1 < \alpha < 2 with initial and impulsive boundary conditions. A novel existence result is presented based on the fixed-point theorem of Dhage for multi-valued operators with some assumptions. Finally, two examples are provided to explicate the applicability of the main result

Exponential stability of Cohen-Grossberg neural networks with multiple time-varying delays and distributed delays

Maybe because Cohen-Grossberg neural networks with multiple time-varying delays and distributed delays cannot be converted into the vector-matrix forms, the stability results of such networks are relatively few and the stability conditions in the linear matrix inequality forms have not been established. So this paper investigates the exponential stability of the networks and gives the sufficient condition in the linear matrix inequality forms. Two examples are provided to demonstrate the effectiveness of the theoretical results

Global exponential periodicity of nonlinear neural networks with multiple time-varying delays

Global exponential periodicity of nonlinear neural networks with multiple time-varying delays is investigated. Such neural networks cannot be written in the vector-matrix form because of the existence of the multiple delays. It is noted that although the neural network with multiple time-varying delays has been investigated by Lyapunov-Krasovskii functional method in the literature, the sufficient conditions in the linear matrix inequality form have not been obtained. Two sets of sufficient conditions in the linear matrix inequality form are established by Lyapunov-Krasovskii functional and linear matrix inequality to ensure that two arbitrary solutions of the neural network with multiple delays attract each other exponentially. This is a key prerequisite to prove the existence, uniqueness, and global exponential stability of periodic solutions. Some examples are provided to demonstrate the effectiveness of the established results. We compare the established theoretical results with the previous results and show that the previous results are not applicable to the systems in these examples

Synchronization for networks of coupled non-linear systems with external disturbances

International audienceBased on the integral sliding mode control method, some theoretical criteria for the robust synchronization of multi-coupled general non-linear systems with external disturbances are presented, the ultimate error bounds are estimated simultaneously. Furthermore, as an application, the detailed analysis and conclusions are derived for a network of multi-coupled FitzHugh–Nagumo (FHN) systems with external disturbances. Finally, some numerical examples, with two or more coupled FHN systems, are given to illustrate the effectiveness of the proposed theoretical results

Synchronization and parameter identification of uncertain complex network via adaptive-impulsive control

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Exponential stability of periodic solution for stochastic neural networks involving multiple time-varying delays

This paper discusses the exponential stability of periodic solutions for stochastic neural networks with multiple time-varying delays. For these networks, sufficient conditions in the linear matrix inequality forms are rare in the literature. We constructed an appropriate Lyapunov-Krasovskii functional to eliminate the items with multiple delays and establish some sufficient conditions in linear matrix inequality forms, to ensure exponential stability of the periodic solutions. Several examples are provided to demonstrate that our results are effective and less conservative than previous ones