Xiaofeng Chen

Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales

In this paper, the complex-valued neural networks with both leakage time delay and discrete time delay as well as two types of activation functions on time scales are considered. By using the fixed point theory, a criterion for checking the existence, uniqueness of the equilibrium point for the considered complex-valued neural networks is presented. By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global stability of the addressed complex-valued neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Three examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.

Global exponential stability of the periodic solution of delayed Cohen-Grossberg neural networks with discontinuous activations

In the paper, the problem on the stability of periodic solutions is investigated for delayed Cohen-Grossberg neural networks with discontinuous activations. For the neural networks under study, the traditional assumptions on the Lipschitz continuity and some sort of linear growth for the activation functions are not required. By employing the theory of differential equations with discontinuous right-hand side, theory of fixed point and Lyapunov approach, several sufficient conditions for checking the existence, uniqueness and global exponential stability of periodic solution for the considered neural networks are given. Three numerical examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.

Quasi-uniform synchronization of fractional-order memristor-based neural networks with delay

Quasi-uniform synchronization of delayed fractional-order memristor-based neural networks (FMNNs) is discussed in this paper. On the basis of the theory of fractional differential equations and the theory of differential inclusion, the synchronization error system between the concerned drive system and the associated response system is formulated, and then, by employing Hlder inequality, Cp inequality and Gronwall-Bellman inequality, several sufficient criteria are proposed to ensure the quasi-uniform synchronization for the considered delayed FMNNs. Three simulation examples are also presented to illustrate the availability and correctness of the theoretical results.

Global µ-stability analysis of discrete-time complex-valued neural networks with leakage delay and mixed delays

In this paper, the problem of µ-stability for discrete-time complex-valued neural networks with three kinds of time-delays including leakage delay, discrete delay and distributed delay is considered. Based on contraction mapping theorem and homeomorphism mapping theorem in complex domain, some sufficient conditions are proposed for the existence and uniqueness of the equilibrium point of the addressed neural networks. By constructing an appropriate Lyapunov-Krasovskii functional, and employing the matrix inequality techniques, several delay-dependent criteria for checking the global µ-stability of the complex-valued neural networks are established in linear matrix inequalities (LMIs), which can be checked numerically using the effective YALMIP Tool in MATLAB. As direct applications of these results, we get some criteria on the exponential stability, power-stability and log-stability of the neural networks.

Multistability of complex-valued neural networks with time-varying delays

In this paper, the multistability problem is studied for an n-dimensional delayed complex-valued neural networks with two general classes of activation functions. After splitting the state space to multiple subsets, based on the fixed point theorem, it is shown that such complex-valued neural networks can have 9n equilibria, each of which is located in one of the subsets. Furthermore, some sufficient conditions are derived for the local exponential stability of some equilibria by employing the property of activation functions and inequality technique. As an application of these results, some criteria are obtained for checking the coexistence and exponential stability of multiple equilibria of real-valued neural networks. Two examples are performed to illustrate and validate the theoretical findings.

Global -Stability of Complex-Valued Neural Networks with Unbounded Time-Varying Delays

The complex-valued neural networks with unbounded time-varying delays are considered. By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global -stability of the addressed complex-valued neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.

Stability analysis of nonlinear fractional-order systems with variable-time impulses

This paper aims at analyzing the stability analysis for a class of variable-time impulsive fractional-order nonlinear systems. Based on the theory of fractional calculus, the theory of impulsive differential equation, inequality techniques, and the B-equivalence method, the variable-time jump operator of the considered system can be updated as a fixed-time substitution, and the fractional-order system with the latter operator can be regarded as the comparison system of the original system. In addition, both graphic illustration and theoretical explanation are presented. Finally, two numerical examples are shown to demonstrate the validity and feasibility of the obtained results.

Global μ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays

The impulsive complex-valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks is proposed in terms of linear matrix inequality (LMI). By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global -stability of the complex-valued neural networks are established in LMIs. As direct applications of these results, several criteria on the exponential stability, power-stability, and log-stability are obtained. Two examples with simulations are provided to demonstrate the effectiveness of the proposed criteria.

Stability Analysis of Continuous-Time and Discrete-Time Quaternion-Valued Neural Networks With Linear Threshold Neurons

This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

Global

The complex-valued neural networks with unbounded time-varying delays are considered. By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global -stability of the addressed complex-valued neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.