Global point dissipativity of neural networks with mixed time-varying delays

An Extended Analysis on Robust Dissipativity of Uncertain Stochastic Generalized Neural Networks with Markovian Jumping Parameters

The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical systems are subject to uncertainties. As a result, we take the norm-bounded parameter uncertainties, as well as stochastic disturbances into consideration in our study. To address the task, we formulate the appropriate Lyapunov–Krasovskii functional (LKF), and through the use of effective integral inequalities, simplified linear matrix inequality (LMI) based sufficient conditions are derived. We validate the feasible solutions through numerical examples using MATLAB software. The simulation results are analyzed and discussed, which positively indicate the feasibility and effectiveness of the obtained theoretical findings.

Global dissipativity of stochastic Lotka–Volterra system with feedback controls

In this paper, a class of stochastic Lotka–Volterra system with feedback controls is considered. The purpose is to establish some criteria to ensure the system is globally dissipative in the mean square. By constructing suitable Lyapunov functions as well as combining with Jensen inequality and It[Formula: see text] formula, the sufficient conditions are established and they are expressed in terms of the feasibility to a couple linear matrix inequalities (LMIs). Finally, the main results are illustrated by examples.

Global robust dissipativity of interval recurrent neural networks with time-varying delay and discontinuous activations

In this paper, the problems of robust dissipativity and robust exponential dissipativity are discussed for a class of recurrent neural networks with time-varying delay and discontinuous activations. We extend an invariance principle for the study of the dissipativity problem of delay systems to the discontinuous case. Based on the developed theory, some novel criteria for checking the global robust dissipativity and global robust exponential dissipativity of the addressed neural network model are established by constructing appropriate Lyapunov functionals and employing the theory of Filippov systems and matrix inequality techniques. The effectiveness of the theoretical results is shown by two examples with numerical simulations.

Global dissipativity analysis on uncertain neural networks with mixed time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for uncertain neural networks with discrete time-varying delay and distributed time-varying delay as well as general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing Newton-Leibniz formulation and linear matrix inequality (LMI) technique, several new criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in terms of LMI, which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness and decreased conservatism of the proposed criteria in comparison with some existing results. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.

Robust Stability of Switched Cohen–Grossberg Neural Networks With Mixed Time-Varying Delays

By combining Cohen-Grossberg neural networks with an arbitrary switching rule, the mathematical model of a class of switched Cohen-Grossberg neural networks with mixed time-varying delays is established. Moreover, robust stability for such switched Cohen-Grossberg neural networks is analyzed based on a Lyapunov approach and linear matrix inequality (LMI) technique. Simple sufficient conditions are given to guarantee the switched Cohen-Grossberg neural networks to be globally asymptotically stable for all admissible parametric uncertainties. The proposed LMI-based results are computationally efficient as they can be solved numerically using standard commercial software. An example is given to illustrate the usefulness of the results.

Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness, and global exponential stability of periodic solution for shunting inhibitory cellular neural networks with impulses, dx(ij)dt=-a(ij)x(ij)- summation operator(C(kl)inN(r)(i,j))C(ij) (kl)f(ij)[x(kl)(t)]x(ij)+L(ij)(t), t>0,t not equal t(k); Deltax(ij)(t(k))=x(ij)(t(k) (+))-x(ij)(t(k) (-))=I(k)[x(ij)(t(k))], k=1,2,...] . Furthermore, the numerical simulation shows that our system can occur in many forms of complexities, including periodic oscillation and chaotic strange attractor. To the best of our knowledge, these results have been obtained for the first time. Some researchers have introduced impulses into their models, but analogous results have never been found.