Abstract
In this paper, we prove the existence and uniqueness of the equilibrium solution of the system by using the M-matrix and the topological degree technique and study the boundedness and robustness of dynamics of reaction–diffusion high-order Markovian jump Cohen–Grossberg neural networks (CGNNs) with p-Laplacian diffusion, including the common reaction–diffusion CGNNs. The obtained criteria are applicable to computer Matlab LMI-toolbox, which is suitable for large-scale calculations of actual complex engineering. Finally, a numerical example demonstrates the effectiveness of the proposed method.
Highlights
All the time neural networks have attracted much attention for its wide application [1,2,3,4,5,6,7]
Markovian jump dynamics have been applied to various complex systems, such as dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback, slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations, finitetime nonfragile l2–l∞ control for jumping stochastic systems subject to input constraints via an event-triggered mechanism, and so on ([26,27,28,29] and the references therein)
We present a sufficient condition for the boundedness and robust stability of the reaction– diffusion high-order Markovian jump Cohen–Grossberg neural network with nonlinear Laplacian diffusion
Summary
All the time neural networks have attracted much attention for its wide application [1,2,3,4,5,6,7]. ∂ ui (t,x) ∂ xj was replaced by the Dirichlet boundary condition ui(t, x)|∂Ω = 0 in system (2.1), we would not derive a formula similar to (3.2), since system (2.1) involves αi (the input from outside the networks), so that ui = ui – u∗i = –u∗i on ∂Ω, that is, the equilibrium solution u∗i is not necessarily zero. Remark 3 It is the first time that the boundedness of p-Laplacian reaction–diffusion highorder neural networks is investigated and the robust stability criterion is derived for such complex systems.
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