Abstract
This paper concerns the issues of exponential stability in Lagrange sense for a class of stochastic Cohen–Grossberg neural networks (SCGNNs) with Markovian jump and mixed time delay effects. A systematic approach of constructing a global Lyapunov function for SCGNNs with mixed time delays and Markovian jumping is provided by applying the association of Lyapunov method and graph theory results. Moreover, by using some inequality techniques in Lyapunov-type and coefficient-type theorems we attain two kinds of sufficient conditions to ensure the global exponential stability (GES) through Lagrange sense for the addressed SCGNNs. Ultimately, some examples with numerical simulations are given to demonstrate the effectiveness of the acquired result.
Highlights
First and foremost, Cohen and Grossberg initiate the Cohen–Grossberg neural networks (CGNNs) in 1983 [6]
In NNs, the information processing is a fastening event that occurred in the modes, the modes can be concerned with expressing finite state description from a trained network
Inspired by the aforementioned works, we considered the Lagrange stability analysis of CGNNs with Markovian jumping and mixed time delay
Summary
First and foremost, Cohen and Grossberg initiate the Cohen–Grossberg neural networks (CGNNs) in 1983 [6]. Even though the graph-theoretic approach is frequently used in the study of stability; see [7, 11, 27, 31, 34] In this novel approach, to the best of the authors knowledge, researchers have not correlated them with NNs, there are one or two of them in NNs. Inspired by the aforementioned works, we considered the Lagrange stability analysis of CGNNs with Markovian jumping and mixed time delay. Compared with the outcome of some existing research work, the contribution of this work is formulated by: (i) Novel method that depends on the incorporation of graph theory principles as well as Lyapunov method, which are applied to investigate the GES issues in Lagrange sense for a new class of SCGNNs with delays and Markovian jump effects.
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