Existence and Exponential Stability of Solutions for Stochastic Cellular Neural Networks with Piecewise Constant Argument

Abstract

By using the concept of differential equations with piecewise constant argument of generalized type, a model of stochastic cellular neural networks with piecewise constant argument is developed. Sufficient conditions are obtained for the existence and uniqueness of the equilibrium point for the addressed neural networks.pth moment exponential stability is investigated by means of Lyapunov functional, stochastic analysis, and inequality technique. The results in this paper improve and generalize some of the previous ones. An example with numerical simulations is given to illustrate our results.

Unpredictable solutions of quasilinear differential equations with generalized piecewise constant arguments of mixed type

“…The ideas suggested in these papers became very useful not only in modeling but also in methodological sense, since the construction of equivalent integral equations for EPCAG has opened the research gate for methods of operator theory and functional analysis [7,9,24,26,28,29,32,43,48,49,50,52,53]. This was also confirmed with applications in neuroscience [8,9,11,25,41,42,44,47,50,51]. In the present research, we have joined the chaos concept with the most flexible and convenient functional differential equations for applications.…”

Robustness Analysis of BAM Cellular Neural Network with Deviating Arguments of Generalized Type

“…Akhmet et al explored the stability of several type neural networks with deviating arguments in [22,23]. In [24], Li investigates the ES of stochastic CNN with deviating argument by using Lyapunov functional. In [25], the stability of semi-linear stochastic diferential equation with deviating argument is discussed.…”

Convergence and stability of the Milstein scheme for stochastic differential equations with piecewise continuous arguments

“…Stochastic differential equations with piecewise continuous arguments (SDEPCAs) are an important part of the stochastic theory. Such models are applicable in a wide range of areas including control science, biology, and neural networks( [10,14,22]). Since most of SDEPCAs do not have explicit solutions, it becomes extremely important to solve them by numerical methods.…”