Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps

Abstract

In this paper, we main investigate the almost sure exponential stability of stochastic delay Hopfield neural networks with jumps on numerical solutions. The methods we used are Euler approach and backward Euler approach. By giving some conditions of theoretical significance, we verify that not only Euler approach but also backward Euler approach is almost sure exponential stability. However, the range of application of Euler approach is smaller than that of backward Euler approach. Moreover, our main research tool is the discrete semimartingale convergence theorem. Lastly, we give an example as illustration.