Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps

Abstract

The paper devoted to asymptotic mean-square boundedness of several numerical methods for stochastic complex-valued neural networks with Poisson jumps.The definition of asymptotic mean-square boundedness of the numerical solution is presented, and some sufficient conditions for the underlying systems which are asymptotic mean-square boundedness are derived. By taking the advantage of the compensated split-step backward Euler (CSSBE) method and compensated backward Euler (CBE) method, sufficient criteria promising the asymptotic mean-square boundedness of CVNNs without any restriction on time stepsize, while the split-step backward Euler (SSBE) method and backward Euler (BE) method can derive asymptotic mean-square boundedness under a time stepsize constraint. The obtained theoretical results show that the compensated numerical methods own an incredible advantage over the noncompensated numerical methods on the part of asymptotic mean-square boundedness. Finally, an example is proposed and analyzed to demonstrate the effectiveness and feasibility of the proposed results.