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.