Mean-square dissipativity of numerical methods for a class of stochastic neural networks with fractional Brownian motion and jumps

In this paper, we introduce a class of stochastic neural networks with fractional Brownian motion (fBm) and Poisson jumps. We also concern mean-square dissipativity of numerical methods applied to a class of stochastic neural networks with fBm and jumps. The conditions under which the underlying systems are mean-square dissipative are considered. It is shown that the mean-square dissipativity is preserved by the compensated split-step backward Euler method and compensated backward Euler method without any restriction on stepsize, while the split-step backward Euler method and backward Euler method could reproduce mean-square dissipativity under a stepsize constraint. The results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of mean-square dissipativity. Finally, an example is given for illustration.

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