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

作者：Ma, Weijun; Ding, Baocang^*; Yang, Hongfu; Zhang, Qimin

来源：Neurocomputing, 2015, 166: 256-264.

DOI：10.1016/j.neucom.2015.03.072

• Stochastic neural networks
• Mean-square dissipativity
• Numerical methods
• Fractional Brownian motion
• Poisson 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.

• 出版日期2015-10-20
• 单位宁夏大学; 北方民族大学; 西安交通大学