Periodic measures of impulsive stochastic Hopfield-type lattice systems

Abstract

This paper is concerned with the periodic measures of the stochastic impulsive Hopfield-type lattice systems driven by nonlinear noise. By the properties of periodic Markov processes, the existence of periodic measures for the impulsive stochastic lattice systems is established. To this end, we employ the idea of uniform estimates on the tails of the solutions to show the tightness of a family of distributions of the solutions of the lattice systems.

Keywords:

• Periodic measure
• impulsive
• Hopfield-type lattice system

Acknowledgment

The authors would like to thank the anonymous referee for the useful suggestions and comments.

Additional information

Funding

This work was supported by NSFC (11971394 and 11871049), Sichuan Science and Technology Program (2019YJ0215), Fundamental Research Funds for the Central Universities (2682021ZTPY057) and Natural Science Foundation of Chongqing Municipality of China(cstc2019jcyj-msxmX0722).