Periodic orbit analysis for the delayed Filippov system

Cai, Zuowei; Huang, Jianhua; Huang, Lihong

doi:10.1090/proc/13883

Periodic orbit analysis for the delayed Filippov system

Authors: Zuowei Cai, Jianhua Huang and Lihong Huang
Journal: Proc. Amer. Math. Soc. 146 (2018), 4667-4682
MSC (2010): Primary 39A23, 34K09, 34K10; Secondary 34K30
DOI: https://doi.org/10.1090/proc/13883
Published electronically: August 7, 2018
MathSciNet review: 3856136
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Abstract: In this paper, a general class of the delayed differential equation with a discontinuous right-hand side is considered. Under the extended Filippov differential inclusions framework, some new criteria are obtained to guarantee the existence of a periodic solution by employing Kakutani's fixed point theorem of set-valued maps and matrix theory. Then, we apply these criteria to the time-delayed neural networks with discontinuous neuron activations. Our analysis method and theoretical results are of great significance in the design of time-delayed neural network circuits with discontinuous neuron activation under a periodic environment.

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