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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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Additional Information

Zuowei Cai
Affiliation: Department of Information Technology, Hunan Women’s University, Changsha, Hunan 410002, People’s Republic of China
Email: caizuowei01@126.com

Jianhua Huang
Affiliation: College of Science, National University of Defense Technology, Changsha, Hunan 410073, People’s Republic of China
Email: jhhuang32@nudt.edu.cn

Lihong Huang
Affiliation: School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, People’s Republic of China
Email: lhhuang@hnu.edu.cn

DOI: https://doi.org/10.1090/proc/13883
Keywords: Delayed differential inclusions, Filippov solution, periodic solution, neural networks
Received by editor(s): March 30, 2017
Received by editor(s) in revised form: June 30, 2017
Published electronically: August 7, 2018
Additional Notes: The first author was supported in part by NSF of China (No.11626100), NSF of Hunan Province (No.2016JJ3078), Scientific Research Youth Project of Hunan Provincial Education Department (No.16B133) and China Postdoctoral Science Foundation (No.2017M613361).
Communicated by: Wenxian Shen
Article copyright: © Copyright 2018 American Mathematical Society