Periodic orbit analysis for a delayed model of malicious signal transmission in wireless sensor networks with discontinuous control

Abstract

This paper employs a discontinuous temporary immunity control to obtain the periodic orbit for a class of delayed malicious signal transmission model in wireless sensor networks under the framework of differential inclusion. The positivity and boundedness of the solution for the discontinuous system is proved first. Then, by using the Kakutani's fixed point theorem of set‐valued maps, the existence of a periodic orbit is obtained under some assumptions and constraints. Furthermore, the globally exponentially stable ω$$ \omega $$‐periodic orbit is investigated using the Lyapunov functional method. The obtained results can help us better understand the dynamic characteristics of discontinuous delayed systems and have direct applications to the wireless sensor networks for guaranteeing fast response to malicious signals. Finally, the numerical simulations of three examples are given to validate the correctness of the theoretical results.