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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. [ABSTRACT FROM AUTHOR]

This article presents sufficient conditions on Finite-Time Input-to-State Stability (FTISS) of nonlinear impulsive systems, which gathers the analysis of Input-to-State stability (ISS) and finite-time convergence rate. By utilising the Finite-Time Stable Function Pair (FTSFP) and Generalised K L ( G K L ) function, we established an unified FTISS criterion for nonlinear impulsive systems, in which the impulses maybe beneficial to stabilisation or detrimental to stabilisation. Moreover, a relaxed Lyapunov Function (LF) method is used to investigate FTISS. Compared with the traditional LF method, the main advantage is that the constructed LF is permitted to own indefinite-derivative. As a special case of FTISS, a corollary on Finite-Time Stability (FTS) is established, which is applicable to investigate the realisation of FTS for nonlinear system via impulsive control strategy. Finally, the proposed results are supported by two practical numerical examples. [ABSTRACT FROM AUTHOR]

Nonlinear systems described by differential equations are of great theoretical significance and do frequently arise in practice. Lan et al. [[4]] considered a generalized delayed stage-structured prey-predator model possessing fear effect and prey refuge. Based on the implicit function derivative rule and the function monotonicity theory, the existence of a coexistence equilibrium point of the prey-predator model was analyzed. [Extracted from the article]

By employing Leray-Schauder alternative theorem of set-valued maps and non-Lyapunov method (non-smooth analysis, inequality analysis, matrix theory), this paper investigates the problems of periodicity and stabilization for time-delayed Filippov system with perturbation. Several criteria are obtained to ensure the existence of periodic solution of time-delayed Filippov system by using differential inclusion. By designing appropriate switching state-feedback controller, the asymptotic stabilization and exponential stabilization control of Filippov system are realized. Applying these criteria and control design method to a class of time-delayed neural networks with perturbation and discontinuous activation functions under a periodic environment. The developed theorems improve the existing results and their effectiveness are demonstrated by numerical example. [ABSTRACT FROM AUTHOR]