Polynomial Noises for Nonlinear Systems with Nonlinear Impulses and Time-Varying Delays

Lichao Feng, Qiaona Wang, Chunyan Zhang and Dianxuan Gong
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Lichao Feng: College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China
Qiaona Wang: College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China
Chunyan Zhang: College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China
Dianxuan Gong: College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China

Mathematics, 2022, vol. 10, issue 9, 1-13

Abstract: It is known that random noises have a significant impact on differential systems. Recently, the influences of random noises for impulsive systems have been started. Nevertheless, the existing references on this issue ignore the significant phenomena of nonlinear impulses and time-varying delays. Therefore, we see the necessity to study the influences of random noises for impulsive systems with the above two factors. Stimulated by the above, a polynomial random noise is introduced to suppress the potential explosive behavior of the nonlinear impulsive differential system with time-varying delay. Fortunately, the stochastically controlled impulsive delay differential system admits a unique global solution, is bounded, and grows at most in the polynomial form.

Keywords: impulsive systems; time-varying delays; random noises; explosive solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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