Existence and Uniqueness Theorem on Uncertain Nonlinear Switching Systems with Time Delay

Yadong Shu and Ting Jin ()
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Yadong Shu: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Ting Jin: School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China

Mathematics, 2025, vol. 13, issue 18, 1-18

Abstract: This paper considers an uncertain nonlinear switching system with time delay, which is denoted as a series of uncertain delay differential equations. Previously, there were few published results on such kinds of uncertain switching systems. To fill this void, the internal property of the solutions is thoroughly explored for uncertain switching systems with time delay in state. Under the linear growth condition and the Lipschitz condition, existence and uniqueness with respect to the solutions are derived almost surely in the form of a judgement theorem. The theorem is strictly verified by applying uncertainty theory and the contraction mapping principle. In the end, the validity of above theoretical results is illustrated through a microbial symbiosis model.

Keywords: nonlinear switching systems; time delay in state; existence and uniqueness; uncertainty theory; contraction mapping principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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