PERIODIC FLOWS IN SWITCHING DYNAMICAL SYSTEMS THROUGH DISCRETE IMPLICIT MAPPINGS

Han Xu; Xilin Fu

doi:10.11948/20240545

2026 Volume 16 Issue 1

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Han Xu, Xilin Fu. PERIODIC FLOWS IN SWITCHING DYNAMICAL SYSTEMS THROUGH DISCRETE IMPLICIT MAPPINGS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 229-245. doi: 10.11948/20240545

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Han Xu, Xilin Fu. PERIODIC FLOWS IN SWITCHING DYNAMICAL SYSTEMS THROUGH DISCRETE IMPLICIT MAPPINGS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 229-245. doi: 10.11948/20240545

PERIODIC FLOWS IN SWITCHING DYNAMICAL SYSTEMS THROUGH DISCRETE IMPLICIT MAPPINGS

Han Xu^1,2,,
Xilin Fu^1, ,

1.
School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China
2.
School of Mathematics and Statistics, Linyi University, Linyi 276005, China

Author Bio: Email: xuhan1979@126.com(H. Xu)
Corresponding author: Email: xilinfu@hotmail.com(X. Fu)
Fund Project: The authors were supported by the National Natural Science Foundation of China (11971275)

Abstract

Abstract

In this paper, we investigate the periodic flow in a switching dynamical system through an implicit mapping method. By the given accuracy and the transport law, discrete implicit mappings at switching points are obtained and the corresponding interpolation points are achieved. Discrete implicit mappings at non-switching points are obtained by the discretization of differential equations of the switching system and the corresponding interpolation points are also determined. Then the periodic flow expressed by interpolation points in one period is determined. A two-order impulsive system with a pulse at a fixed time is presented as an example. The implicit mapping method may provide a plan for the periodic flows in discontinuous dynamical systems.
- Switching systems /
- implicit mappings /
- mapping structures /
- periodic flows
MSC: 93C30, 37C27

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References

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