Chaotic performance and circuitry implement of piecewise logistic-like mapping

Caiwen Chen; Tianxiu Lu; Ping Gao; Caiwen Chen; Tianxiu Lu; Ping Gao

doi:10.3934/era.2025006

Electronic Research Archive

2025, Volume 33, Issue 1: 102-120. doi: 10.3934/era.2025006

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Theory article

Chaotic performance and circuitry implement of piecewise logistic-like mapping

1.
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
2.
Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, Zigong 643000, China

Received: 10 November 2024 Revised: 18 December 2024 Accepted: 03 January 2025 Published: 14 January 2025

Discrete chaotic systems are now a meaningful research area due to their intricate dynamical characteristics. This paper introduces a novel piecewise logistic-like mapping chaotic system and rigorously establishes its Devaney chaoticity through mathematical proofs. Experimental findings demonstrate that, compared to the traditional logistic mapping, the logistic-like mapping exhibits more complex dynamic behaviors, such as bifurcation diagram, Lyapunov exponents, permutation entropy, sensitivity, and distribution of function sequences. Furthermore, in order to implement the suggested new chaotic system, a simulation circuit is designed, and a PSIM simulation model is established to validate feasibility of the simulation circuit.
- chaos,
- piecewise logistic-like mapping,
- Devaney chaos,
- circuit implementation
Citation: Caiwen Chen, Tianxiu Lu, Ping Gao. Chaotic performance and circuitry implement of piecewise logistic-like mapping[J]. Electronic Research Archive, 2025, 33(1): 102-120. doi: 10.3934/era.2025006

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Abstract

Discrete chaotic systems are now a meaningful research area due to their intricate dynamical characteristics. This paper introduces a novel piecewise logistic-like mapping chaotic system and rigorously establishes its Devaney chaoticity through mathematical proofs. Experimental findings demonstrate that, compared to the traditional logistic mapping, the logistic-like mapping exhibits more complex dynamic behaviors, such as bifurcation diagram, Lyapunov exponents, permutation entropy, sensitivity, and distribution of function sequences. Furthermore, in order to implement the suggested new chaotic system, a simulation circuit is designed, and a PSIM simulation model is established to validate feasibility of the simulation circuit.

References

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