Chaos criteria and chaotification schemes on a class of first-order partial difference equations

Zongcheng Li; Jin Li; Zongcheng Li; Jin Li

doi:10.3934/mbe.2023161

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 3425-3454. doi: 10.3934/mbe.2023161

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Chaos criteria and chaotification schemes on a class of first-order partial difference equations

Zongcheng Li ^,,
Jin Li

School of Science, Shandong Jianzhu University, Jinan 250101, China

Received: 19 September 2022 Revised: 07 November 2022 Accepted: 28 November 2022 Published: 06 December 2022

This article is involved in chaos criteria and chaotification schemes on one kind of first-order partial difference equations having non-periodic boundary conditions. Firstly, four chaos criteria are achieved by constructing heteroclinic cycles connecting repellers or snap-back repellers. Secondly, three chaotification schemes are obtained by using these two kinds of repellers. For illustrating the usefulness of these theoretical results, four simulation examples are presented.
- first-order partial difference equation,
- heteroclinic cycle connecting repellers,
- snap-back repeller,
- chaotification,
- chaos
Citation: Zongcheng Li, Jin Li. Chaos criteria and chaotification schemes on a class of first-order partial difference equations[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3425-3454. doi: 10.3934/mbe.2023161

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Abstract

This article is involved in chaos criteria and chaotification schemes on one kind of first-order partial difference equations having non-periodic boundary conditions. Firstly, four chaos criteria are achieved by constructing heteroclinic cycles connecting repellers or snap-back repellers. Secondly, three chaotification schemes are obtained by using these two kinds of repellers. For illustrating the usefulness of these theoretical results, four simulation examples are presented.

References

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