Analysis and anti-control of period-doubling bifurcation for the one-dimensional discrete system with three parameters and a square term
In certain nonlinear systems, period-doubling bifurcations are a common way to cause chaos. Additionally, bifurcation advance or delay can be realized using anti-control of period-doubling bifurcation. To address the practical needs of engineering, anti-control of period-doubling bifurcation is a ty...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025150 |
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| Summary: | In certain nonlinear systems, period-doubling bifurcations are a common way to cause chaos. Additionally, bifurcation advance or delay can be realized using anti-control of period-doubling bifurcation. To address the practical needs of engineering, anti-control of period-doubling bifurcation is a typical method of applying chaos. Based on these reasons, we conducted the following research: First, we proposed a new one-dimensional discrete system with three parameters and a square term. Existence and stability at the fixed point were studied for the one-dimensional discrete system with three parameters and a square term. Furthermore, bifurcation theory was used to determine the conditions of existence for transcritical bifurcation and period-doubling bifurcation. Numerical experiments verified the theoretical assessments of the bifurcation's results. Then, the state linear feedback control approach was used to implement the anti-control of period-doubling bifurcation in order to realize period-doubling bifurcation advance for the one-dimensional discrete system with three parameters and a square term. The conditions of the appropriate control parameters were analyzed in theory. Numerical experiments confirmed the efficiency and robustness of anti-control of period-doubling bifurcation for the one-dimensional discrete system with three parameters and a square term. The one-dimensional discrete system with three parameters and a square term with the anti-controller has advantages in image encryption. |
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| ISSN: | 2473-6988 |