Hidden Dynamics of a New Jerk-like System with a Smooth Memristor and Applications in Image Encryption

Zuolei Wang, Lizhou Zhuang, Jianjiang Yu, Haibo Jiang, Wanjiang Xu and Xuerong Shi ()
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Zuolei Wang: School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China
Lizhou Zhuang: School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China
Jianjiang Yu: School of Information Engineering, Yancheng Teachers University, Yancheng 224002, China
Haibo Jiang: School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China
Wanjiang Xu: School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China
Xuerong Shi: School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China

Mathematics, 2023, vol. 11, issue 22, 1-18

Abstract: Considering the dynamic characteristics of memristors, a new Jerk-like system without an equilibrium point is addressed based on a Jerk-like system, and the hidden dynamics are investigated. When changing system parameter b and fixing other parameters, the proposed system shows various hidden attractors, such as a hidden chaotic attractor ( b = 5), a hidden period-1 attractor ( b = 3.2), and a hidden period-2 attractor ( b = 4). Furthermore, bifurcation analysis suggests that not only parameter b , but also the initial conditions of the system, have an effect on the hidden dynamics of the discussed system. The coexistence of various hidden attractors is explored and different coexistences of hidden attractors can be found for suitable system parameters. Offset boosting of different hidden attractors is discussed. It is observed that offset boosting can occur for hidden chaotic attractor, period-1 attractor, and period-2 attractor, but not for period-3 attractor and period-4 attractor. The antimonotonicity of the proposed system is debated and a full Feigenbaum remerging tree can be detected when system parameters a or b change within a certain range. On account of the complicated dynamics of the proposed system, an image encryption scheme is designed, and its encryption effectiveness is analyzed via simulation and comparison.

Keywords: 4D Jerk-like system; hidden attractor; coexisting attractors; antimonotonicity; image encryption (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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