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The infinite-scroll attractor and energy transition in chaotic circuit

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Abstract

Nonlinear oscillators composed of multi-scroll chaotic attractor show much more complicate and rich chaotic dynamics and are often used for generating complex secure keys and carrying wave for secure communication or image encryption. Indeed, controllers designed as piecewise-linear functions are used to induce multi-scroll attractors in nonlinear circuits by generating a group of equilibrium points. In this paper, we present a feasible but practical scheme which can generate infinite-scroll attractor by replacing the nonlinear terms in the improved Chua circuit with a sine function. It is found that the number of multi-scroll attractor increases with the calculating period increasing as infinite equilibrium points could be induced for the sine function. Interestingly, the Hamilton energy of the circuits composed of multi-scroll attractor, defined by the Helmholtz’ s theorem, is decreased with the number increasing of multi-scroll attractor. This result indicates that power consumption of circuit devices could be decreased when multi-scroll attractor is stabilized. Furthermore, a scheme is presented to stabilize the multi-scroll attractor by applying negative type of coupling on the chaotic system.

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Acknowledgments

This work was supported partially by the Natural Science Foundation of Zhejiang Province under Grants No. LY16A050001, the National Natural Science Foundation of China under Grants Nos. 11205103 and 11275129 (C. G. Yao), and the National Science Foundation for Post-doctoral Scientists of China under Grants No. 0660-K83003 (C. G. Yao). We thank the four anonymous referees very much for comments and suggestions.

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Authors and Affiliations

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China

    Fan Li

  2. Department of Mathematics, Shaoxing University, Shaoxing, China

    Chenggui Yao

  3. University of Chinese Academy of Sciences, Beijing, 100049, China

    Fan Li

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  1. Fan Li
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Correspondence to Chenggui Yao.

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Li, F., Yao, C. The infinite-scroll attractor and energy transition in chaotic circuit. Nonlinear Dyn 84, 2305–2315 (2016). https://doi.org/10.1007/s11071-016-2646-z

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