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A class of initials-dependent dynamical systems

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  • Ma, Jun
  • Wu, Fuqiang
  • Ren, Guodong
  • Tang, Jun

Abstract

Nonlinear term is critical for emergence of chaos in autonomous dynamical systems. The sampled time series in chaotic system are dependent on the initial selection of variables, while the attractors are invariant for fixed parameters. In this paper, the dynamical behavior of a class of dynamical system is investigated at fixed parameter region. It is found that the state selection is dependent on the initials and the potential mechanism is discussed. It is confirmed that the system can be switched between stable state, periodical state and even chaotic state by selecting appropriate initials even the parameters are fixed. We think that nonlinear cross terms with higher order could account for the emergence of this behavior. It indicates that initial selection and resetting can be also effective to control some chaotic systems, and these chaotic systems could enhance security for possible secure communication because the chaotic attractor depends on the parameter and initials selection as well. In the case of secure communication, the reconstruction of phase space becomes more difficult because the attractors are changed arbitrarily, thus the safety for secure keys is enhanced. For chaos control, when the initials are reset, the controller can be removed and the system can develop to step into the desired target by itself.

Suggested Citation

  • Ma, Jun & Wu, Fuqiang & Ren, Guodong & Tang, Jun, 2017. "A class of initials-dependent dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 65-76.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:65-76
    DOI: 10.1016/j.amc.2016.11.004
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    References listed on IDEAS

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    1. Bao, Haibo & Park, Ju H. & Cao, Jinde, 2015. "Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 543-556.
    2. Volos, Ch. K. & Kyprianidis, I.M. & Stouboulos, I.N. & Vaidyanathan, S. & Pham, V.-T., 2016. "Analysis, adaptive control and circuit simulation of a novel nonlinear finance systemAuthor-Name: Tacha, O.I," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 200-217.
    3. Mathiyalagan, K. & Park, Ju H. & Sakthivel, R., 2015. "Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 967-979.
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    Cited by:

    1. Gao, Chenghua & Qiao, Shuai & An, Xinlei, 2022. "Global multistability and mechanisms of a memristive autapse-based Filippov Hindmash-Rose neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Liu, Yong & Ren, Guodong & Zhou, Ping & Hayat, Tasawar & Ma, Jun, 2019. "Synchronization in networks of initially independent dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 370-380.
    3. Ma, Jun & Xu, Wenkang & Zhou, Ping & Zhang, Ge, 2019. "Synchronization between memristive and initial-dependent oscillators driven by noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    4. Zhang, Ge & Ma, Jun & Alsaedi, Ahmed & Ahmad, Bashir & Alzahrani, Faris, 2018. "Dynamical behavior and application in Josephson Junction coupled by memristor," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 290-299.
    5. Wu, Fuqiang & Zhou, Ping & Alsaedi, Ahmed & Hayat, Tasawar & Ma, Jun, 2018. "Synchronization dependence on initial setting of chaotic systems without equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 124-132.
    6. Han Bao & Tao Jiang & Kaibin Chu & Mo Chen & Quan Xu & Bocheng Bao, 2018. "Memristor-Based Canonical Chua’s Circuit: Extreme Multistability in Voltage-Current Domain and Its Controllability in Flux-Charge Domain," Complexity, Hindawi, vol. 2018, pages 1-13, March.
    7. Li Xiong & Zhenlai Liu & Xinguo Zhang, 2017. "Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System," Complexity, Hindawi, vol. 2017, pages 1-23, November.
    8. Ren, Guodong & Xue, Yuxiong & Li, Yuwei & Ma, Jun, 2019. "Field coupling benefits signal exchange between Colpitts systems," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 45-54.
    9. Wang, Chunni & Liu, Zhilong & Hobiny, Aatef & Xu, Wenkang & Ma, Jun, 2020. "Capturing and shunting energy in chaotic Chua circuit," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    10. Ping Zhou & Meihua Ke, 2017. "A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes," Complexity, Hindawi, vol. 2017, pages 1-7, November.

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