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Cyclic organization of stable periodic and chaotic pulsations in Hartley’s oscillator

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  • Freire, Joana G.
  • Gallas, Jason A.C.

Abstract

A recent conjecture in this Journal, concerning the existence of spiral stability phases in Hartley’s oscillator, is corroborated amply. We report numerically computed stability phase diagrams indicating precisely where spirals of periodicity and chaos may be found in several control planes of the system. In addition, we describe some remarkable parameter loops in control space which allow one to trace identical dynamical behaviors by tuning totally independent parameters.

Suggested Citation

  • Freire, Joana G. & Gallas, Jason A.C., 2014. "Cyclic organization of stable periodic and chaotic pulsations in Hartley’s oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 129-134.
    • Handle: RePEc:eee:chsofr:v:59:y:2014:i:c:p:129-134
    DOI: 10.1016/j.chaos.2013.12.007
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    Cited by:

    1. N. C. Pati, 2023. "Bifurcations and multistability in a physically extended Lorenz system for rotating convection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-15, August.
    2. Ahmad Taher Azar & Ngo Mouelas Adele & Kammogne Soup Tewa Alain & Romanic Kengne & Fotsin Hilaire Bertrand, 2018. "Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators," Complexity, Hindawi, vol. 2018, pages 1-12, January.
    3. da Silva, Rodrigo A. & Rech, Paulo C., 2015. "Spiral periodic structures in a parameter plane of an ecological model," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 9-13.
    4. Xu, Lu & Chu, Yan-Dong & Yang, Qiong, 2020. "Novel dynamical Scenario of the two-stage Colpitts oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Zhang, Yunzhen & Liu, Zhong & Wu, Huagan & Chen, Shengyao & Bao, Bocheng, 2019. "Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 354-363.
    6. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.
    7. Fu, Min & Xia, Jun & Fan, Xinghua & Tian, Lixin & Wang, Minggang, 2015. "New non-equilibrium cobweb dynamical evolution model and its application," Economic Modelling, Elsevier, vol. 51(C), pages 544-550.

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