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Complex dynamics of a three-dimensional continuous-time autonomous system

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  • Prants, Fabiola G.
  • Rech, Paulo C.

Abstract

Results in a recent paper, concerning a novel three-dimensional chaotic system consisting of a particular set of three autonomous first-order nonlinear ordinary differential equations, are quite extended. We report on numerically computed parameter plane plots for a six-parameter system. The dynamical behavior of each point is characterized by using Lyapunov exponents, or by counting the number of maxima of one of the variables, in one complete trajectory in the phase-space. Each of these diagrams indicates parameter values for which chaos or periodicity may be found, i.e., each one of them shows delimited regions of both chaos and periodicity. Moreover, we show that several of these parameter planes display self-organized periodic structures, embedded in a chaotic region.

Suggested Citation

  • Prants, Fabiola G. & Rech, Paulo C., 2017. "Complex dynamics of a three-dimensional continuous-time autonomous system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 132-139.
    • Handle: RePEc:eee:matcom:v:136:y:2017:i:c:p:132-139
    DOI: 10.1016/j.matcom.2017.01.001
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    References listed on IDEAS

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    1. Soriano-Sánchez, A.G. & Posadas-Castillo, C. & Platas-Garza, M.A. & Diaz-Romero, D.A., 2015. "Performance improvement of chaotic encryption via energy and frequency location criteria," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 112(C), pages 14-27.
    2. Fabiola Prants & Paulo Rech, 2014. "Organization of periodic structures in a damped-forced oscillator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(9), pages 1-4, September.
    3. Huang, Li-Lian & Zhang, Juan & Shi, Shuai-Shuai, 2015. "Circuit simulation on control and synchronization of fractional order switching chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 113(C), pages 28-39.
    4. Singh, Anuraj & Gakkhar, Sunita, 2015. "Controlling chaos in a food chain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 115(C), pages 24-36.
    5. Kundu, Amitava & Das, Pritha & Roy, A.B., 2016. "Stability, bifurcations and synchronization in a delayed neural network model of n-identical neurons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 12-33.
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