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Numerical investigation concerning the dynamics in parameter planes of the Ehrhard–Müller system

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  • da Silva, Angela
  • Rech, Paulo C.

Abstract

In this paper we investigate the nonlinear dynamics of the Ehrhard–Müller system, which is modeled by a set of three-parameter, three autonomous first-order nonlinear ordinary differential equations. More specifically, here we report on numerically computed parameter plane diagrams for this three-parameter system. The dynamical behavior of each point, in each parameter plane, was characterized by using Lyapunov exponents spectra, or independently by counting the number of local 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. In other words, each of these diagrams displays delimited regions of both behaviors, chaos and periodicity. We show that these parameter planes contain self-organized typical periodic structures embedded in a chaotic region. We also show that multistability is present in the Ehrhard–Müller system.

Suggested Citation

  • da Silva, Angela & Rech, Paulo C., 2018. "Numerical investigation concerning the dynamics in parameter planes of the Ehrhard–Müller system," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 152-157.
    • Handle: RePEc:eee:chsofr:v:110:y:2018:i:c:p:152-157
    DOI: 10.1016/j.chaos.2018.03.022
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    References listed on IDEAS

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    1. 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.
    2. Wiggers, Vinícius & Rech, Paulo C., 2017. "Multistability and organization of periodicity in a Van der Pol–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 632-637.
    3. 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.
    4. de Souza, S.L.T. & Batista, A.M. & Baptista, M.S. & Caldas, I.L. & Balthazar, J.M., 2017. "Characterization in bi-parameter space of a non-ideal oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 224-231.
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