Extreme multistability in a fractional-order thin magnetostrictive actuator (TMA)

Abstract

In this paper, we consider and investigate the dynamics of a fractional-order thin magnetostrictive actuato with quintic nonlinearity. The energy balance method is used to establish the motion equation of the system. Numerical solutions of the system are studied using the Caputo method and Adams Bashforth Moulton scheme. In order to analyze the dynamical behaviors of the proposed system, some mathematical tools including bifurcation diagrams, Lyapunov exponents, two-parameter bifurcation diagrams, time series plots and phase portraits are exploited. The bifurcation diagrams show that the system under consideration exhibits rich and intriguing behaviors including period-doubling route to chaos, complex phase space trajectory and extreme multistability. One of the most novelty of the proposed system is that its exhibits extreme multistability, which was not yet reported in the existing thin magnetostrictive actuators discussed in the literature to the author’s knowledge. The results carried out in this work may help us in better understanding of the thin magnetostrictive actuators.

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Correspondence to Kamdoum Tamba Victor.

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Sylvain, Z.N., Victor, K.T., Bruno, N.G. et al. Extreme multistability in a fractional-order thin magnetostrictive actuator (TMA). SeMA (2021). https://doi.org/10.1007/s40324-020-00238-7

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Keywords

  • Thin magnetostrictive actuator
  • Quintic nonlinearity
  • Fractional-order derivative
  • Mathematical modeling
  • Bifurcation analysis
  • Extreme multistability

Mathematics subject classification

  • 65P99
  • 70K75