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Resonant oscillations and fractal basin boundaries of a particle in a φ6 potential

Author

Listed:
  • Tchoukuegno, R.
  • Nana Nbendjo, B.R.
  • Woafo, P.

Abstract

This paper considers the dynamics of a periodically forced particle in a φ6 potential. Harmonic, subharmonic and superharmonic oscillatory states are obtained using the multiple time scales method. From the Melnikov theory, we derive the analytical criteria for the occurrence of transverse intersections on the surface of homoclinic and heteroclinic orbits both for the three potential well case and a single potential well case. Our analytical investigations are complemented by the numerical simulations from which we show the fractality of the basins of attraction.

Suggested Citation

  • Tchoukuegno, R. & Nana Nbendjo, B.R. & Woafo, P., 2002. "Resonant oscillations and fractal basin boundaries of a particle in a φ6 potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 304(3), pages 362-378.
    • Handle: RePEc:eee:phsmap:v:304:y:2002:i:3:p:362-378
    DOI: 10.1016/S0378-4371(01)00500-3
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    Cited by:

    1. Feng, Jingjing & Zhang, Qichang & Wang, Wei, 2012. "Chaos of several typical asymmetric systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 950-958.
    2. Gao, Mingyuan & Wang, Yuan & Wang, Yifeng & Yao, Ye & Wang, Ping & Sun, Yuhua & Xiao, Jieling, 2020. "Modeling and experimental verification of a fractional damping quad-stable energy harvesting system for use in wireless sensor networks," Energy, Elsevier, vol. 190(C).

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