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The occurrence of locally riddled basins and on-off intermittency in a parametric nonlinear system

Author

Listed:
  • Oshagh, M.
  • Ghane, F.H.
  • Zaj, M.

Abstract

In this paper, a one parameter family (Fβ)β∈(0,1) of maps of the unit square I×I is studied. We observe that, for some values of parameter, our model exhibits one chaotic attractor Aβ,0, lying in the invariant subspace I×{0}, with a locally riddled basin of attraction. Rigorous analysis for the occurrence of locally riddled basin is given. Using the monotonicity and concavity of the fiber maps in our model, we give a classification, with respect to the number of attracting invariant graphs. We examine the bifurcation effects that appear in our model on varying parameter; in particular, a nonregular temporal bursting and the appearance of an on-off intermittency is investigated. Finally, we show that the model undergoes a nonhysteretic blowout bifurcation.

Suggested Citation

  • Oshagh, M. & Ghane, F.H. & Zaj, M., 2021. "The occurrence of locally riddled basins and on-off intermittency in a parametric nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921009267
    DOI: 10.1016/j.chaos.2021.111572
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