The occurrence of riddled basins and blowout bifurcations in a parametric nonlinear system
| Autor: | Rabiee, M., Ghane, F. H., Zaj, M., Karimi, S. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.physd.2022.133291 |
| Popis: | In this paper, a two parameters family $F_{\beta_1,\beta_2}$ of maps of the plane living two different subspaces invariant is studied. We observe that, our model exhibits two chaotic attractors $A_i$, $i=0,1$, lying in these invariant subspaces and identify the parameters at which $A_i$ has a locally riddled basin of attraction or becomes a chaotic saddle. Then, the occurrence of riddled basin in the global sense is investigated in an open region of $\beta_1\beta_2$-plane. We semi-conjugate our system to a random walk model and define a fractal boundary which separates the basins of attraction of the two chaotic attractors, then we describe riddled basin in detail. We show that the model undergos a sequence of bifurcations: "a blowout bifurcation", "a bifurcation to normal repulsion" and "a bifurcation by creating a new chaotic attractor with an intermingled basin". Numerical simulations are presented graphically to confirm the validity of our results. Comment: 26 pages, 15 figures |
| Databáze: | arXiv |
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