Physica D: Nonlinear Phenomena, Volume (435), No (1), Year (2022-7) , Pages (133291-133304)

Title : ( The occurrence of riddled basins and blowout bifurcations in a parametric nonlinear system )

Authors: Maryam Rabiee Farahani , Fateme Helen Ghane Ostadghassemi , marzie zaj , Sohrab Karimi ,

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Abstract

In this paper, a two parameters family Fβ1,β2 of maps of the plane having two different invariant subspaces is studied. We observe that, our model exhibits two chaotic attractors Ai, i = 0, 1, lying in these invariant subspaces and identify the parameters at which Ai 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 β1β2-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 undergoes a sequence of bifurcations: ‘‘a blowout bifurcation’’, ‘‘a bifurcation to normal repulsion\\\\\\\" and ‘‘a bifurcation to emergence a new chaotic attractor with an intermingled basin’’. Numerical simulations are presented graphically to confirm the validity of our results.

Keywords

, Milnor attractor with riddled basin of attraction, Blowout bifurcation, Random walk model, Intermingled basin
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@article{paperid:1089941,
author = {Rabiee Farahani, Maryam and Ghane Ostadghassemi, Fateme Helen and Zaj, Marzie and Karimi, Sohrab},
title = {The occurrence of riddled basins and blowout bifurcations in a parametric nonlinear system},
journal = {Physica D: Nonlinear Phenomena},
year = {2022},
volume = {435},
number = {1},
month = {July},
issn = {0167-2789},
pages = {133291--133304},
numpages = {13},
keywords = {Milnor attractor with riddled basin of attraction; Blowout bifurcation; Random walk model; Intermingled basin},
}

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%0 Journal Article
%T The occurrence of riddled basins and blowout bifurcations in a parametric nonlinear system
%A Rabiee Farahani, Maryam
%A Ghane Ostadghassemi, Fateme Helen
%A Zaj, Marzie
%A Karimi, Sohrab
%J Physica D: Nonlinear Phenomena
%@ 0167-2789
%D 2022

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