Bifurcations and chaos in Mira 2 map. (English) Zbl 1383.37038
Summary: In this paper, Mira 2 map is investigated. The conditions of the existence for fold bifurcation, flip bifurcation and Naimark-Sacker bifurcation are derived by using center manifold theorem and bifurcation theory. And the conditions of the existence for chaos in the sense of Marroto are obtained. Numerical simulation results not only show the consistence with the theoretical analysis but also display complex dynamical behaviors, including period-n orbits, crisis, some chaotic attractors, period-doubling bifurcation to chaos, quasi-period behaviors to chaos, chaos to quasi-period behaviors, bubble and onset of chaos.
MSC:
| 37H20 | Bifurcation theory for random and stochastic dynamical systems |
| 39A28 | Bifurcation theory for difference equations |
| 39A33 | Chaotic behavior of solutions of difference equations |
| 37G10 | Bifurcations of singular points in dynamical systems |
| 37M20 | Computational methods for bifurcation problems in dynamical systems |
Software:
DynamicsReferences:
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