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 JAMP  Vol.5 No.9 , September 2017
Bifurcation of Parameter-Space and Chaos in Mira 2 Map
Abstract:
In this paper, we investigate Mira 2 map in parameter-space (A-B) and obtain some interesting dynamical behaviors. According to the parameter space of Mira 2 map, we take A and B as some groups of values and display complex dynamical behaviors, including period-1, 2, 3, 4, 5, ???, 38, ??? orbits, Arnold tongues observed in the circle map [7], crisis, some chaotic attractors, period-doubling bifurcation to chaos, quasi-period behaviors to chaos, chaos to quasi-period behaviors, bubble and onset of chaos.
Cite this paper: Jiang, T. and Yang, Z. (2017) Bifurcation of Parameter-Space and Chaos in Mira 2 Map. Journal of Applied Mathematics and Physics, 5, 1899-1907. doi: 10.4236/jamp.2017.59160.
References

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[3]   Jiang, T. and Yang, Z.Y. (2017) Bifurcations and Chaos in Mira 2 Map. Acta Mathematicae Applicatae Sinica, English Series (Accepted).

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[5]   Cartwright, J.H.E. (1999) Nonlinear Stiffness, Lyapunov Exponents, and Attractor Dimension. Physics Letters A, 26, 298-302. https://doi.org/10.1016/S0375-9601(99)00793-8

[6]   Agiza, H.N., Elabbssy, E.M., El-Metwally, H. and Elsadany, A.A. (2009) Chaotic Dynamics of a Discrete Prey-Predator Model with Holling Type II. Nonlinear Analyse: Real World Application, 10, 116-129. https://doi.org/10.1016/j.nonrwa.2007.08.029

[7]   Schuster, H.G. and Just, W. (2005) Deterministic Chaos: An Introduction. 4th Edition, Wiley-VCH Verlag GmbH & Co., Weinheim. https://doi.org/10.1002/3527604804

 
 
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