The generalized time-delayed Henon map: bifurcations and dynamics

Bilal, Shakir ; Ramaswamy, Ramakrishna (2013) The generalized time-delayed Henon map: bifurcations and dynamics International Journal of Bifurcation and Chaos, 23 (03). Article ID 1350045, 7 pages. ISSN 0218-1274

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We analyze the bifurcations of a family of time-delayed Hénon maps of increasing dimension and determine the regions where the motion is attracted to different dynamical states. As a function of parameters that govern nonlinearity and dissipation, boundaries that confine asymptotic periodic motion are determined analytically, and we examine their dependence on the dimension d. For large d these boundaries converge. In low dimensions both the period-doubling and quasiperiodic routes to chaos coexist in the parameter space, but for high dimensions the latter predominates and prior to the onset of chaos, the systems exhibit multistability. When the nonlinearity parameter is varied, the dimension of chaotic attractors in the systems changes smoothly with increasing number of non-negative Lyapunov exponents.

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing Co Pte Ltd.
Keywords:High Dimension; Diffeomorphism; Dissipative Map; Normal Form Coefficient; Limiting Curves; Hyperchaos
ID Code:98808
Deposited On:14 May 2015 06:56
Last Modified:14 May 2015 06:56

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