Universal bifurcation property of two- or higher-dimensional dissipative systems in parameter space: Why does 1D symbolic dynamics work so well?

Details Universal bifurcation property of two- or higher-dimensional dissipative systems in parameter space: Why does 1D symbolic dynamics work so well? Universal bifurcation property of two- or higher-dimensional dissipative systems in parameter space: Why does 1D symbolic dynamics work so well?

1995-06-02

arxiv.org/abs/chao-dyn/9506001v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, figures can be obtained from the author, will appeared in J. Phys. A

Scientific paper

10.1088/0305-4470/28/14/011

The universal bifurcation property of the H\'enon map in parameter space is studied with symbolic dynamics. The universal-$L$ region is defined to characterize the bifurcation universality. It is found that the universal-$L$ region for relative small $L$ is not restricted to very small $b$ values. These results show that it is also a universal phenomenon that universal sequences with short period can be found in many nonlinear dissipative systems.

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