Chaotic motion at the emergence of the time averaged energy decay

Details Chaotic motion at the emergence of the time averaged energy decay Chaotic motion at the emergence of the time averaged energy decay

2009-05-29

arxiv.org/abs/0905.4940v1

Physica D 238, 1688 (2009).

Nonlinear Sciences

Chaotic Dynamics

18 pages and 10 figures

Scientific paper

10.1016/j.physd.2009.05.004

A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the $N$ environment oscillators and becomes chaotic in the interval $13\le N\le15$, where the system time averaged energy starts to decay. To characterize the nonlinear motion we estimate the Lyapunov exponent (LE), determine the power spectrum and the Kaplan-Yorke dimension. For much larger values of $N$ the energy of the system particle is completely transferred to the environment and the corresponding LEs decrease. Numerical evidences show the connection between the variations of the {\it amplitude} of the particles energy time oscillation with the time averaged energy decay and trapped trajectories.

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