Volume 90, Number 3, May 2010
|Number of page(s)||6|
|Published online||25 May 2010|
Basin boundary metamorphoses and phase control
Departamento de Física, Universidad Rey Juan Carlos - Tulipán s/n, 28933 Madrid, Spain, EU
Accepted: 20 April 2010
Basin boundary metamorphoses are characteristic in some kinds of chaotic dynamical systems. They take place when one parameter of the system is varied and it passes through a certain critical value. In this paper we show that a parametric harmonic perturbation can produce basin boundary metamorphoses in periodically driven chaotic dynamical systems even when its amplitude is smaller than the amplitude of the main driving. The physical context of this work is related with the phenomenon of trajectories escaping from a potential well, which is illustrated by using as prototype model the Helmholtz oscillator. One of the main contributions of our research is to analyze the role of the phase difference between the parametric harmonic perturbation and the main driving in the appearance of a basin boundary metamorphosis. We also analyze the variation of the size of the basins and the fractal dimension of the corresponding boundaries when this phenomenon occurs. Finally, Melnikov analysis of this phenomenon is carried out. We expect that this work can be useful for a better understanding of basin boundary metamorphoses phenomena.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.45.Df – Fractals / 05.45.Pq – Numerical simulations of chaotic systems
© EPLA, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.