Efeitos causados pela modulação de parâmetros no mapa de hénon / Effects caused by the parameters modulation in the hénon map

AUTOR(ES)
DATA DE PUBLICAÇÃO

2011

RESUMO

The Hénon map is a paradigmatic two-dimensional discrete-time dynamical system, which was originally proposed as a model to the Poincaré section of the continuous-time Lorenz system, and has been extensively investigated in the last years. Apart from its theoretical importance, some practical applications are possible. As an example, it can be used to model CO2 lasers in the limit of strong dissipation. The Hénon map is characterized by two parameters, namely the nonlinearity and the dissipativity. In this work we consider a situation where these two parameters of one Hénon map are linearly modulated by the solution of another Hénon map whose parameters are constants in time, but which can be adjusted. We investigate periodic and chaotic modulations of the first Hénon map, due to the second, and show that method is able to destroy or create attractors in the phase-space. More specifically, the modulation is able to control the multistability (bistability in the considered case) present in the Hénon map, leading the system to monostability. Finally, we investigate the dynamics of the Hénon map when its parameters are modulated by another Hénon map in a regime close to the conservative limit and in a regime close to the dissipative limit. Lyapunov exponents, bifurcation diagrams, basins of attraction, parameter space and phase-space diagrams are used to characterize the dynamics of the modulated system.

ASSUNTO(S)

modulação de parâmetros fisica hénon map parameters modulation multistability mapa de hénon multiestabilidade

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