Transient Chaos, Hyperchaotic Dynamics, and Transport Properties in a Bailout Embedding Web Map

Abstract

In this work, we show that the bailout embedding method is responsible for creating different dynamical behaviors and for destroying intrinsic features present in mixed phase spaces of the area-preserving Hamiltonian maps, where the sticking to regular (or resonant) islands degrades chaotic properties. In particular, the base map chosen for the study is the two-dimensional (2D) Web Map (WM). The four-dimensional (4D) embedded Web Map dynamics is governed by four-parameters: ([Formula: see text]) in the WM control the nonlinearity and the type of symmetry structures (crystalline or quasi-crystalline) in phase space, respectively; ([Formula: see text]) in the embedding equations determine the mass density ratio and dissipation, respectively. For specific parameter combinations we explore the existence of transient chaos phenomenon, hyperchaotic dynamics and control the degradation of the underlying diffusive behaviors observed in phase space of the WM. If the WM is subjected to large enough dissipation through the embedding equations, stable periodic points (inside resonance islands) become sinks attracting almost all the surrounding orbits, destroying all invariant curves which divide the phase space into chaotic and regular domains. As area-preserving maps obtained from Hamiltonian flows usually share the crucial property that resonance islands can be found immersed in chaotic sea (characterizing the mixed phase space) for appropriated parameter combinations, the results obtained here for the 4D embedded WM should be considered generic for such whole class of nonlinear systems.