Destruction of quasiperiodic oscillations and appearance of attractors
with complex structure
T. Vadivasova, O. Sosnovtseva, A. Tsarev
Laboratory of Nonlinear Dynamics, Saratov State University, Saratov,
Russia
Except of the well-known strange attractor (SCA), such nonregular attractors as strange nonchatic attractor (SNA) and nonstrange chaotic attractor (NCA) or ergodic chaos can be observed in nonlinear systems.
SNA is characterized by a fractal structure while an exponentional divergence of trajectories on it is absent. There are two mechanisms of SNA appearance: 1) torus crisis (torus band merging or merging of two tori coexisting in phase space), 2) gradual fractalization. We have shown that SNA can be observed not only in the systems with quasiperiodic forcing but in autonomous systems as well as in systems with harmonic excitation. Thus, appearance of SNA is related with destruction of quasiperiodic oscillations (both two-dimensional and three-dimensional tori). We investigate this process in the system of two coupled ring map and in the system of differential equations describing the dynamics of auto-oscillator with harmonic forcing.
NCA is characterized by the integer dimension while there exists the exponentional divergence of the trajectories. In this case phase trajectories cover tightly (though with different dencity) a manifold in phase space and motion remains ergodic. NCA is observed on three-dimensional torus and, obviously, precedes its destruction.