Coexisting chaotic attractors, their basin of attractions and synchronization of chaos in two coupled Duffing oscillators

摘要

Two coupled Duffing oscillators equations with several coexisting chaotic attractors are considered. Six coexisting chaotic attractors are observed for the range of initial conditions considered in our study. For two attractors the basin of attraction is a simple disconnected straight line, while for the rest of the attractors it appears to be very complex. Phase portraits of (two) subsystems are found to be distinct for two attractors while identical for the other four attractors. Among these four attractors, state variables of the subsystems are perfectly synchronized for two attractors and asynchronized for the other two attractors. Synchronization of subsystems is studied by employing a continuous feedback method.