Multiple attractors and generalized synchronization in delayed Mackey--Glass systems

Nonlinear dynamics of the time-delayed Mackey--Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincaré section. Synchronizations of the drive--response Mackey--Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found.