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Coupling multistable systems: uncertainly due to the initial positions on the attractors.
(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2014) Kuźma, Patrycja; Kapitaniak, Marcin; Kapitaniak, Tomasz
We consider the coupling of multistable nonidentical systems. For small values of the coupling coefficient the behavior of the coupled system strongly depends on the actual position of trajectories on their attractors in the moment when the coupling is introduced. After reaching the coupling threshold value, this dependence disappears. We give an evidence that this behavior is robust as it exists for a wide range of parameters and different types of coupling. We argue why this behavior cannot be considered as a dependence on the initial conditions.
Coupling multistable systems: uncertainty due to the initial positions on the attractors
(2014) Kuźma, Patrycja; Kapitaniak, Marcin; Kapitaniak, Tomasz
We consider the coupling of multistable nonidentical systems. For small values of the coupling coefficient the behavior of the coupled system strongly depends on the actual position of trajectories on their attractors in the moment when the coupling is introduced. After reaching the coupling threshold value, this dependence disappears. We give an evidence that this behavior is robust as it exists for a wide range of parameters and different types of coupling. We argue why this behavior cannot be considered as a dependence on the initial conditions.
Lag Synchronization in Coupled Multistable van der Pol-Duffing Oscillators
(2014) Dudkowski, Dawid; Kuźma, Patrycja; Kapitaniak, Tomasz
We consider the system of externally excited identical van der Pol-Duffing oscillators unidirectionally coupled in a ring. When the coupling is introduced, each of the oscillator’s trajectories is on different attractor. We study the changes in the dynamics due to the increase in the coupling coefficient. Studying the phase of the oscillators, we calculate the parameter value for which we obtain the antiphase lag synchronization of the system and also the bifurcation values for which we observe qualitative changes in the dynamics of already synchronized system. We give evidence that lag synchronization is typical for coupled multistable systems.