Dynamics in a ring of delayed coupled oscillators

Przemyslaw Perlikowski

Humboldt Universität zu Berlin, Institut für Mathematik, Berlin, Germany

The investigation consider the ring of unidirectionally delayed coupled Stuart-Landau oscillators . We show the analytical analyze of steady state stability, presenting its property with respect to delay in coupling and number of oscillators. We applied the idea of Pseudocontinuous spectrum and Asymptotic Continuous Spectrum showing how one is changing into another. When oscillators undergo Hopf bifurcations the multiple periodic solutions appears. We find coexisting stable periodic solutions, i.e., Eckhaus scenario showing the influence of delay in coupling and number of oscillators on the stable area.

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