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Controlling complex networks: interplay of structure, noise and delay

Dr. Anna Zakharova:

 

We investigate both deterministic and stochastic dynamical systems with different types of coupling including time-delay. In particular, we study noise-induced phenomena such as stochastic bifurcations, coherence resonance, stochastic synchronization as well as a special type of oscillation suppression - oscillation death. The systems we consider in the present study are the paradigmatic models of nonlinear dynamics: generalized Van der Pol system and Stuart-Landau oscillator. We perform analytical calculations, numerical simulations and relate these to the experiments on an electronic circuit. In particular, we show both experimentally and numerically that stochastic oscillations that appear due to noise in a system with a subcritical Hopf bifurcation, can be partially synchronized even outside the oscillatory regime of the deterministic system. Moreover, for a model of coupled Stuart-Landau oscillators we show that symmetry-breaking oscillation death can occur in time-delayed systems.

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