Vulnerability of Synchronization in Complex Networks due to the Existence of Chaotic Saddles

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The main objective of this proposal is to study the role of transient chaos in networked systems. The presence of chaotic saddles can lead to complete desynchronization of initially completely synchronized networks by perturbing one unit in the network at a particular time-instant (state-dependent vulnerability of synchronization). We will investigate the dynamical origin of the transition from the globally stable synchronized state to the completely desynchronized state, and clarify whether even a chaotic attractor instead of a saddle is established depending on the coupling strength of the units and the network topology. Furthermore, we will study the statistical properties of this super-persistent chaotic behavior e.g. the violation of the scaling laws for transient chaos and compare it with noise-induced attractors to find commonalities and differences. Moreover, we will identify different classes of systems in which state-dependent vulnerability occurs to prove its generality. Those classes are related with the mechanisms in which chaotic saddles appear: basin-boundary metamorphosis, boundary crisis and period-adding cascades. Finally, we will study different applications in ecology as well as in brain and heart dynamics in order to design control strategies either to keep the synchronized state stable or to break synchrony.