Journal
JOURNAL OF PHYSICS-COMPLEXITY
Volume 2, Issue 3, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/2632-072X/abedc2
Keywords
chaotic saddle; synchronization; networks
Categories
Funding
- FAPESP [2018/03211-6, 2013/26598-0, 2015/50122-0, 2017/05521-0]
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [163436311-SFB 910]
- Hungarian Academy of Sciences
- CNPq [401264/2017-3]
- DFG through itsMajor Research Instrumentation Program [INST 184/157-1 FUGG]
- Ministry of Science and Culture (MWK) of the Lower Saxony State, Germany
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A chaotic saddle is a common nonattracting chaotic set that generates finite-time chaotic behavior in low and high-dimensional systems. When coupled into networks, the chaotic saddle traps network trajectories indefinitely, creating an alternative persistent desynchronized state that threatens the synchronized state.
A chaotic saddle is a common nonattracting chaotic set well known for generating finite-time chaotic behavior in low and high-dimensional systems. In general, dynamical systems possessing chaotic saddles in their state-space exhibit irregular behavior with duration lengths following an exponential distribution. However, when these systems are coupled into networks the chaotic saddle plays a role in the long-term dynamics by trapping network trajectories for times that are indefinitely long. This process transforms the network's high-dimensional state-space by creating an alternative persistent desynchronized state coexisting with the completely synchronized one. Such coexistence threatens the synchronized state with vulnerability to external perturbations. We demonstrate the onset of this phenomenon in complex networks of discrete-time units in which the synchronization manifold is perturbed either in the initial instant of time or in arbitrary states of its asymptotic dynamics. The role of topological asymmetries of Erdos-Renyi and Barabasi-Albert graphs are investigated. Besides, the required coupling strength for the occurrence of trapping in the chaotic saddle is unveiled.
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