Stability threshold approach for complex dynamical systems

Acknowledgments This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, and supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS). The first author thanks Dr Roman Ovsyannikov for valuable discussions regarding estimation of the mistake probability.Peer reviewedPreprintPublisher PD

Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.Comment: To be published in CHAO

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We study the influence of the initial topology of connections on the organization of synchronous behavior in networks of phase oscillators with adaptive couplings. We found that networks with a random sparse structure of connections predominantly demonstrate the scenario as a result of which chimera states are formed. The formation of chimera states retains the features of the hierarchical organization observed in networks with global connections [D.V. Kasatkin, S. Yanchuk, E. Schöll, V.I. Nekorkin, Phys. Rev. E 96, 062211 (2017)], and also demonstrates a number of new properties due to the presence of a random structure of network topology. In this case, the formation of coherent groups takes a much longer time interval, and the sets of elements that form these groups can be significantly rearranged during the evolution of the network. We also found chimera states, in which along with the coherent and incoherent groups, there are subsets, whose different elements can be synchronized with each other for sufficiently long periods of time