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arXiv · 2411.03311

Extreme events at the onset of epileptic-like intermittent activity of FitzHugh-Nagumo oscillators on small-world networks

Javier Cubillos-Cornejo·Miguel Escobar Mendoza·Ignacio Bordeu
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Abstract

In this work, we explore the influence of coupling strength, network size, and randomness on the collective dynamics of FitzHugh-Nagumo oscillators on complex networks. Using Watts-Strogatz small-world network connectivities, we identify four distinct dynamical phases: chaotic, intermittent, partially synchronized, and fully synchronized. The intermittent phase is characterized by the coexistence of chaotic behavior and chimera states, reminiscent of epileptic-seizure-related (ESR) intermittency observed in the brain. We analyze the inter-spike intervals of the individual oscillators, and the existence, duration, and frequency of ESR events as a function of the system parameters. Furthermore, we study the transitions into and out of the intermittent phase and show that peaks in the probability of extreme events--short transients of anomalously high synchronization--precede the transitions from chaos to intermittency and from partial to full synchronization. These transitions are followed by significant changes in the maximum Lyapunov exponent and Kaplan-Yorke dimension. Finally, we discuss how the coupling strength and network properties can be leveraged to control the system's state and the potential applications of extreme event analysis in the study of neural data.

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Javier Cubillos-Cornejo, Miguel Escobar Mendoza, Ignacio Bordeu. 2025-03-17. Extreme events at the onset of epileptic-like intermittent activity of FitzHugh-Nagumo oscillators on small-world networks. https://doi.org/10.1016/j.chaos.2025.116000

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