Exploring Synchronization Mechanisms via Bifurcation Analysis - A Unified Approach Across Neuronal, Ecological and Physical Realms
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| Year of publication | 2023 |
| Type | Appeared in Conference without Proceedings |
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| Description | Synchronization mechanisms are crucial to many dynamical systems, from networks of neurons to physical dynamical systems like superconductive junctions. We introduce a unified method focusing on bifurcation theory tools like Arnold tongues and cycle manifolds on tori using the continuation program MatCont.This approach can elucidate synchronization scenarios in various dynamical systems. We highlight bistability in the synchronization patterns of coupled neurons, which might be linked to very high-frequency EEG signals near epileptic foci. Although this connection remains unconfirmed, it offers insights into pathological brain activity. Furthermore, we demonstrate our method's efficacy in analyzing Shapiro steps in superconductive junctions and seasonal synchronization in population models. This underscores its broad applicability, encouraging further use and adaptation of this approach in understanding synchronization across diverse systems. |
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