Chimera and solitary states in the ring of nonlocally coupled FitzHugh-Nagumo neurons with Lévy noise
Elena V. Rybalova1, Galina I. Strelkova1.
1Saratov State University, Saratov, Russia
Abstract
Understanding the stochastic dynamics of neural systems is crucial for explaining complex brain behaviors and developing cognitive technologies. This study investigates the dynamics of a ring of non-locally coupled FitzHugh–Nagumo oscillators subjected to Lévy noise, characterized by heavy-tailed jumps that mimic real neural fluctuations. We demonstrate that this non-Gaussian noise can actively manipulate and enhance system order. Specifically, controlling the noise parameters allows for modulating the number of solitary states up to their complete suppression, while simultaneously increasing the probability of establishing chimera states. Furthermore, we examine the impact of noise parameter variations on the existence area of solitary states and the number of solitary nodes in the "coupling strength – noise intensity" parameter plane. We also analyze the distribution of the normalized number of solitary nodes and the space-averaged cross-correlation coefficient in the "stability index – skewness" parameter plane, and built the dependencies of the normalized number of solitary nodes on the coupling strength. This research emphasizes the dual role of noise in neural networks, where it can not only disrupt dynamics but also induce various spatiotemporal patterns. These findings offer promising insights into developing novel methods for suppressing pathological synchronization in biological neural networks.
Speaker
Nataliia N. Nikishina
Saratov State University
Russia
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