Delay and Lévy noise influence on the behavior of a ring of FitzHugh—Nagumo neurons
Nikishina Nataliya1, Bukh Andrei 1; 1Saratov State University, Saratov, Russia
Abstract
The system of connected neurons serves as a prototype of the human brain. Such a system demonstrates various regimes depending on the time delay and the magnitude of the noise impact. At the same time, the dynamics of the system are also affected by the values of the parameters of the system itself. The delay in the system of connected neurons can form various regimes: the elements of the system can enter the synchronization mode, or they can switch to the traveling wave mode, etc.
Moreover, under the influence of noise, a transition between different states can occur. The influence of noise and time delay can have therapeutic effects on both brain diseases (Parkinson's disease) and heart diseases (cardiac arrhythmia), which indicates the relevance of this study.
To determine the nature of the influence of coupling delay parameters and Lévy noise on the dynamics of a network of coupled FitzHugh–Nagumo neurons, an ensemble is studied.
A ring of coupled FitzHugh-Nagumo neurons exhibits traveling wave modes that are robust for certain values of the delay parameter. However, some regimes of the system are susceptible to certain values of noise. The results provide insight into the effect of the delay parameter on the robustness of traveling wave regimes to Lévy noise.
This work was supported by the Russian Science Foundation (project No. 23-72-10040,
https://www.rscf.ru/project/23-72-10040/).
Speaker
Nikishina Nataliya
Saratov State University, Saratov, Russia
Russia
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