2023/07/13 by Éva Kaslik, Kaslik, Eva, Emanuel-Attila Kökövics +3
Computer Science · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2307.06628
openalex publication_date 2023/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Building upon our previous work on the Wilson-Cowan equations with distributed delays, we study the dynamic behavior in a system of two coupled Wilson-Cowan pairs. We focus in particular on understanding the mechanisms that govern the transitions in and out of oscillatory regimes associated with pathological behavior. We investigate these mechanisms under multiple coupling scenarios, and we compare the effects of using discrete delays versus a weak Gamma delay distribution. We found that, in order to trigger and stop oscillations, each kernel emphasizes different critical combinations of coupling weights and time delay, with the weak Gamma kernel restricting oscillations to a tighter locus of coupling strengths, and to a limited range of time delays. We finally illustrate the general analytical results with simulations for two particular applications: generation of beta-rhytms in the basal ganglia, and alpha oscillations in the prefrontal-limbic system.