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abstract:
The talk motivates the study of additive noise by a numerical study of a neural field model involving nonlocal spatial interactions and finite transmission speeds. The system evolves close to a Hopf bifurcation and the numerical study reveals a shift of the stability of the system by additive noise. A subsequent analytical study of a simplified model close to a non-oscillatory based on stochastic delayed center manifolds introduces into the mathematical analysis and elucidates the mechanism of the stability shift. The final center manifold study close to a Hopf bifurcation closes the work. |
