论文标题
噪声驱动的分叉在非线性fokker-Planck系统中描述随机神经场
Noise-driven bifurcations in a nonlinear Fokker-Planck system describing stochastic neural fields
论文作者
论文摘要
建立了从空间均匀的固定状态的噪声驱动的分叉的存在和表征，该状态的非线性非本地fokker- planck型部分偏微分方程描述了描述随机神经场的偏微分方程。所得理论扩展到模拟嘈杂网格单元的部分微分方程系统。结果表明，随着噪声水平的降低，出现了均匀稳态的多个分叉。此外，分叉点处的分支的形状在局部表征。该理论由导致分叉的条件，沿相应局部分叉分支的模式以及同质状态的稳定性和最普遍的模式的一组数字说明支持：六边形。
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential equation describing stochastic neural fields is established. The resulting theory is extended to a system of partial differential equations modelling noisy grid cells. It is shown that as the noise level decreases, multiple bifurcations from the homogeneous steady state occur. Furthermore, the shape of the branches at a bifurcation point is characterised locally. The theory is supported by a set of numerical illustrations of the condition leading to bifurcations, the patterns along the corresponding local bifurcation branches, and the stability of the homogeneous state and the most prevalent pattern: the hexagonal one.
