Dynamics of delayed neural field models in two-dimensional spatial domains

Delayed neural field models can be viewed as a dynamical system in an appropriate functional analytic setting. On two dimensional rectangular space domains, and for special class of connectivity delay functions, we describe the spectral properties linearized equation. We transform characteristic integral equation differential (DDE) into linear partial (PDE) with boundary conditions. demonstrate that finding eigenvalues eigenvectors DDE is equivalent obtaining nontrivial solutions this value problem (BVP). When kernel consists single exponential, construct basis BVP forms complete set L2. This gives characterization spectrum used to solution resolvent problem. As application give example Hopf bifurcation compute first Lyapunov coefficient.