TY - GEN A1 - Atay, Fatihcan M. A1 - Hutt, Axel T1 - Stability and Bifurcations in Neural Fields with Axonal Delay and General Connectivity N2 - A stability analysis is presented for neural field equations in the presence of axonal delays and for a general class of connectivity kernels and synap- tic properties. Sufficient conditions are given for the stability of equilibrium solutions. It is shown that the delays play a crucial role in non-stationary bifurcations of equilibria, whereas the stationary bifurcations depend only on the kernel. Bounds are determined for the frequencies of bifurcating periodic solutions. A perturbative scheme is used to calculate the types of bifurca- tions leading to spatial patterns, oscillatory solutions, and traveling waves. For high transmission speeds a simple method is derived that allows the de- termination of the bifurcation type by visual inspection of the Fourier trans- forms of the connectivity kernel and its first moment. Results are numerically illustrated on a class of neurologically plausible second order systems with combinations of Gaussian excitatory and inhibitory connections. Y1 - 2004 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/41 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-415 ER -