We analyze a large system of heterogeneous quadratic integrate-and-fire (QIF) neurons with
time delayed, all-to-all synaptic coupling. The model is exactly reduced to a system of firing …

In this paper, a class of simplified bidirectional associative memory (BAM) neural networks
with multiple delays are considered. By analyzing the associated characteristic …

The Nunez model for the generation of electroencephalogram (EEG) signals is naturally
described as a neural field model on a sphere with space-dependent delays. For simplicity …

The traditional geometric singular perturbation theory and the slow–fast analysis method
cannot be directly used to explore the mechanism of the relaxation oscillations in the forced …

We investigate the modes of oscillation of heterogeneous ring networks of quadratic
integrate-and-fire (QIF) neurons with nonlocal, space-dependent coupling. Perturbations of …

The paper deals with the stability and bifurcation analysis of a class of simplified five-neuron
bidirectional associative memory neural networks with four delays. By discussing the …

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of
neural activity. The mechanisms underlying the generation of such patterns are largely …

A neural field models the large scale behaviour of large groups of neurons. We extend
previous results for these models by including a diffusion term into the neural field, which …

In this paper, we perform the parameter-dependent center manifold reduction near the
generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf, and transcritical-Hopf bifurcations in delay …

We consider a ring of phase oscillators interacting with distance-dependent time delays in
general forms. It is found that the distance-dependent interaction delay is an essential …