Distributed nonlocal feedback delays may destabilize fronts in neural fields, distributed transmission delays do not

Dynamics of unidirectionally-coupled ring neural network with discrete and distributed delays

In this paper, we consider a ring neural network with one-way distributed-delay coupling between the neurons and a discrete delayed self-feedback. In the general case of the distribution kernels, we are able to find a subset of the amplitude death regions depending on even (odd) number of neurons in the network. Furthermore, in order to show the full region of the amplitude death, we use particular delay distributions, including Dirac delta function and gamma distribution. Stability conditions for the trivial steady state are found in parameter spaces consisting of the synaptic weight of the self-feedback and the coupling strength between the neurons, as well as the delayed self-feedback and the coupling strength between the neurons. It is shown that both Hopf and steady-state bifurcations may occur when the steady state loses stability. We also perform numerical simulations of the fully nonlinear system to confirm theoretical findings.

Aging transition in systems of oscillators with global distributed-delay coupling

We consider a globally coupled network of active (oscillatory) and inactive (nonoscillatory) oscillators with distributed-delay coupling. Conditions for aging transition, associated with suppression of oscillations, are derived for uniform and gamma delay distributions in terms of coupling parameters and the proportion of inactive oscillators. The results suggest that for the uniform distribution increasing the width of distribution for the same mean delay allows aging transition to happen for a smaller coupling strength and a smaller proportion of inactive elements. For gamma distribution with sufficiently large mean time delay, it may be possible to achieve aging transition for an arbitrary proportion of inactive oscillators, as long as the coupling strength lies in a certain range.