Local excitation-lateral inhibition interaction yields oscillatory instabilities in nonlocally interacting systems involving finite propagation delay

The work studies wave activity in spatial systems, which exhibit nonlocal spatial interactions at the presence of a finite propagation speed. We find analytically propagation delay-induced oscillatory instabilities for various local excitatory and lateral inhibitory spatial interactions. Further, the work shows for general nonlocal interactions analytically that the first kernel Fourier moment defines the stability thresholds. The final numerical simulation confirms the analytical results.