Absolute stability and synchronization in neural field models with transmission delays

• Absolute stability and synchronization for delay neural field models are established.
• Global dynamics are concluded by an iterative argument termed sequential contracting.
• Transparent condition for global asymptotic stability of steady states is derived.

Neural fields model macroscopic parts of the cortex which involve several populations of neurons. We consider a class of neural field models which are represented by integro-differential equations with transmission time delays which are space-dependent. The considered domains underlying the systems can be bounded or unbounded. A new approach, called sequential contracting, instead of the conventional Lyapunov functional technique, is employed to investigate the global dynamics of such systems. Sufficient conditions for the absolute stability and synchronization of the systems are established. Several numerical examples are presented to demonstrate the theoretical results.