Abstract
We consider a class of neural field models represented by a second-order nonlinear system of integro-differential equations with space-dependent delays. Such a system models interaction of populations of neurons, each with a continuum description. We justify the existence and uniqueness of solution for the system in a suitable function space. Global existence and boundedness of solutions for the system are confirmed. Two methodologies, the comparison argument and sequential contracting, are developed to establish sufficient conditions for absolute stability and synchronization among different populations of the system. Finally, we present some numerical examples to demonstrate the theoretical results.
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