Properties of an equation for neural fields in a bounded domain

Abstract

In this work we study the global dynamics of an evolution equation for neural fields, where the flow generated by this equation in the phase space $L^2(S^1)$, is $C^1$. Furthermore we exhibit a continuous Lyapunov functional and use it for proving that this flow has the gradient property.

Keywords

• Well-posedness
• smooth orbit
• gradient flow