Linear matrix inequality tests for synchrony of diffusively coupled nonlinear systems

In a recent publication we presented a condition that guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction-diffusion PDE with Neumann boundary conditions. This condition makes use of the Jacobian matrix of the reaction terms and the second Neumann eigenvalue of the Laplacian operator on the given spatial domain. In the present paper we derive an analogous result for the synchronization of a network of identical ODE models coupled by diffusion terms.