On the Stability of Discrete Reaction-Diffusion System of Networked Dynamical Systems
This paper establishes a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems with heterogeneous node dynamics, demonstrating that stability can be guaranteed by the diagonal dominance of the spatially averaged Jacobian and a lower bound on the network's algebraic connectivity, even in the absence of dispersal losses and without requiring identical patch dynamics.