Spatiotemporal stability of one-way open coupled nonlinear systems

The present paper investigates the spatiotemporal stability of homogeneous solutions in one-way open coupled nonlinear systems. We show that the $H_{\infty }$ norm concept, which has been used as an important index in the field of robust control theory, allows us to grasp the mechanism of spatial instability in coupled systems. Spatial instability occurs only when the $H_{\infty }$ norm of the transfer function of each site is greater than 1. It is shown that numerical simulations for one-way open coupled double scroll circuits are in good agreement with our theoretical results.