Controlling dynamics in spatially extended systems

Abstract

Spatially extended systems exhibit a variety of spatiotemporal dynamics - from stable to chaotic. These dynamics can change under pathological conditions and impair normal functions. Thus, having the ability to control the altered dynamics for improved functioning has the potential for wide ranging applications in real and artificial systems. Here we propose a simple and general method that can be used to target the spatiotemporal dynamics, both globally and in spatially localized regions, in either direction - i.e., towards the stable or unstable manifold - by simply changing the strength and the sign of an externally applied perturbation or pinning. The method is applicable to both chaotic and nonchaotic systems, with discrete and continuous local dynamics, and for different topologies of interactions. We also apply it to simulate an experiment on epileptogenic neuronal activity in rat hippocampal tissue [B. J. Gluckman et al., J. Neurophys. 76, 6202 (1996)]. This unified approach for differential targeting of global and local dynamics promises to be useful for systems spanning large spatial scales and having structural and functional heterogeneity.