Controlling Spatiotemporal Dynamics in Excitable Systems

Spatially extended excitable systems exhibit a variety of spatiotemporal dynamics — from stable to chaotic. These dynamics can change under pathological conditions and impair normal functions. Thus being able to control the altered dynamics for improved functioning has 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 (“control”) or unstable (“anti-control”) manifold by simply changing the sign of an externally applied perturbation or pinning. The method is applicable to both chaotic and non-chaotic 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 [1]. 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.