Neural implementation of chaos control improves both speed and reliability

Abstract

Event Abstract Back to Event Neural implementation of chaos control improves both speed and reliability Christian Bick1, 2, 3, Christoph Kolodziejski1, 2, 4* and Marc Timme1, 2, 4 1 Max Planck Institute for Dynamics and Self-Organization, Network Dynamics Group, Germany 2 Bernstein Center for Computational Neuroscience Göttingen, Germany 3 Georg-August-Universität Göttingen, Mathematisches Institut, Germany 4 Georg-August-Universität Göttingen, Institute for Physics – Nonlinear Dynamics, Germany Chaos control has applications in many fields [1], for example, it has been demonstrated in neural circuits [2] and we have recently used it in order to control robot behavior [3]. One way to achieve chaos control, i.e., rendering unstable fixed points stable, is by adding control perturbations [4, 5]. In a neural implementation of chaos control the application of the control perturbations are restrained by the underlying neural substrate. Hence, the neural implementation itself poses challenges. At the same time, the chaos control method itself is subject to a serious limitation. Convergence speed of such a mechanism becomes very slow when stabilizing more and more periodic points. This has immediate consequences. Take for example an organism, natural or artificial, with a neurally implemented chaos control mechanism where a specific movement is linked to the period of some periodic orbit. For the organism to react to changing environments, new periodic orbits with different periods have to be stabilized as fast as possible resulting in corresponding reactive movements. Hence, reaction time is linked to the convergence time of the stabilization mechanism. We show that a delay, inevitable due to the neural implementation, improves not only convergence characteristics like speed and reliability but, interestingly, also extends the accessibility of periodic orbits in terms of stabilization. Chaos control methods usually are parameter-dependent and the parameter influences the speed of convergence. A priori, however, the optimal parameter value is unknown. We systematically study the performance of different adaptation schemes [6], including heuristical [3] methods, that can be used to find the optimal parameter values dynamically. The result is an adaptive, neurally implemented chaos control algorithm that may have wide applications in the dynamics of neural systems.