Preserving chaos: Control strategies to preserve complex dynamics with potential relevance to biological disorders

Abstract

This paper considers the situation in which an originally chaotic orbit would, in the absence of intervention, become periodic as a result of slow system drift through a bifurcation. In the biological context, such a bifurcation is often undesirable: there are many cases, occurring in a wide variety of different situations, where loss of complexity and the emergence of periodicity are associated with pathology (such situations have been called ‘‘dynamical disease’’). Motivated by this, we investigate the possibility of using small control perturbations to preserve chaotic motion past the point where it would otherwise bifurcate to periodicity.