Augmented dynamics of nonlinear systems: A review

Abstract

Abstract We discuss a simple yet powerful control technique called “Linear Augmentation” (LA) for nonlinear dynamical systems. The linear augmentation can be perceived as a type of interaction that may occur naturally in dynamical systems as an environmental effect, or can be explicitly added to a system in order to control its collective dynamical behavior. LA has been known to effectively regulate resulting dynamics of various dynamical systems and can be used as a powerful control strategy in various applications. Examples include targeting attractor(s), regulating multistable dynamics, suppression of extreme events, and controlling chimera states in the nonlinear dynamical systems.