Developing local control strategies for the dynamics of self-organizing systems

Abstract

In nature, the remarkable efficiency with which some groups of living systems self-organize, forming swarms capable of collectively solving problems, has inspired scientific efforts to replicate this capability in artificial versions of such self-organizing systems. Much progress has been made in understanding how a swarm's self-organized collective behavior emerges from mechanisms that ensure cohesion, separation, and alignment among its elements. However, the development of localized strategies to externally control these systems remains limited. To address this need, we utilize computational and analytical tools to examine various structural and dynamical aspects of self-organized collective states in swarms. We aim to formulate novel control strategies that can switch the collective behavior of these systems to a desired state by locally intervening in their individual elements. To achieve this objective, we employ high-dimensional mathematical models of self-organizing systems that comprehensively account for element features, including inertia, energy admission/dissipation, and interactions. In this context, our proposed control strategy stands out by taking advantage of the system's internal nonlinear feedback, giving rise to various phenomena such as multistability, fractal basin boundaries, criticalities, nontrivial phase response, and parameter sensitivity. These phenomena are all valuable for controllability but have remained largely unexplored for controlling self-organizing systems in general. Therefore, the control strategies proposed here introduce new perspectives for harnessing the collective motion of artificial systems and even intervening in natural ones. Additionally, although we develop control for collective systems in a physical state space, our main propositions may also be applicable to local interventions within systems featuring alternative state spaces. For example, these principles can be employed to intervene in keystone species within ecosystems, thereby stabilizing complex food webs, critical supply chains to support sustainable urban growth, and specific cellular chemical pathways to prevent cellular death. (AU)