Reviving networked multidimensional dynamical systems
Phys. Rev. E 114, 044309 – Published 8 October, 2026
DOI: https://doi.org/10.1103/qqwq-7j7j
Abstract
From gene regulatory networks to mutualistic networks, controlling a small portion of nodes in complex networks can drive such dynamical systems from nonideal states to ideal ones. Currently, there are only methods for handling linear systems and one-dimensional nonlinear systems. However, real-world complex systems are typically nonlinear and multidimensional, such as mutualistic systems involving flowering plants and pollinating insects. In such systems, nodal dynamics are governed by multiple nonlinear differential equations. To address this limitation, we develop a method for controlling a single node to revive networked multidimensional dynamical systems. The uncontrolled nodes are stratified based on their shortest path to the controlled node. In this way, a large-scale dynamical system can ultimately be replaced by a much simpler one. Through analysis of the reduced system, we can predict the degree of control required to revive the system to its ideal state. We apply this method across diverse domains, achieving successful revival in various multidimensional complex dynamical systems.
