Taming explosive growth through linear augmentation

¹ Department of Physics, Central University of Rajasthan - Ajmer, 305 817 Rajasthan, India
² Amity Institute of Integrative Sciences and Health, Amity University Haryana - Gurugram, Manesar, 122 413 Haryana, India
³ Department of Physics and Astrophysics, University of Delhi - New Delhi, 110 007 Delhi, India

Received: 19 July 2024
Accepted: 25 September 2024

Abstract

Nonlinear coupling among dynamical systems has found widespread applications in real-world systems. Such interactions may lead to an undesired explosive growth of dynamical variables. We employ a control technique to drive such unstable dynamics (explosive growth) of dynamical systems to stable dynamics through the scheme of linear augmentation. The efficacy of our scheme in suppressing the explosive growth of trajectories in a network of limit cycles is illustrated and the dynamics of the unaugmented and augmented networked systems are discussed. We also introduce the concept of “dynamic augmentation” and exhibited the robustness of our scheme by successfully controlling the explosive growth of chaotic trajectories. Our results may be useful in controlling and preventing explosive growths of trajectories in a wide range of devices in the engineering fields.