Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Abstract

In recent times, studies on discrete nonlinear systems received much attention among researchers because of their potential applications in real-world problems. In this study, we conducted an in-depth exploration into the stability of synchronization within discrete nonlinear systems, specifically focusing on the Hindmarsh–Rose map, the Chialvo neuron model, and the Lorenz map. Our methodology revolved around the utilization of the master stability function approach. We systematically examined all conceivable coupling configurations for each model to ascertain the stability of synchronization manifolds. The outcomes underscored that only distinct coupling schemes manifest stable synchronization manifolds, while others do not exhibit this trait. Furthermore, a comprehensive analysis of the master stability function’s behavior was performed across a diverse range of coupling strengths $\left(\sigma \right)$ and system parameters. These findings greatly enhance our understanding of network dynamics, as discrete-time dynamical systems adeptly replicate the dynamics of continuous-time models, offering significant reductions in computational complexity.