Enhancing Synchronizability in Identical Chaotic Complex Networks: Application of Genetic Algorithms for Edge Rewiring

Synchronization is one of the key behaviours observed in chaotic oscillatory networks. The efficient operation of numerous biological and industrial networks depends on the synchronization of their subsystems. This paper aims to improve the synchronizability of identical complex chaotic networks while preserving the associated synchronization cost. In this context, the master stability function (MSF) diagram can be utilized to analyze the synchronization of identical chaotic oscillator networks. In Type-II MSF diagrams, the synchronizability of the network can be enhanced through optimization of the parameter 𝜆 2. Furthermore, in Type-III and higher MSF diagrams, synchronization can be improved by optimizing the 𝜆 𝑁 𝜆 2 ratio. This study utilizes the genetic algorithm (GA) to improve the synchronizability of complex chaotic networks by optimizing their structure through rewiring, focusing on synchronization parameters enhancement. Furthermore, constraints are introduced to the genetic algorithm to facilitate the identification of optimal solutions and to reduce the search space. The application of the algorithm proposed in this paper to various networks, including scale-free, random, and small-world types, demonstrates that the genetic algorithm, with optimized runtime, effectively refines the network's structure exclusively through rewiring to enhance its synchronization. The primary advantage of the method proposed in this paper is its versatility, as it is not limited to a specific type of oscillator or network. It can be applied to all types of unweighted networks. Moreover, the method proposed in this paper has the potential to be generalized for application to weighted networks.