Circulant systems can get synchronized with cross-variable coupling

¹ Center for Research, SRM Easwari Engineering College - Chennai, India
² Center for Research, SRM Institute of Science and Technology-Ramapuram - Chennai, India
³ Intelligent Sound Processing Laboratory (ISP-Lab), Faculty of Computer Science and Engineering, Shahid Beheshti University - Tehran, Iran
⁴ Ministry of Higher Education and Scientific Research - Baghdad, 10024, Iraq
⁵ Department of Computer Technology Engineering, College of Information Technology, Imam Ja'afar Al-Sadiq University - Baghdad, Iraq
⁶ Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic) - Tehran, Iran
⁷ Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic) - Tehran, Iran

Received: 20 October 2024
Accepted: 17 February 2025

Abstract

Diffusive coupling plays a crucial role in numerous applications by facilitating the diffusion of energy or information among systems. Typically, this type of coupling is defined by the same variables in coupled systems. However, this paper demonstrates that in circulant systems, diffusive coupling can be applied to cross-variables with cyclical symmetry. This approach results in a unique form of synchronization known as circulant synchronization, occurring among the cross-variables. Furthermore, a dynamic analysis reveals that these systems can exhibit various synchronization manifolds, including periodic, quasiperiodic, and chaotic attractors.