Circulant systems can get synchronized with cross-variable coupling

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.