C-lscillators in a homogeneous ring of diffusively coupled dynamical systems: existence, stability and fusion of cluster structures

Existence and stability of stationary cluster structures in a homogeneous ring of dynamical systems (oscillators) is studied in the framework of interpretation of cluster structures as a classical synchronization of structure forming objects called C-oscillators and simple cells. A set of types of C-oscillators and simple cells is determined for the lattice under consideration. Examples of the fusion of lattices of different geometries that contain cluster structures based on synchronization of C-oscillators of a ring are presented.