Multi-clusters in networks of adaptively coupled phase oscillators networks

Abstract

Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase oscillators inspired by neuronal networks with synaptic plasticity. One important behaviour of such systems reveals splitting of the network into clusters of oscillators with the same frequencies, where different clusters correspond to different frequencies. Starting from one-cluster solutions we provide existence criteria for multi-cluster solutions and present their explicit form. The phases of the oscillators within one cluster can be organized in different patterns: antipodal, double antipodal, and splay type. Interestingly, multi-clusters are shown to exist where different clusters exhibit different patterns. For instance, an antipodal cluster can coexist with a splay cluster. We also provide stability conditions for one- and multi-cluster solutions. These conditions, in particular, reveal a high level of multistability.

38 pages, 14 figures

References in corpus (5)

• Adaptive Coevolutionary Networks: A Review
• Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Emergent explosive synchronization in adaptive complex networks
• Identical phase oscillator networks: bifurcations, symmetry and reversibility for generalized coupling

Cited by in corpus (21)

• Desynchronization transitions in adaptive networks
• Birth and stabilization of phase clusters by multiplexing of adaptive networks
• Hierarchical frequency clusters in adaptive networks of phase oscillators
• What adaptive neuronal networks teach us about power grids
• Perspectives on adaptive dynamical systems
• Solitary states in adaptive nonlocal oscillator networks
• Heterogeneous nucleation in finite size adaptive dynamical networks
• Hierarchical clusters in neuronal populations with plasticity
• Synchronization in temporal simplicial complexes
• Generalized splay states in phase oscillator networks
• Exotic states induced by co-evolving connection weights and phases in complex networks
• Interlayer antisynchronization in degree-biased duplex networks
• Synchronization transitions in Kuramoto networks with higher-mode interaction
• Self-organized Multi-Frequency Clusters in an Oscillating Electrochemical System with Strong Nonlinear Coupling
• Recurrent chaotic clustering and slow chaos in adaptive networks
• Emulating complex networks with a single delay differential equation
• Modeling active optical networks
• Synchronization transitions in adaptive simplicial complexes with cooperative and competitive dynamics
• Modelling power grids as pseudo adaptive networks
• A General View on Double Limits in Differential Equations
• Emergence of solitary and chimera states in adaptive pendulum networks under diverse learning rules