Benjamin-Feir instabilities on directed networks
arXiv:1607.06301 · doi:10.1016/j.chaos.2016.11.018
Abstract
The Complex Ginzburg-Landau equation is studied assuming a directed network of coupled oscillators. The asymmetry makes the spectrum of the Laplacian operator complex, and it is ultimately responsible for the onset of a generalized class of topological instability, reminiscent of the Benjamin-Feir type. The analysis is initially carried out for a specific class of networks, characterized by a circulant adjacency matrix. This allows us to delineate analytically the domain in the parameter space for which the generalized instability occurs. We then move forward to considering the family of non linear oscillators coupled via a generic direct, though balanced, graph. The characteristics of the emerging patterns are discussed within a self-consistent theoretical framework.
References in corpus (13)
- Synchronization in complex networks
- Diffusion dynamics on multiplex networks
- Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
- Turing patterns in network-organized activator-inhibitor systems
- Topology-driven instabilities: the theory of pattern formation on directed networks
- Pattern formation in multiplex networks
- Turing patterns in multiplex networks
- Quasi-cycles in a spatial predator-prey model
- Epidemic spreading and risk perception in multiplex networks: a self-organized percolation method
- Self-organized alternating chimera states in oscillatory media
- Diffusion-induced instability and chaos in random oscillator networks
- Multiple scale theory of topology driven pattern on directed networks
- Drift-induced Benjamin-Feir instabilities
Cited by in corpus (8)
- Synchronization induced by directed higher-order interactions
- Ginzburg-Landau approximation for self-sustained oscillators weakly coupled on complex directed graphs
- Turing instability and pattern formation on directed networks
- Resilience for stochastic systems interacting via a quasi-degenerate network
- Desynchronization and pattern formation in a noisy feedforward oscillators network
- Graph spectral characterisation of the XY model on complex networks
- Stabilizing Stuart-Landau oscillators via time-varying networks
- Synchronization of nonlinearly coupled Stuart-Landau oscillators on networks