Coherence in scale-free networks of chaotic maps

Abstract

We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) random scale-free topology, (ii) deterministic pseudo-fractal scale-free network, and (iii) Apollonian network. For the random scale-free topology we find a coupling strength threshold beyond which full synchronization is attained. This threshold scales as $k^{-\mu }$, where $k$ is the outgoing connectivity and $\mu$ depends on the local nonlinearity. For deterministic scale-free networks coherence is observed only when the coupling strength is proportional to the neighbor connectivity. We show that the transition to coherence is of first-order and study the role of the most connected nodes in the collective dynamics of oscillators in scale-free networks.

arXiv comment9 pages, 8 figures

References in corpus (21)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Evolution of networks
• Synchronization in small-world systems
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Halting viruses in scale-free networks
• Fast Response and Temporal Coding on Coherent Oscillations in Small-World Networks
• Pseudofractal Scale-free Web
• Deterministic Scale-Free Networks
• Delays, connection topology, and synchronization of coupled chaotic maps
• Spectral Properties and Synchronization in Coupled Map Lattices
• Factors that predict better synchronizability on complex networks
• Force network ensemble: a new approach to static granular matter
• Efficiency and reliability of epidemic data dissemination in complex networks
• Opinion Formation on a Deterministic Pseudo-fractal Network
• Mutual synchronization and clustering in randomly coupled chaotic dynamical networks
• Anisotropy in granular media: classical elasticity and directed force chain network
• Exactly solvable scale-free network model
• Weak localization in multiterminal networks of diffusive wires
• Chaos synchronization in long-range coupled map lattices
• Mathematical Analysis and Simulations of the Neural Circuit for Locomotion in Lamprey

Cited by in corpus (34)

• Synchronization in complex networks
• Spatial Networks
• Critical phenomena in complex networks
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Synchronization is optimal in non-diagonalizable networks
• Maximum Performance at Minimum Cost in Network Synchronization
• Spreading gossip in social networks
• Enhance synchronizability by structural perturbations
• Relations between Average Distance, Heterogeneity and Network Synchronizability
• Evolving Apollonian Networks with Small-world Scale-free topologies
• A general geometric growth model for pseudofractal scale-free web
• Exact analytical solution of average path length for Apollonian networks
• Evolving small-world scale-free networks consist of cliques
• Coherent transport on Apollonian networks and continuous-time quantum walks
• Bounding network spectra for network design
• Better Synchronizability Predicted by Crossed Double Cycle
• Correlations in random Apollonian network
• Deterministic weighted scale-free small-world networks
• Synchronizabilities of Networks: A New index
• Impact of bistability in the synchronization of chaotic maps with delayed coupling
• Minimal models of weighted scale-free networks
• Synchronization on Effective Networks
• Sync in Complex Dynamical Networks: Stability, Evolution, Control, and Application
• Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling
• Coupled Hypergraph Maps and Chaotic Cluster Synchronization
• Rewiring hierarchical scale-free networks: Influence on synchronizability and topology
• Structural network heterogeneities and network dynamics: a possible dynamical mechanism for hippocampal memory reactivation
• Effect of chaotic agent dynamics on coevolution of cooperation and synchronization
• Some aspects of the synchronization in coupled maps
• Complete synchronization equivalence in asynchronous and delayed coupled maps
• Amplitude death in coupled replicator map lattice: averting migration dilemma
• From synchronous to one-time delayed dynamics in coupled maps
• Coherence in complex networks of oscillators
• A stylised view on structural and functional connectivity in dynamical processes in networks