The spark of synchronization in heterogeneous networks of chaotic maps
arXiv:2310.07942 · doi:10.1063/5.0173546
Abstract
We investigate the emergence of synchronization in heterogeneous networks of chaotic maps. Our findings reveal that a small cluster of highly connected maps is responsible for triggering the spark of synchronization. After the spark, the synchronized cluster grows in size and progressively moves to less connected maps, eventually reaching a cluster that may remain synchronized over time. We explore how the shape of the network's degree distribution affects the onset of synchronization and derive an expression based on the network's construction that determines the expected time for a network to synchronize. Understanding how the network structure affects the spark of synchronization is particularly important for the control and design of more robust systems that require some level of coherence between a subset of units for better functioning. Numerical simulations in finite-sized networks are consistent with this analysis.
References in corpus (17)
- Emergence of scaling in random networks
- Assortative mixing in networks
- Synchronization in complex networks
- Defining and identifying communities in networks
- Dynamical and correlation properties of the Internet
- The Kuramoto model in complex networks
- Spontaneous synchrony in power-grid networks
- The Rich-Club Phenomenon In The Internet Topology
- Coupling functions: Universal insights into dynamical interaction mechanisms
- Frequency synchronization in random oscillator network
- Synchronization transition in scale-free networks: Clusters of synchrony
- Synchronizability determined by coupling strengths and topology on Complex Networks
- Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling
- The emergence of coherence in complex networks of heterogeneous dynamical systems
- Volcano transition in a solvable model of oscillator glass
- Exponentially long transient time to synchronization of coupled chaotic circle maps in dense random networks
- Emergence of chaotic cluster synchronization in heterogeneous networks