The Efficiency of Synchronization Dynamics and the Role of Network Syncreactivity
arXiv:2404.16864 · doi:10.1038/s41467-024-52486-0
Abstract
Synchronization of coupled oscillators is a fundamental process in both natural and artificial networks. While much work has investigated the asymptotic stability of the synchronous solution, the fundamental question of the transient behavior toward synchronization has received far less attention. In this work, we present the transverse reactivity as a metric to quantify the instantaneous rate of growth or decay of desynchronizing perturbations. We first use the transverse reactivity to design a coupling-efficient and energy-efficient synchronization strategy that involves varying the coupling strength dynamically according to the current state of the system. We find that our synchronization strategy is able to synchronize networks in both simulation and experiment over a significantly larger (often by orders of magnitude) range of coupling strengths than is possible when the coupling strength is constant. Then, we characterize the effects of network topology on the transient dynamics towards synchronization by introducing the concept of network syncreactivity: A network with a larger syncreactivity has a larger transverse reactivity at every point on the synchronization manifold, independent of the oscillator dynamics. We classify real-world examples of complex networks in terms of their syncreactivity.
arXiv commentAccepted for publication in Nature Communications
References in corpus (18)
- Synchronization in complex networks
- Synchronization in small-world systems
- Pinning-controllability of complex networks
- Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies
- Spectrum of Controlling and Observing Complex Networks
- The synchronized dynamics of time-varying networks
- Predictability and suppression of extreme events in complex systems
- Nonnormal amplification in random balanced neuronal networks
- Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators
- Nonequilibrium thermodynamics of coupled molecular oscillators: The energy cost and optimal design for synchronization
- Giant amplification of noise in fluctuation-induced pattern formation
- Topological resilience in non-normal networked systems
- Efficient synchronization of structurally adaptive coupled Hindmarsh-Rose neurons
- Network structural origin of instabilities in large complex systems
- Centrality measures and the role of non-normality for network control energy reduction
- From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior
- Single-Integrator Consensus Dynamics over Minimally Reactive Networks
- Pinning control of networks: dimensionality reduction through simultaneous block-diagonalization of matrices