Coupling functions: Universal insights into dynamical interaction mechanisms
arXiv:1706.01810 · doi:10.1103/RevModPhys.89.045001
Abstract
The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. Here, we aim to present a coherent and comprehensive review encompassing the rapid progress made recently in the analysis, understanding and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally-coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.
Rev. Mod. Phys. 89, 045001 (2017)
References in corpus (85)
- Statistical mechanics of complex networks
- Measuring Information Transfer
- Recurrence Plots for the Analysis of Complex Systems
- Synchronization in complex networks
- Multilayer Networks
- Synchronization in small-world systems
- Surrogate time series
- Chimera States for Coupled Oscillators
- The Kuramoto model in complex networks
- Nonlinear collective effects in photon-photon and photon-plasma interactions
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- On the performance of different synchronization measures in real data: a case study on EEG signals
- Network Physiology reveals relations between network topology and physiological function
- Time Delay in the Kuramoto Model of Coupled Oscillators
- Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks
- Analysis of a power grid using the Kuramoto-like model
- Colloquium: Nonlinear collective interactions in quantum plasmas with degenerate electron fluids
- Pinning-controllability of complex networks
- A Robust Method for Detecting Interdependences: Application to Intracranially Recorded EEG
- Amplitude Death: The emergence of stationarity in coupled nonlinear systems
- Chimera Death: Symmetry Breaking in Dynamical Networks
- Revealing Network Connectivity From Dynamics
- Characterizing dynamics with covariant Lyapunov vectors
- Phase reduction approach to synchronization of nonlinear oscillators
- Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
- Causal Network Inference by Optimal Causation Entropy
- Phase oscillators with global sinusoidal coupling evolve by Mobius group action
- Weak chimeras in minimal networks of coupled phase oscillators
- Master Stability Functions for Coupled Near-Identical Dynamical Systems
- Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise
- Synchronizing distant nodes: a universal classification of networks
- Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
- Semi-passivity and synchronization of diffusively coupled neuronal oscillators
- Evolving networks in the human epileptic brain
- Amplitude death in coupled chaotic oscillators
- General mechanism for amplitude death in coupled systems
- Dynamics of Limit Cycle Oscillator Subject to General Noise
- Time dependent couplings in the dark sector: from background evolution to nonlinear structure formation
- Topological Speed Limits to Network Synchronization
- Network reconstruction from random phase-resetting
- Chaos in generically coupled phase oscillator networks with nonpairwise interactions
- Stochastic phase reduction for a general class of noisy limit cycle oscillators
- Experimental Observations of Group Synchrony in a System of Chaotic Optoelectronic Oscillators
- Scaling and singularities in the entrainment of globally-coupled oscillators
- Phase reduction of stochastic limit cycle oscillators
- Cluster Synchrony in Systems of Coupled Phase Oscillators with Higher-Order Coupling
- Oscillation death in diffusively coupled oscillators by local repulsive link
- The combined effect of chemical and electrical synapses in small Hindmarsch-Rose neural networks on synchronisation and on the rate of information
- Inference of a nonlinear stochastic model of the cardiorespiratory interaction
- Reconstructing phase dynamics of oscillator networks
- Collective behavior of heterogeneous neural networks
- Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
- The Kuramoto Model with Time-Varying Parameters
- Invariant submanifold for series arrays of Josephson junctions
- Key bifurcations of bursting polyrhythms in 3-cell central pattern generators
- Unstable Attractors: Existence and Robustness in Networks of Oscillators With Delayed Pulse Coupling
- Chaos in Symmetric Phase Oscillator Networks
- Glassy states and superrelaxation in populations of coupled phase oscillators
- Phase Response Curves of Coupled Oscillators
- Phase Reduction Method for Strongly Perturbed Limit Cycle Oscillators
- Dynamical Bayesian Inference of Time-evolving Interactions: From a Pair of Coupled Oscillators to Networks of Oscillators
- Time delay control of symmetry-breaking primary and secondary oscillation death
- Stable and transient multi-cluster oscillation death in nonlocally coupled networks
- Synchronization by Reactive Coupling and Nonlinear Frequency Pulling
- Computing covariant vectors, Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study
- Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems
- Towards a general theory for coupling functions allowing persistent synchronization
- Do Small Worlds Synchronize Fastest?
- On the equivalence of phase-oscillator and integrate-and-fire models
- Synchronization of a Josephson junction array in terms of global variables
- Connectivity-Driven Coherence in Complex Networks
- Clustering in Globally Coupled Oscillators Near a Hopf Bifurcation: Theory and Experiments
- Diverse routes to oscillation death in a coupled oscillator system
- Self-sustained irregular activity in an ensemble of neural oscillators
- Effective phase dynamics of noise-induced oscillations in excitable systems
- Non-chaotic dynamics in general-relativistic and scalar-tensor cosmology
- Synchronization of oscillators in a Kuramoto-type model with generic coupling
- Collective fluctuations in networks of noisy components
- Qualitative and Quantitative Stability Analysis of Penta-rhythmic Circuits
- Dynamics of Coupling Functions in Globally Coupled Maps: Size, Periodicity and Stability of Clusters
- Self-Sustained Collective Oscillation Generated in an Array of Non-Oscillatory Cells
- Multi-cluster dynamics in coupled phase oscillator networks
- A proposal of an orbital-dependent correlation energy functional for energy-band calculations
- Formation of antiwaves in gap-junction-coupled chains of neurons
- Synchronization of Chaos
Cited by in corpus (80)
- Complex network approaches to nonlinear time series analysis
- What are higher-order networks?
- Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
- Multiorder Laplacian for synchronization in higher-order networks
- Autonomous inference of complex network dynamics from incomplete and noisy data
- Using Machine Learning to Assess Short Term Causal Dependence and Infer Network Links
- Stabilisation of dynamics of oscillatory systems by non-autonomous perturbation
- Emergent hypernetworks in weakly coupled oscillators
- Dynamical robustness of network of oscillators
- Coherence resonance in influencer networks
- Reconstructing Network Dynamics of Coupled Discrete Chaotic Units from Data
- Dynamics of Reaction-Diffusion Oscillators in Star Networks
- Generic criterion for explosive synchronization in heterogeneous phase oscillator populations
- Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling
- Global Robustness vs. Local Vulnerabilities in Complex Synchronous Networks
- Nonautonomous driving induces stability in network of identical oscillators
- Asymmetry-induced order in multilayer networks
- Analysis and data-driven reconstruction of bivariate jump-diffusion processes
- Enlarged Kuramoto Model: Secondary Instability and Transition to Collective Chaos
- Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems
- Heteroclinic Dynamics of Localized Frequency Synchrony: Heteroclinic Cycles for Small Populations
- Aging transition under discrete time-dependent coupling: Restoring rhythmicity from aging
- On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators
- How to couple identical ring oscillators to get Quasiperiodicity, extended Chaos, Multistability and the loss of Symmetry
- A mean-field game model for homogeneous flocking
- Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time series data
- Ordinal methods for a characterization of evolving functional brain networks
- Revealing dynamics, communities and criticality from data
- Coupling functions in climate
- Adjoint-based phase reduction analysis of incompressible periodic flows
- Emergent noise-aided logic through synchronization
- Detecting Directed Interactions of Networks by Random Variable Resetting
- Designs toward synchronization of optical limit cycles with coupled silicon photonic crystal microcavities
- A practical method for estimating coupling functions in complex dynamical systems
- Emulating the local Kuramoto model with an injection-locked photonic crystal laser array
- State-dependent effective interactions in oscillator networks through coupling functions with dead zones
- Noise-induce coexisting firing patterns in hybrid-synaptic interacting networks
- Phase dynamics of oscillating magnetizations coupled via spin pumping
- Recovering sparse networks: Basis adaptation and stability under extensions
- Spin-current driven spontaneous coupling of ferromagnets
- Fluctuation Response Patterns of Network Dynamics -- an Introduction
- Delta-alpha cross-frequency coupling for different brain regions
- Estimating the master stability function from the time series of one oscillator via reservoir computing
- Decoupling approximation robustly reconstructs directed dynamical networks
- Feedback-induced desynchronization and oscillation quenching in a population of globally coupled oscillators
- Sequential escapes: onset of slow domino regime via a saddle connection
- Phase and amplitude description of complex oscillatory patterns in reaction-diffusion systems
- Enhancing the accuracy of a data-driven reconstruction of bivariate jump-diffusion models with corrections for higher orders of the sampling interval
- Locating line and node disturbances in networks of diffusively coupled dynamical agents
- Discrete Shilnikov attractor and chaotic dynamics in the system of five identical globally coupled phase oscillators with biharmonic coupling
- Exponentially long transient time to synchronization of coupled chaotic circle maps in dense random networks
- Phase autoencoder for rapid data-driven synchronization of rhythmic spatiotemporal patterns
- Setting of the Poincaré section for accurately calculating the phase of rhythmic spatiotemporal dynamics
- Emergence of multistability and strongly asymmetric collective modes in two quorum sensing coupled identical ring oscillators
- Mathematical modeling for the synchronization of two interacting active rotors
- Gaussian Process Phase Interpolation for estimating the asymptotic phase of a limit cycle oscillator from time series data
- Robust reconstruction of sparse network dynamics
- Extracting phase coupling functions between collectively oscillating networks directly from time-series data
- Effects of time-varying habitat connectivity on metacommunity persistence
- Chaotic behavior in diffusively coupled systems
- The spark of synchronization in heterogeneous networks of chaotic maps
- Resonant features in a forced population of excitatory neurons
- Mixed measurements and the detection of phase synchronization in networks
- Chimera state in neural network with the Proportional-Integral-Derivative coupling
- Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic coupling
- Networks with asymmetric inputs: lattice of synchrony subspaces
- High-Order Phase Reduction for Coupled Oscillators
- Two-dimensional hydrodynamic simulation for synchronization in coupled density oscillators
- Non-equilibrium critical scaling and universality in a quantum simulator
- Reconstruction of phase-amplitude dynamics from electrophysiological signals
- Distinguishing pairwise and higher-order interactions in coupled oscillators from time series
- Designing topological cluster synchronization patterns with the Dirac operator
- Path Signature Area-Based Causal Discovery in Coupled Time Series
- Noise stability of synchronization and optimal network structures
- Energy Transmission and Harmonic Propagation in Unidirectionally Coupled Plasma Oscillator Networks
- Phase reduction analysis of traveling breathers in reaction--diffusion systems
- Phase demodulation with iterative Hilbert transform embeddings
- Mean-field and fluctuations for hub dynamics in heterogeneous random networks
- Phase reconstruction from oscillatory data with iterated Hilbert transform embeddings -- benefits and limitations
- Dead zones and phase reduction of coupled oscillators