Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling
arXiv:1704.03632 · doi:10.1103/PhysRevE.96.012223
Abstract
We consider optimization of linear stability of synchronized states between a pair of weakly coupled limit-cycle oscillators with cross coupling, where different components of state variables of the oscillators are allowed to interact. On the basis of the phase reduction theory, the coupling matrix between different components of the oscillator states that maximizes the linear stability of the synchronized state under given constraints on overall coupling intensity and on stationary phase difference is derived. The improvement in the linear stability is illustrated by using several types of limit-cycle oscillators as examples.
arXiv comment12 pages, 13 figures, revised version, to be published in PRE
References in corpus (23)
- Mathematical frameworks for oscillatory network dynamics in neuroscience
- Coupling functions: Universal insights into dynamical interaction mechanisms
- Phase reduction approach to synchronization of nonlinear oscillators
- Synchronization is optimal in non-diagonalizable networks
- Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions
- Optimal synchronization of complex networks
- Maximum Performance at Minimum Cost in Network Synchronization
- Collective Phase Sensitivity
- Optimal waveform for the entrainment of a weakly forced oscillator
- Robustness of Optimal Synchronization in Real Networks
- Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems
- Optimizing Synchronization Stability of the Kuramoto Model in Complex Networks and Power Grids
- Phase reduction theory for hybrid nonlinear oscillators
- Collective phase description of oscillatory convection
- Phase description of oscillatory convection with a spatially translational mode
- Maximizing coherence of oscillations by external locking
- Design of Easily Synchronizable Oscillator Networks Using the Monte Carlo Optimization Method
- Circadian clocks optimally adapt to sunlight for reliable synchronization
- Optimal synchronization of directed complex networks
- Design of Oscillator Networks with Enhanced Synchronization Tolerance against Noise
- Optimizing mutual synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems
- Optimal implementations for reliable circadian clocks
- Thermodynamic Characterization of Synchronization-Optimized Oscillator-Networks
Cited by in corpus (12)
- Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory
- Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations
- Optimizing mutual synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems
- Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators
- Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators
- Optimization of linear and nonlinear interaction schemes for stable synchronization of weakly coupled limit-cycle oscillators
- A Central Pattern Generator Network for Simple Control of Gait Transitions in Hexapod Robots based on Phase Reduction
- Optimal coupling functions for fast and global synchronization of weakly coupled limit-cycle oscillators
- Phase-Amplitude Reduction and Optimal Phase Locking of Collectively Oscillating Networks
- Sparse optimization of mutual synchronization in collectively oscillating networks
- Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators
- Deep Reinforcement Learning for Neural Control