Collective phase description of oscillatory convection

Abstract

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shaw cells exhibiting oscillatory convection on the basis of the derived phase equations.

16 pages, 4 figures, to appear in Chaos

References in corpus (5)

• Collective Phase Sensitivity
• Noise-induced Turbulence in Nonlocally Coupled Oscillators
• Collective phase description of globally coupled excitable elements
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case
• Propagation Of Waves In Periodic-Heterogeneous Bistable Systems

Cited by in corpus (24)

• Phase reduction approach to synchronization of nonlinear oscillators
• On the Concept of Dynamical Reduction : The Case of Coupled Oscillators
• Phase-response analysis of synchronization for periodic flows
• Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems
• Semiclassical Phase Reduction Theory for Quantum Synchronization
• Phase reduction theory for hybrid nonlinear oscillators
• Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory
• Phase-based control of periodic fluid flows
• Phase description of oscillatory convection with a spatially translational mode
• Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations
• Phase-synchronization properties of laminar cylinder wake for periodic external forcings
• Optimizing mutual synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems
• Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling
• Optimal waveform for fast synchronization of airfoil wakes
• Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators
• Noise-induced synchronization of oscillatory convection and its optimization
• Optimization of linear and nonlinear interaction schemes for stable synchronization of weakly coupled limit-cycle oscillators
• Adjoint-based phase reduction analysis of incompressible periodic flows
• Phase and amplitude description of complex oscillatory patterns in reaction-diffusion systems
• 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
• Two-dimensional hydrodynamic simulation for synchronization in coupled density oscillators
• Phase reduction analysis of traveling breathers in reaction--diffusion systems
• Phase reduction of reaction-diffusion systems with delay