Amplitude and phase dynamics in oscillators with distributed-delay coupling

DOI10.1098/rsta.2012.0466zbMath1353.34045arXiv1209.0133OpenAlexW2039006574MaRDI QIDQ2955564

Eckehard Schöll, Konstantin B. Blyuss, Yuliya N. Kyrychko

Publication date: 13 January 2017

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.0133

Mathematics Subject Classification ID

Stability theory of functional-differential equations (34K20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Analytic circuit theory (94C05) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)

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Cites Work

• Phase models and oscillators with time delayed coupling
• Oscillator death in populations of all to all coupled nonlinear oscillators
• The effect of time-delay on anomalous phase synchronization
• Control of unstable steady states in neutral time-delayed systems
• Multiparameter bifurcation diagrams in predator-prey models with time lag
• Discrete delay, distributed delay and stability switches
• Influence of delayed viral production on viral dynamics in HIV-1 infected patients
• Approximating the stability region of a neural network with a general distribution of delays
• Time delay effects on coupled limit cycle oscillators at Hopf bifurcation
• Amplitude death in an array of limit-cycle oscillators.
• Stability and bifurcations in an epidemic model with varying immunity period
• Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics
• Positive travelling fronts for reaction–diffusion systems with distributed delay
• Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback
• Delayed complex systems: an overview
• Time-delayed feedback in neurosystems
• Extinction and wavefront propagation in a reaction-diffusion model of a structured population with distributed maturation delay
• Synchronization properties of network motifs: Influence of coupling delay and symmetry
• Amplitude and phase effects on the synchronization of delay-coupled oscillators
• Stabilization of time-delay systems with a Controlled time-varying delay and applications
• On the Use of Delay Equations in Engineering Applications
• An Exact Method for the Stability Analysis of Linear Consensus Protocols With Time Delay
• Sufficient conditions for stability of linear differential equations with distributed delay

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