Convergence and stability of generalized gradient systems by Łojasiewicz inequality with application in continuum Kuramoto model

DOI10.3934/dcds.2019014zbMath1419.34145OpenAlexW2898373173MaRDI QIDQ1633134

Yi Liu, Zhuchun Li, Xiao-Ping Xue

Publication date: 19 December 2018

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2019014

zbMATH Keywords

stabilityconvergenceŁojasiewicz inequalityasymptotic theory in Banach spacescontinuum Kuramoto model

Mathematics Subject Classification ID

Asymptotic theory of functional-differential equations (34K25) Population dynamics (general) (92D25) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Asymptotic properties of solutions to ordinary differential equations (34D05) Applications of functional analysis to differential and integral equations (46N20) Synchronization of solutions to ordinary differential equations (34D06)

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Uniform-in-time continuum limit of the lattice winfree model and emergent dynamics ⋮ Emergent behaviors of the continuum thermodynamic Kuramoto model in a large coupling regime ⋮ Uniform-in-Time Continuum Limit of the Winfree Model on an Infinite Cylinder and Emergent Dynamics ⋮ Synchronization conditions of a mixed Kuramoto ensemble in attractive and repulsive couplings

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