Traveling Waves in a Simplified Model of Calcium Dynamics

DOI10.1137/120867949zbMath1260.34055OpenAlexW1968539151MaRDI QIDQ4904539

Vivien Kirk, Je-Chiang Tsai, James Sneyd, Wen-Jun Zhang

Publication date: 30 January 2013

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/7634d0c3118467417bb283f65d48df617fef4e49

zbMATH Keywords

stabilityreaction-diffusion systemtraveling wavescalcium dynamicsFitzHugh-Nagumo

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell biology (92C37) Multiple scale methods for ordinary differential equations (34E13) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Boundary value problems on infinite intervals for ordinary differential equations (34B40) Traveling wave solutions (35C07)

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Stable foliations near a traveling front for reaction diffusion systems ⋮ Instability of small-amplitude periodic waves from fold-Hopf bifurcation ⋮ Perturbation of the spectra for asymptotically constant differential operators and applications ⋮ Dual mechanisms of Ca\(^{2+}\) oscillations in hepatocytes ⋮ Sharp relaxation rates for plane waves of general reaction-diffusion models ⋮ A network model of the periodic synchronization process in the dynamics of calcium concentration in GnRH neurons ⋮ Stability of a Planar Front in a Class of Reaction-Diffusion Systems ⋮ Speed of traveling waves for monotone reaction-diffusion systems as a function of diffusion coefficients

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