Center manifold theory for the 1-dimensional collective motions of camphor disks with delta functions in the \(L^2\)-framework

DOI10.3934/DCDS.2023024zbMath1518.37077OpenAlexW4323905476MaRDI QIDQ6042882

Kota Ikeda

Publication date: 4 May 2023

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

Full work available at URL: https://doi.org/10.3934/dcds.2023024

zbMATH Keywords

center manifold theorytraveling wave solutioncollective motioncongestion and clustering

Mathematics Subject Classification ID

Invariant manifold theory for dynamical systems (37D10) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)

Cites Work

• Geometric theory of semilinear parabolic equations
• Pulse-pulse interaction in reaction-diffusion systems
• Interaction of non-radially symmetric camphor particles
• Bifurcation of a helical wave from a traveling wave
• Perturbation theory for linear operators.
• A theoretical and experimental study on the unidirectional motion of a camphor disk
• Center manifold theory for the motions of camphor boats with delta function
• On a numerical bifurcation analysis of a particle reaction-diffusion model for a motion of two self-propelled disks
• A weak solution for a point mass camphor motion.
• Existence and non-existence of asymmetrically rotating solutions to a mathematical model of self-propelled motion
• Traveling Curved Waves in Two-Dimensional Excitable Media
• A free boundary problem arising in some reacting–diffusing system
• The motion of weakly interacting pulses in reaction-diffusion systems

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