Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation

DOI10.1007/s00285-014-0842-3zbMath1329.35052OpenAlexW1994538318WikidataQ51024898 ScholiaQ51024898MaRDI QIDQ500341

Pietro-Luciano Buono, Raluca Eftimie

Publication date: 2 October 2015

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00285-014-0842-3

zbMATH Keywords

Hopf bifurcationsperiodic boundary conditionsparabolic limitanimal communicationnonlocal hyperbolic modelsnonlocal parabolic models

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) First-order nonlinear hyperbolic equations (35L60) Bifurcations in context of PDEs (35B32) General biology and biomathematics (92B05) Group-invariant bifurcation theory in infinite-dimensional spaces (58E09) Symmetries, invariants, etc. in context of PDEs (35B06) Pattern formations in context of PDEs (35B36)

Related Items (5)

Non-local kinetic and macroscopic models for self-organised animal aggregations ⋮ Eckhaus instability of stationary patterns in hyperbolic reaction-diffusion models on large finite domains ⋮ Biological modeling with nonlocal advection–diffusion equations ⋮ Non-local parabolic and hyperbolic models for cell polarisation in heterogeneous cancer cell populations ⋮ On the consistency of the reaction-telegraph process within finite domains

Uses Software

• Chemotaxis

Cites Work

• A nonlocal continuum model for biological aggregation
• Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review
• Travelling waves in hyperbolic chemotaxis equations
• Derivation of hyperbolic models for chemosensitive movement
• Traveling bands of chemotactic bacteria: a theoretical analysis
• Weakly nonlinear analysis of a hyperbolic model for animal group formation
• PDE models for chemotactic movements: parabolic, hyperbolic and kinetic.
• A Poincaré-Bendixson theorem for scalar reaction diffusion equations
• Double milling in self-propelled swarms from kinetic theory
• A stochastic model related to the telegrapher's equation
• A non-local model for a swarm
• Invariance principles for hyperbolic random walk systems
• The symmetry perspective. From equilibrium to chaos in phase space and physical space
• A continuum approach to modelling cell-cell adhesion
• Modeling group formation and activity patterns in self-organizing collectives of individuals
• The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations
• Simultaneous use of different communication mechanisms leads to spatial sorting and unexpected collective behaviours in animal groups
• State transitions and the continuum limit for a 2D interacting, self-propelled particle system
• The Diffusion Limit of Transport Equations II: Chemotaxis Equations
• INDIVIDUAL-BASED MODELS FOR BACTERIAL CHEMOTAXIS IN THE DIFFUSION ASYMPTOTICS
• Hyperbolic versus Parabolic Asymptotics in Kinetic Theory toward Fluid Dynamic Models
• PEDESTRIAN FLOW MODELS WITH SLOWDOWN INTERACTIONS
• ANALYSIS OF HOPF/HOPF BIFURCATIONS IN NONLOCAL HYPERBOLIC MODELS FOR SELF-ORGANISED AGGREGATIONS
• Codimension-Two Bifurcations in Animal Aggregation Models with Symmetry
• DIFFUSION IN A CONTINUUM MODEL OF SELF-PROPELLED PARTICLES WITH ALIGNMENT INTERACTION
• The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes
• Spatial Structures and Periodic Travelling Waves in an Integro-Differential Reaction-Diffusion Population Model
• Complex spatial group patterns result from different animal communication mechanisms
• Unnamed Item
• Unnamed Item

This page was built for publication: Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation