Localised spatial structures in the Thomas model

DOI10.1016/j.matcom.2021.10.030OpenAlexW3211975201MaRDI QIDQ2076739

Fahad Al Saadi, Annette L. Worthy, Haifaa Alrihieli, Mark I. Nelson

Publication date: 22 February 2022

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2021.10.030

zbMATH Keywords

homoclinic snakingTuring bifurcationweakly nonlinear stability analysislocalised patternsbelyakov-Devaney transition

Mathematics Subject Classification ID

Biology and other natural sciences (92-XX) Dynamical systems and ergodic theory (37-XX)

Uses Software

• AUTO
• AUTO-07P
• GitHub

Cites Work

• Unnamed Item
• A non-linear analysis for spatial structure in a reaction-diffusion model
• Defect-mediated snaking: a new growth mechanism for localized structures
• Snakes and ladders: localized states in the Swift-Hohenberg equation
• Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
• Exponential asymptotics of localised patterns and snaking bifurcation diagrams
• A simple global characterization for normal forms of singular vector fields
• Hysteresis, oscillations, and pattern formation in realistic immobilized enzyme systems
• A case of the generation of a periodic motion with homoclinic curves
• Abundance of stable stationary localized solutions to the generalized 1D Swift-Hohenberg equation
• Cellular buckling in long structures
• Long-time behavior of the solutions of Murray-Thomas model for interacting chemicals
• Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
• Pattern formation in a nonlinear model for animal coats
• Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
• Dissecting the snake: transition from localized patterns to spike solutions
• Bistability, wave pinning and localisation in natural reaction-diffusion systems
• Spatially localized structures in lattice dynamical systems
• Dynamics and spatiotemporal pattern formations of a homogeneous reaction-diffusion Thomas model
• Predicting the bifurcation structure of localized snaking patterns
• A three level finite element approximation of a pattern formation model in developmental biology
• Localised structures in a virus-host model
• Breathing pulses in singularly perturbed reaction-diffusion systems
• Spatially localized states in Marangoni convection in binary mixtures
• Snakes, Ladders, and Isolas of Localized Patterns
• Homoclinic snaking: Structure and stability
• Homoclinic Snakes Bounded by a Saddle-Center Periodic Orbit
• Localized patterns and semi-strong interaction, a unifying framework for reaction–diffusion systems
• Nonlinear Physics of Ecosystems
• MULTIPARAMETRIC BIFURCATIONS IN AN ENZYME-CATALYZED REACTION MODEL
• Pattern formation outside of equilibrium
• Moving and Breathing Localized Structures in Reaction-diffusion Systems

This page was built for publication: Localised spatial structures in the Thomas model