Turing instabilities at Hopf bifurcation
From MaRDI portal
Publication:1041278
DOI10.1007/s00332-009-9041-6zbMath1188.35104OpenAlexW2060665770MaRDI QIDQ1041278
M. R. Ricard, Stéphane Mischler
Publication date: 2 December 2009
Published in: Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00332-009-9041-6
Reaction-diffusion equations (35K57) Averaging method for ordinary differential equations (34C29) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)
Related Items (27)
Pattern formation of a coupled two-cell Schnakenberg model ⋮ Pattern formation of a diffusive predator-prey model with strong allee effect and nonconstant death rate ⋮ Turing instability of the periodic solutions for reaction-diffusion systems with cross-diffusion and the patch model with cross-diffusion-like coupling ⋮ Nonlinear stability and numerical simulations for a reaction-diffusion system modelling Allee effect on predators ⋮ Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction-diffusion model ⋮ Bifurcation analysis and spatiotemporal patterns in delayed Schnakenberg reaction-diffusion model ⋮ Destabilization of synchronous periodic solutions for patch models ⋮ Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay ⋮ Patterning of nonlocal transport models in biology: the impact of spatial dimension ⋮ Chaotic behavior in diffusively coupled systems ⋮ Pattern formation, long-term transients, and the Turing-Hopf bifurcation in a space- and time-discrete predator-prey system ⋮ Global existence and boundedness in a reaction-diffusion-taxis system with three species ⋮ Matrix-oriented discretization methods for reaction-diffusion PDEs: comparisons and applications ⋮ Devising efficient numerical methods for oscillating patterns in reaction-diffusion systems ⋮ Diffusion-driven destabilization of spatially homogeneous limit cycles in reaction-diffusion systems ⋮ Transient behaviour in RDA systems of the Schnakenberg type ⋮ Bifurcations and synchronization in networks of unstable reaction-diffusion systems ⋮ Bifurcations in Twinkling Patterns for the Lengyel–Epstein Reaction–Diffusion Model ⋮ Bifurcation analysis of reaction-diffusion Schnakenberg model ⋮ Formulation of the normal form of Turing-Hopf bifurcation in partial functional differential equations ⋮ Turing instability and pattern formations for reaction-diffusion systems on 2D bounded domain ⋮ Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation ⋮ Stochastic phenomena in pattern formation for distributed nonlinear systems ⋮ Turing-Hopf patterns on growing domains: the torus and the sphere ⋮ Turing instability and Turing-Hopf bifurcation in diffusive Schnakenberg systems with gene expression time delay ⋮ Bifurcation analysis in a diffusive Segel-Jackson model ⋮ Stability analysis and pattern selection of a plankton system with nonlocal predation
Cites Work
- Unnamed Item
- Unnamed Item
- Asymptotic methods for reaction-diffusion systems: past and present
- Geometric theory of semilinear parabolic equations
- Nonlinear differential equations and dynamical systems
- The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
- Elements of applied bifurcation theory.
- Asymptotic analysis of interactions between highly conducting cylinders
- Mathematical analysis of the smallest chemical reaction system with Hopf bifurcation
- Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model
- No limit cycle in two species second order kinetics.
- Target patterns and spirals in planar reaction-diffusion systems
- Mathematical biology. Vol. 2: Spatial models and biomedical applications.
- Essential instabilities of fronts: bifurcation, and bifurcation failure
- Asymmetric Spotty Patterns for the Gray-Scott Model in R2
- Stability of a periodic solution for a system of parabolic equations
- The chemical basis of morphogenesis
- Stability of spatially periodic pulse patterns in a class of singularly perturbed reaction-diffusion equations
- Averaging methods in nonlinear dynamical systems
This page was built for publication: Turing instabilities at Hopf bifurcation
