Stripes or spots? Nonlinear effects in bifurcation of reaction—diffusion equations on the square

Keywords

Quadratic equation, Bifurcation, Square (algebra), Nonlinear system, Diffusion

References

• Mathematical Aspects of Reacting and Diffusing SystemsPaul C. Fife — 1979
• On the theory of synchronization of lateral optic-nerve responses in Limulus. I. uniform excitation of the homogeneous retinaJ.A. Maxwell, George H. Renninger — 1980
• Non-linear properties of thermal convectionF. H. Busse — 1978
• Lectu re Notes in BiomathematicsSimon A. Levin — 1983
• Stability and bifurcationD. Sattinger — 1979

Cited by

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• Spatial patterns created by cross-diffusion for a three-species food chain modelCanrong Tian, Zhi Ling, Zhigui Lin — 2014
• Waves and Oscillations in Model Neuronal NetworksRodica Curtu — 2003
• Nonlinear analysis methods in neural field models. (Méthodes d'analyse non linéaires appliquées aux modèles des champs neuronaux)Romain Veltz — 2011
• Self-organization of grid fields under supervision of place cells in a neuron model with associative plasticityAndrey Stepanyuk — 2015
• Volume-filling and quorum-sensing in models for chemosensitive movementKevin J. Painter, Thomas Hillen — 2002
• Concentrated patterns in biological systemsMatthias Winter — 2003
• Cross-diffusion induced Turing instability in two-prey one-predator systemYing Yu, Yahui Chen, You Zhou — 2015
• Self-organization of grid fields under supervision of place cells in the model of neuron with associative plasticityAndrey Stepanyuk — 2015
• Pattern Selection and the Direction of Stripes in Two-Dimensional Turing Systems for Skin Pattern Formation of FishesHiroto Shoji, Yoh Iwasa — 2003
• Spatial patterning in modified Turing systems: Application to pigmentation patterns on marine fishJ. L. Aragón, C. Varea, Rafael A. Barrio — 1998
• Mathematically guided approaches to distinguish models of periodic patterningTom W. Hiscock, Sean G. Megason — 2015
• The mechanisms for compression and reflection of cortical wavesJulie Goulet, G. Bard Ermentrout — 2011
• Pattern selection by dynamical biochemical signals.David Palau-Ortin, Pau Formosa-Jordan, J. M. Sancho — 2015
• Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and PulsesDavid Pinto, G. Bard Ermentrout — 2001
• Dynamical transitions of Turing patternsHans G. Kaper, Shouhong Wang, Masoud Yari — 2009
• Using mathematical models to help understand biological pattern formation.Philip K. Maini — 2004
• Chemically Based Mathematical Model for Development of Cerebral Cortical Folding PatternsDeborah A. Striegel, Monica K. Hurdal — 2009
• A model for colour pattern formation in the butterfly wing of Papilio dardanusToshio Sekimura, Anotida Madzvamuse, Andrew J. Wathen — 2000
• Spontaneous polarization in eukaryotic gradient sensing: a mathematical model based on mutual inhibition of frontness and backness pathways.Atul Narang — 2005

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