Analysis of the effects of geometry and cross-diffusion in pattern formation

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• Gulsemay YIGIT (Bahcesehir University)
• Thursday 07 December 2023, 14:00-15:00
• Seminar Room 2, Newton Institute.

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MMV - Mathematics of movement: an interdisciplinary approach to mutual challenges in animal ecology and cell biology

Co-Authors:  Wakil Sarfaraz, Raquel Barreira, Anotida Madzvamuse In this talk, we present analysis of reaction-diffusion systems to understand the role of geometry and linear cross-diffusion. By deriving conditions on the domain length for rectangular, circular and annular geometries, we generate parameter spaces associated with Turing difusion-driven instability, Hopf and trascritical instabilities. Furthermore, by selecting model parameters from the parameter spaces generated under appropriate geometry and linear cross-diffusion, we are able to demonstrate that linear cross-diffusion coupled with appropriate geometry is able to generate patterns which cannot be obtained through the classical long-range inhibition, and short-range activation mechanism for pattern formation. To support theoretical findings, finite element numerical simulations on rectangular, circular and annular geometries are presented.     

This talk is part of the Isaac Newton Institute Seminar Series series.

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