57 citations · 116 across the 6 of their papers we have counts for
6 papers
Subcritical Turing bifurcation and the morphogenesis of localised patterns
Víctor Breña-Medina, Alan Champneys
Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism.…
Multiple Local and Global Bifurcations and Their Role in Quorum Sensing Dynamics
Mariana Harris, Viviana Rivera-Estay, Pablo Aguirre +1
Quorum sensing governs bacterial communication, playing a crucial role in regulating population behaviour. We propose a mathematical model that uncovers chaotic dynamics within quo…
Hybrid reaction-diffusion and clock-and-wavefront model for the arrest of oscillations in the somitogenesis segmentation clock
Jesús Pantoja-Hernández, Víctor F. Breña-Medina, Moisés Santillán
The clock and wavefront paradigm is arguably the most widely accepted model for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based u…
A case study of multiple wave solutions in a reaction-diffusion system using invariant manifolds and global bifurcations
Edgardo Villar-Sepúlveda, Pablo Aguirre, Víctor F. Breña-Medina
A thorough analysis is performed to find traveling waves in a qualitative reaction-diffusion system inspired by a predator-prey model. We provide rigorous results coming from a sta…
Spot dynamics in a reaction-diffusion model of plant root hair initiation
D. Avitabile, V. F. Breña-Medina, M. J. Ward
We study pattern formation in a 2-D reaction-diffusion (RD) sub-cellular model characterizing the effect of a spatial gradient of a plant hormone distribution on a family of G-prot…
Stripe to spot transition in a plant root hair initiation model
V. F. Breña-Medina, D. Avitabile, A. R. Champneys +1
A generalised Schnakenberg reaction-diffusion system with source and loss terms and a spatially dependent coefficient of the nonlinear term is studied both numerically and analytic…