Pattern Formation and Oscillatory Dynamics in a Two-Dimensional Coupled Bulk-Surface Reaction-Diffusion System

Pattern formation in a general glycolysis reaction–diffusion system

A general reaction–diffusion system modelling glycolysis is investigated. The parameter regions for the stability and instability of the unique constant steady-state solution is derived, and the existence of time-periodic orbits and non-constant steady-state solutions are proved by the bifurcation method and Leray–Schauder degree theory. The effect of various parameters on the existence and non...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Oscillatory Dynamics for a Coupled Membrane-Bulk Diffusion Model with Fitzhugh-Nagumo Membrane Kinetics

Oscillatory dynamics associated with the coupled membrane-bulk PDE-ODE model of Gomez et al. [Phys. Rev. Lett., 98(16), (2007), 168303] in one spatial dimension is analyzed using a combination of asymptotic analysis, linear stability theory, and numerical bifurcation software. The mathematical model consists of two dynamically active membranes with Fitzhugh-Nagumo kinetics, separated spatially ...

Synchronized Oscillatory Dynamics for a 1-D Model of Membrane Kinetics Coupled by Linear Bulk Diffusion

Spatio-temporal dynamics associated with a class of coupled membrane-bulk PDE-ODE models in one spatial dimension is analyzed using a combination of linear stability theory, numerical bifurcation software, and full time-dependent simulations. In our simplified 1-D setting, the mathematical model consists of two dynamically active membranes, separated spatially by a distance 2L, that are coupled...

Pattern Formation by Reaction-diffusion

PROBLEM DEFINITION In biology, embryological development of the structure of an organism or limb is referred to as morphogenesis. As a result of morphogenesis, complex shapes and patterns can form starting from just a single cell. Two main mechanisms that contribute to the embryo’s development are cell movement and cell specialization based on cell position. These mechanisms are influenced by s...