PDE

At this point, you may be asking yourself: ‘All nice and well, but how can I control the relative time scales between the various models?’ And I’d respond:

Introduction A 2D activator-inhibitor model (Gierer and Meinhardt, 1972), solved in a irregular domain that is loaded from an image file. Spot pattern in Gierer-Meinhardt model with irregular domain.

In this course, we have constructed a small multiscale model in which an ODE model, a CPM model and a PDE model are mutually coupled to each other. The main aim was to show how one can couple such models with relative ease in Morpheus and how you can control such couplings.

Introduction This model shows the pattern formation abilities of Turing’s linear activator-inhibitor model (Miyazawa et al., 2010). It shows how to vary parameters as a function of space. Spots and stripes appear under various conditions in linear Turing model.

Introduction This example uses the Barkley model of excitable media, similar to the Fitzhugh-Nagumo model to show how to model and visualize reaction-diffusion models in 3D. Scroll wave appears in Barkley model of excitable media in 3D.

Spatio-temporal model of self-organisation inside the zebrafish posterior lateral line primordium Introduction The zebrafish posterior lateral line primordium is the precursor of the neuromasts, which form sensory organs responding to fluid flow.

Spatio-temporal model of BMP signaling Introduction Juxtaposed sources of bone morphogenetic protein (BMP) and Nodal signaling molecules induce the formation of a full body axis in zebrafish embryos. Soh et al.

Introduction Larvae of the nematode Caenorhabditis elegans aggregate into clusters of several hundred moving individuals when starved during their first larval stage (see video below). Avery et al. proposed that starved larvae produce and respond chemotactically to two diffusible chemical signals, a short-range attractant and a longer range repellent.

Introduction This paper describes the regimes of behaviour of a 1D spatial (PDE) model for the mutually antagonistic Rac-Rho GTPases, with feedback to and from the extracellular matrix (ECM). Description The Rac-Rho submodels are bistable, and ECM enhances Rho activation.

Introduction This paper describes the regimes of behaviour of a 1D spatial (PDE) model for the mutually antagonistic Rac-Rho GTPases, with feedback to and from the extracellular matrix (ECM). Description The Rac-Rho submodels are bistable, and ECM enhances Rho activation.