An activator-inhibitor-substrate model of side-branching used in the context pulmonary vascular and lung development is considered on supposition that spatially localized concentrations activator trigger local side-branching. The consists four coupled reaction-diffusion equations its steady solutions therefore obey an eight-dimensional spatial dynamical system one dimension (1D). Stationary str...

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we analyze the dynamical system model of the TYC strategy, with the aim of studying the viability of the TYC eradication and control strategy of an invasive species. In particular, because the constant introduction of sex-reversed trojan females fo...

Cooperators and defectors can coexist in ecological public goods games. When the game is played in two-dimensional continuous space, a reaction diffusion model produces highly irregular dynamics, in which cooperators and defectors survive in ever-changing configurations (Wakano et al., 2009. Spatial dynamics of ecological public goods. Proc. Natl. Acad. Sci. 106, 7910-7914). The dynamics is rel...

The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In these five lectures I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. These models typically take the form of nonlinear integro-differential equations. Their non-local nature has led to the development of a s...

Based on analytic calculations we identify the local symmetry breaking agent for the generation of asynchronous one dimensional waves. We explicitly show that such antisymmetric oscillatory localized structures supports trains of asynchronous waves moving on opposite sides. It has also been found that a local inhomogeneity is a requirement for such a phenomenon. We have compared our result with...

This article concerns annular ring solutions of the Gray–Scott model. In the monostable regime, annular rings are far-fromequilibrium patterns supported on annuli inside of which the activator is concentrated. The diffusive flux of inhibitor over long length scales toward such an annulus feeds the production of activator there, and the interaction is semi-strong. Numerical and experimental obse...