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Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains and explores geometric singular perturbation theory and its(More)
In this paper we introduce a conceptual model for vegetation patterns that generalizes the Klausmeier model for semi-arid ecosystems on a sloped terrain [23]. Our model not only incorporates downhill flow, but also linear or nonlinear diffusion for the water component. To relate the model to observations and simulations in ecology, we first consider the(More)
In this paper we prove existence of multiple-front solutions in a class of coupled reaction-diiusion equations with a small parameter. By a travelling wave Ansatz we reduce the problem to a four-dimensional system of ordinary diierential equations and prove existence of a large variety of n-jump homoclinic and heteroclinic solutions, n = 1; 2; 3; : : :(More)
In this paper we study the creation of homoclinic orbits by saddle-node bifurca-tions. Inspired on similar phenomena appearing in the analysis of so-calledìocalized structures' in modulation or amplitude equations, we consider a family of nearly in-tegrable, singularly perturbed three dimensional vector elds with two bifurcation parameters a and b. The O(")(More)
In the central nervous system, alpha-motor neurons play a key role in the chain that results in muscles producing force. A new non-invasive technique to measure the electrical activity involved with force production called High Density Surface Electromyography (HDsEMG) has been proven to be effective in providing novel clinical information on the way(More)
The Ginzburg-Landau equation is essential for understanding the dynamics of patterns in a wide variety of physical contexts. It governs the evolution of small amplitude instabilities near criticality. It is well known that the (cubic) Ginzburg-Landau equation has various unstable solitary pulse solutions. However, such localized patterns have been observed(More)
The care of asthmatic children is commonly sub-optimal. Accordingly the costs and benefits of sending a district health authority community nurse, who had specific training in asthma management, into the homes of 43 families with asthmatic children were assessed. During the six months the asthma nurse visited these homes, the children developed and(More)
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