The aim of this work has been to analyse global bifurcations arising in a laser with injected signal and in a catalytic reaction on a surface of Pt, from the point of view of dynamical systems theory. The 3-dimensional ordinary differential equation which models the laser was found to contain a homoclinic orbit to a saddle-focus equilibrium, what corresponds to the Sil'nikov phenomenon. It is well known that under certain eigenvalue relationship, this global bifurcation displays chaotic dynamics. In this problem the fixed point was also involved in a Hopf/saddle-node local bifurcation. The interaction of the Sil'nikov phenomenon and the saddle-node bifurcation was studied by constructing a geometrical model. It was determined that as the homoclinic orbit approaches the saddle-node bifurcation, the chaotic dynamics vanishes. Also "bubbles " of periodic orbits, in the period vs. parameter bifurcation diagram, were analysed in this context. The catalysis model, on the other hand, is an excitable reaction-diffusion equation. This equation, in one spatial dimension, displays a transition to spatiotemporal chaos, where an incoherent collection of pulse-like solutions are found. Homoclinic and heteroclinic orbits in
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