Bifurcation theory and applications

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In the study of systems of mathematical equations, Bifurcation Theory explains how small changes in the parameters of the equations can lead to disproportionate changes in the solutions of the equations. Bifurcation Theory tells us that this "cause and effect" relationship is not arbitrary, but is most likely to occur only in a few typical (or generic) ways, called bifurcations, which mathematicians are beginning to understand fairly well. In the present work, the equations under study are nonlinear systems of differential equations; that is, equations that determine how a system evolves with time. Equations of this kind are widely used in science, and help in the understanding of many kinds of real systems, for example in physics, engineering and biology.