Abstract

Qualitative theory - two-dimensional linear systems two-dimensional almost linear systems existence and non-existence of periodic solutions Floquet's theorem perturbation methods -regular and singular perturbation method of multiple scales method of averaging matched asymptotic expansions stability -definitions Liapunov's direct method - autonomous system Liapunov's direct methods - non-autonomous system hydrodynamic stability bifurcation and catastrophe - examples of bifurcation in one dimension two-dimensional problems discrete systems elementary catastrophe chaos - criteria for chaos routes to chaos.

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