Both bifurcation theory and catastrophe theory are studies of smoothsystems， focusing on properties that seem manifestly non-smooth.Bifurcations are sudden changes that occur in a system as one ormote parameters are vaned_ Catastrophe theory is accurately describedas singularity theory and its applications. These two theories are important tools in the study of differentialequations and of related physical systems. Analyzing the bifurcationsor singularities of a system provides useful qualitative informationabout its behaviour. The authors have written this book with refreshing clarity. Theexposition is masterful， with penetrating insights.
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