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Titlebook: Nonlinear Stability and Bifurcation Theory; An Introduction for Hans Troger,Alois Steindl Book 1991 Springer-Verlag/Wien 1991 chaos.deform

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Representation of systems and definition of stability, description of a system depends on the problem one is interested in studying and on the results one wants to obtain. Hence, dealing with the same problem, completely different descriptions might be adequate if the investigations are aiming in different directions concerning the results. To clarify
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Reduction process, bifurcation equations,-dimensional system to a generally low-dimensional .. In the neighborhood of the bifurcation point this bifurcation system has the same qualitative behavior as the original system, and therefore, completely describes the local stability problem.
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Discussion of the bifurcation equations,order ((3.19) and (3.67)), a set of . difference equations (3.47), or a set of . nonlinear algebraic equations (3.58). The number . is given by the number of eigenvalues with zero real part for differential equations, or of modulus one for difference equations, or by the multiplicity of the critical
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