Reduction process, bifurcation equations
In this chapter the first, basic step in the treatment of nonlinear stability problems is presented, namely, the reduction of the given n- or infinite-dimensional system to a generally low-dimensional bifurcation system. 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.
KeywordsEquilibrium Position Bifurcation Point Invariant Manifold Center Manifold Fredholm Operator
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