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The Existence and Uniqueness of Solutions
Chapter II Integral Curves Solutions of Nonlinear Systems
4 other sections not shown
according to Poisson affine transformation approach the origin asymptotically stable bounded called canonical form characteristic entering characteristic roots characteristic values circle closed curve Conditionally stable contains a regular continuous coordinates corresponding cyclic characteristic defined denote domain dt dt dt dx dx dt dx dx dz dt enters the origin exists field of linear figure finite number given integral curve interval isoclines Lemma Let us assume Liapunov function V(t,x limit cycle limit points limit set linear element linear operator linear systems Lipschitz condition logarithmic spiral metric space nonlinear system Note obtain parameter periodic solution phase plane phase space Proof quadrants region regular point saddle point satisfied segment without contact sense of Liapunov sequence simple singularity singular point spiral approaching spiral point stable according theorem trajectory uniformly stable unique vector field x^Xg