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Boyce e diprima8/31/2023 Instead, conclusions about the stability of a critical point are obtained by constructing a suitable auxiliary function.Ģ Physical Principles Liapunov’s second method is a generalization of two physical principles for conservative systems. In this section we discuss Liapunov’s second method, or direct method, in which no knowledge of the solution is required. Also, for an asymptotically stable critical point, we may want to investigate the basin of attraction, for which the localized almost linear theory provides no information. However, no conclusion can be drawn when the critical point is a center of the corresponding linear system. In Section 9.3 we showed how the stability of a critical point of an almost linear system can usually be determined from a study of the corresponding linear system. DiPrima, ©2009 by John Wiley & Sons, Inc. Boyce."- Presentation transcript:ġ Boyce/DiPrima 9th ed, Ch 9.6: Liapunov’s Second Method Elementary Differential Equations and Boundary Value Problems, 9th edition, by William E. Presentation on theme: "Boyce/DiPrima 9th ed, Ch 9.6: Liapunov’s Second Method Elementary Differential Equations and Boundary Value Problems, 9th edition, by William E.
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