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Approximating the Amplitude and Form of Limit Cycles in the Weakly Nonlinear Regime of Lienard Systems | | Jose-Luis Lopez
; Ricardo Lopez-Ruiz
; | | Date: |
31 Mar 2006 | | Subject: | Adaptation and Self-Organizing Systems | | Abstract: | Li’{e}nard equations, $ddot{x}+epsilon f(x)dot{x}+x=0$, with $f(x)$ an even continuous function are considered. In the weakly nonlinear regime ($epsilon o 0$), the number and an order zero in $epsilon$ approximation of the amplitude of limit cycles present in this type of systems can be obtained by applying a methodology recently proposed by the authors [L’opez-Ruiz R, L’opez JL. Bifurcation curves of limit cycles in some Li’enard systems. Int J Bifurcat Chaos 2000; 10:971-980]. In the present work, that method is carried forward to higher orders in $epsilon$ and is embedded in a general recursive algorithm capable to approximate the form of the limit cycles and to correct their amplitudes as an expansion in powers of $epsilon$. Several examples showing the application of this scheme are given. | | Source: | arXiv, nlin/0603076 | | Services: | Forum | Review | PDF | Favorites | |
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