2011
DOI: 10.1088/1742-6596/319/1/012017
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Renormalization Group as a Probe for Dynamical Systems

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Cited by 6 publications
(13 citation statements)
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References 276 publications
(377 reference statements)
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“…To the authors' knowledge these higher order flow equations are reported for the first time in the literature. We remark that above flow equations match exactly with O(ε 3 ) flow equations of the Van der Pol equation [8]. Although not done explicitly, we expect that the O (ε 4 ) VdP flow equations would also have the equivalent forms.…”
Section: Computation Of Amplitude By Rg Methodsmentioning
confidence: 54%
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“…To the authors' knowledge these higher order flow equations are reported for the first time in the literature. We remark that above flow equations match exactly with O(ε 3 ) flow equations of the Van der Pol equation [8]. Although not done explicitly, we expect that the O (ε 4 ) VdP flow equations would also have the equivalent forms.…”
Section: Computation Of Amplitude By Rg Methodsmentioning
confidence: 54%
“…We report here the RG solution upto order 3. To the authors' knowledge this seems to be the first higher order computation other than second order computations reported so far by various authors [6,8]. A comparison of the amplitude of the periodic cycle with the exact computations reveals that even the present higher order perturbative approximations fails to give accurate estimation for moderate values of ε.…”
Section: Introductionmentioning
confidence: 68%
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“…Similar to the limit cycle, another type of closed orbit observed in both linear and nonlinear systems is called a center [17,84], as illustrated in Fig. 2.1.…”
Section: Limit Cycle Oscillationsmentioning
confidence: 99%
“…2.12d). The amplitude of centers in linear systems is dependent on the initial condition, while centers in conservative nonlinear systems are more robust against any perturbations [84]. Examples of centers are unforced undamped Duffing oscillator, Lotka-Volterra system, Lienard system, etc.…”
Section: Limit Cycle Oscillationsmentioning
confidence: 99%