Continuation of limit cycles near saddle homoclinic points using splines in phase space

Nandakumar, K and Chatterjee, Anindya (2009) Continuation of limit cycles near saddle homoclinic points using splines in phase space. In: Nonlinear Dynamics, 57 (3). pp. 383-399.

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Abstract

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.

Item Type:	Journal Article
Publication:	Nonlinear Dynamics
Publisher:	Springer
Keywords:	Copyright of this article belongs to Springer.
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	31 Jul 2009 03:36
Last Modified:	19 Sep 2010 05:39
URI:	http://eprints.iisc.ac.in/id/eprint/21833

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