Continuation of limit cycles near saddle homoclinic points using splines in phase space |
| |
Authors: | K Nandakumar Anindya Chatterjee |
| |
Institution: | (1) Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India |
| |
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. |
| |
Keywords: | Continuation Limit cycle Index-based variable MATCONT |
本文献已被 SpringerLink 等数据库收录! |
|