| Author(s): |
Sita Ramamurti; David E. Gilsinn; |
| Title: |
Bicubic B-Spline Surface Approximation of Invariant Tori |
| Published: |
October 20, 2010 |
| Abstract: |
The invariant torus of a coupled system of Van der Pol oscillators is approximated using bicubic B-splines. The paper considers the case of strong nonlinear coupling. In particular, the shapes of invariant torii for the Van der Pol coupling parameter $\lambda$ are computed in the range [0.1, 2.0]. Comparisons are given with results obtained by the MATLAB differential equation solver ode45. Very good normed residual errors of the determining equations for the approximate tori for the cases $\lambda = 0.1,\ 0.6$ are shown. At the upper limit of $\lambda = 2.0$ memory errors occured during the optimization phase for solving the determining equations so that full optimization for some knot sets was not achieved, but a visual comparison of the resulting invariant torus figure showed a close similarity to the solution using ode45. |
| Citation: |
NIST Interagency/Internal Report (NISTIR) - 7731 |
| Pages: |
32 pp. |
| Keywords: |
bicubic B-splines; determining equations; invariant torus; large parameter case; optimization; Van der Pol oscillators |
| Research Areas: |
Software, Math |
| PDF version: |
 Click here to retrieve PDF version of paper (2MB) |
