Abstract
The accurate computation of periodic orbits and the precise knowledge of their bifurcation properties are very important for studying the behavior of many dynamical systems of physical interest. In this paper, we present an iterative method for computing periodic orbits, which has the advantage of improving the convergence of previous Newton-like schemes, especially near bifurcation points. This method is illustrated here on a conservative, nonlinear Mathieu equation, for which a sequence of period-doubling bifurcations is followed, long enough to obtain accurate estimates of the two universal scaling constants α, β, as well as the universal rate δ, by which the bifurcation values of a parameter q = qk, k =1, 2, 3, ..., tend to their limiting value, q∞ < ∞, as k increases.
| Original language | English |
|---|---|
| Pages (from-to) | 1-14 |
| Number of pages | 14 |
| Journal | Journal of Computational Physics |
| Volume | 88 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1990 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Computer Science Applications
- Physics and Astronomy(all)
Cite this
A convergence-improving iterative method for computing periodic orbits near Bifurcation Points. / Vrahatis, Michael N.; Bountis, Tassos; Budinsky, Nurit.
In: Journal of Computational Physics, Vol. 88, No. 1, 1990, p. 1-14.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A convergence-improving iterative method for computing periodic orbits near Bifurcation Points
AU - Vrahatis, Michael N.
AU - Bountis, Tassos
AU - Budinsky, Nurit
PY - 1990
Y1 - 1990
N2 - The accurate computation of periodic orbits and the precise knowledge of their bifurcation properties are very important for studying the behavior of many dynamical systems of physical interest. In this paper, we present an iterative method for computing periodic orbits, which has the advantage of improving the convergence of previous Newton-like schemes, especially near bifurcation points. This method is illustrated here on a conservative, nonlinear Mathieu equation, for which a sequence of period-doubling bifurcations is followed, long enough to obtain accurate estimates of the two universal scaling constants α, β, as well as the universal rate δ, by which the bifurcation values of a parameter q = qk, k =1, 2, 3, ..., tend to their limiting value, q∞ < ∞, as k increases.
AB - The accurate computation of periodic orbits and the precise knowledge of their bifurcation properties are very important for studying the behavior of many dynamical systems of physical interest. In this paper, we present an iterative method for computing periodic orbits, which has the advantage of improving the convergence of previous Newton-like schemes, especially near bifurcation points. This method is illustrated here on a conservative, nonlinear Mathieu equation, for which a sequence of period-doubling bifurcations is followed, long enough to obtain accurate estimates of the two universal scaling constants α, β, as well as the universal rate δ, by which the bifurcation values of a parameter q = qk, k =1, 2, 3, ..., tend to their limiting value, q∞ < ∞, as k increases.
UR - http://www.scopus.com/inward/record.url?scp=0011332685&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0011332685&partnerID=8YFLogxK
U2 - 10.1016/0021-9991(90)90239-W
DO - 10.1016/0021-9991(90)90239-W
M3 - Article
AN - SCOPUS:0011332685
VL - 88
SP - 1
EP - 14
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
IS - 1
ER -