CANDYS/QA
CANDYS/QA -- a software system for qualitative analysis of nonlinear dynamical systems Numerical methods are often needed if bifurcation phenomena in nonlinear dynamical systems are studied. In this paper the software system CANDYS/QA for numerical quantitative analysis is presented. A wide class of problems is treated: computation of invariant sets (e.g., steady-states and periodic orbits), path-following (continuation) of such sets, and the related bifurcation phenomena. The following bifurcation situations are detected and the corresponding critical points are calculated during path-following: turning, bifurcation, Hopf bifurcation, period-doubling, torus bifurcation points (one-parameter problems) as well as cusp and Takens-Bogdanov points (two-parameter problems). A number of newly developed methods (e.g., for computation of the Poincaré map) as well as algorithms from the literature are described to demonstrate the whole procedure of a qualitative analysis by numerical means. An illustrative example analyzed by CANDYS/QA is included
Keywords for this software
References in zbMATH (referenced in 9 articles , 1 standard article )
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Sorted by year (- Lloyd, D. J. B.; Champneys, A. R.: Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons (2005)
- Gross, Thilo; Feudel, Ulrike: Analytical search for bifurcation surfaces in parameter space (2004)
- Engelborghs, K.; Lust, K.; Roose, D.: Direct computation of period doubling bifurcation points of large-scale systems of ODEs using a Newton-Picard method (1999)
- Govaerts, W.; Kuznetsov, Yu. A.; Sijnave, B.: Bifurcations of maps in the software package \textttCONTENT (1999)
- Farantos, Stavros C.: POMULT: A program for computing periodic orbits in Hamiltonian systems based on multiple shooting algorithms (1998)
- Loskutov, A. Yu.; Rybalko, S. D.; Feudel, U.; Kurths, J.: Suppression of chaos by cyclic parametric excitation in two-dimensional maps (1996)
- Lu, Xiguan; Li, Yong; Su, Yi: Finding periodic solutions of ordinary differential equations via homotopy method (1996)
- Feudel, Fred; Feudel, Ulrike; Brandenburg, Axel: On the bifurcation phenomena of the Kuramoto-Sivashinsky equation (1993)
- Feudel, Ulrike; Jansen, Wolfgang: CANDYS/QA -- a software system for qualitative analysis of nonlinear dynamical systems (1992)