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Kahaner, D. K.; Lawkins, W. F.; Thompson, S.

On the use of rootfinding ODE software for the solution of a common problem in nonlinear dynamical systems. (English) Zbl 0685.65060

J. Comput. Appl. Math. 28, 219-230 (1989).
This paper describes a FORTRAN code PLOD by E. Agron, G. Gunaranta, the first author and M. A. Reed [Mathematical software: PLOD, plotted solutions of differential equations, IEEE Micro 8(4) (1988)] for the numerical solution of ordinary differential equations (ODEs), which is particularly suited to calculate Poincaré sections for nonlinear models of dynamics and includes graphics capabilities.
The code PLOD is based on Adams and Gear formulas with variable step and variable order, and it has also the so called g-stop facility which allows to stop the integration when some prescribed auxiliary conditions of interest are satisfied. In the paper, the authors briefly outline the possibilities of PLOD in studying numerically some dynamical systems which arise in several problems of real life. In particular, the bifurcations in the model of V. Franceschini [Physica D 6, 285–304 (1983; Zbl 1194.34075)] are computed.
Reviewer: M.Calvo

Cited in 2 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65K10 Numerical optimization and variational techniques
34A34 Nonlinear ordinary differential equations and systems
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
93C10 Nonlinear systems in control theory
37-XX Dynamical systems and ergodic theory

Keywords:

FORTRAN code PLOD; Poincaré sections; Adams and Gear formulas; variable step; variable order; dynamical systems; bifurcations

Citations:

Zbl 1194.34075

Software:

UNCMND; pchip; FORSIM VI
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References:

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