Application for the exploring of dynamical systems, which can be described by Ordinary Differential Equations with simple interface and mostly graphical representation of the results. Includes some special methods for the analysis of dynamical systems like Poincare sections and Lyapunov exponents. Contains great database of known nonlinear dynamical systems. Allows to explore systems of up to 25th order by using efficient numerical methods.
Main features-DEREK allows:
-specify a description of the system as a set of differential equations, initial conditions, as well as the parameters in equations
-find errors in the description of the system, specifying precisely the place and nature of the error;
-automatically choose the parameters of the numerical method for solving the system;
-build visual graphics for solutions and any dependent on solutions variables. DEREK itself can scale to field plots for best display them, but admits to perform a layout manually
-explore the three-dimensional image of the phase trajectory. DEREK can rotate a three-dimensional phase trajectory, as well as zoom in and out of her.
DEREK also includes some special methods for the analysis of dynamical systems:
-construction of a “family” of solutions that depend on one or two parameters, or on a set of different initial conditions;
-building a “Poincare sections” – the set of points of intersection of the system trajectory with a given plane.
-calculation of “Lyapunov exponents” – sets of numbers that characterize the behavior of the system at infinite evolution and do not depend on the initial conditions (except, perhaps, some exceptions).