This application allows the exploration of Ordinary Differential Equation-based dynamical systems through a user-friendly graphical interface. It features a large database of nonlinear systems and provides easy-to-read visual representations of the results.
DEREK is an application designed for exploring dynamical systems described by Ordinary Differential Equations. Offering a simple interface with mostly graphical representations of system results, DEREK boasts a fantastic database of known nonlinear dynamical systems allowing users to explore systems of up to 25th order efficiently.
One of the main features of DEREK is the ability to specify a description of the system as a set of differential equations, initial conditions, as well as the parameters in equations. The software allows you to find errors in the description of the system, specifying precisely the place and nature of the error. DEREK even automatically chooses the parameters of the numerical method for solving the system.
Making it easy to build visual graphics for solutions and any dependent on solution variables, DEREK can even scale field plots to best display them. For more customized results, manual layout is also an option.
Additionally, DEREK allows the exploration of the three-dimensional image of the phase trajectory. The software can rotate a three-dimensional phase trajectory, as well as zoom in and out of it.
DEREK offers various special methods for the analysis of dynamical systems. These include the construction of a "family" of solutions that depend on one or two parameters, or on a set of different initial conditions. DEREK can also build "Poincare sections," which are the set of points of intersection of the system trajectory with a given plane. Finally, the software can calculate "Lyapunov exponents," which are sets of numbers that characterize the behavior of the system at infinite evolution and do not depend on initial conditions (except, perhaps, some exceptions). Overall, DEREK is a versatile and reliable software for exploring dynamical systems.
One of the main features of DEREK is the ability to specify a description of the system as a set of differential equations, initial conditions, as well as the parameters in equations. The software allows you to find errors in the description of the system, specifying precisely the place and nature of the error. DEREK even automatically chooses the parameters of the numerical method for solving the system.
Making it easy to build visual graphics for solutions and any dependent on solution variables, DEREK can even scale field plots to best display them. For more customized results, manual layout is also an option.
Additionally, DEREK allows the exploration of the three-dimensional image of the phase trajectory. The software can rotate a three-dimensional phase trajectory, as well as zoom in and out of it.
DEREK offers various special methods for the analysis of dynamical systems. These include the construction of a "family" of solutions that depend on one or two parameters, or on a set of different initial conditions. DEREK can also build "Poincare sections," which are the set of points of intersection of the system trajectory with a given plane. Finally, the software can calculate "Lyapunov exponents," which are sets of numbers that characterize the behavior of the system at infinite evolution and do not depend on initial conditions (except, perhaps, some exceptions). Overall, DEREK is a versatile and reliable software for exploring dynamical systems.
What's New
Version 3.0: System reconstruction feature added