Systems

In odelab, a system generalizes the notion of a right-hand side. The rationale behind having a class to model it is that there is often a particular structure present in the right hand side.

For example, the system might be a mechanical system, in which case we have to describe which part of the system is a force, and which part is a velocity (or a momentum). A system may also be compose of a fast and a slow component. It may be a partitioned system, i.e., the right-hand side may be different for different components. It may be a sum of a constant, linear part and a non-linear part, in which case some exponential integrators may be used.

It is one of the long-term goals of this project to include all the common dynamical systems used in textbooks on differential equations, such as the van der Pol, Lotka-Volterra, Kepler systems. Some of those are already available as a subclass of odelab.system.System.

Classical Systems

A collection of classical systems.

class odelab.system.classic.VanderPol(mu=1.0)

The van der Pol oscillator, defined by:

\[\begin{split}u_0' &= u_1 \\ u_1' &= μ (1-u_0^2)u_1 - u_0\end{split}\]