Van der Pol oscillator

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Flow* vanderpol.model

Model description

The dynamics of the Van der Pol oscillator can be defined by the following ODE

    \[ \left\{ \begin{array}{lcl} \dot{x} & = & y \\ \dot{y} & = & \mu\cdot(1 - x^2)\cdot y - x \end{array} \right. \]

wherein \mu is a constant whose typical value is 1.

Reachability settings

We consider the initial set x \in [1.25 , 1.55], y \in [2.25 , 2.35] which is used in [1].

vanderpol

Result

As an example, the following figure shows an overapproximation, computed by Flow*, of the reachable set in the time horizon [0,7] .

References

[1] M. Althoff, O. Stursberg, M. Buss. Reachability analysis of nonlinear systems with uncertain parameters using conservative linearization. In Proceedings of the 47th IEEE Conference on Decision and Control (CDC’08), pages 4042 – 4048, IEEE, 2008.