Numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations

摘要

The computation of periodic orbits of autonomous ordinary differential equations is considered. A new method especially suited for computing limit cycles that bifurcate from stationary solutions is established. This novel approach is very easy to implement, the method requiring the programming of the right-hand side only. Another topic of this paper is the demonstration of how a direct method should be applied in the computation of Hopf bifurcation points. These methods solve boundary-value problems by means of standard software only. The methods are tested on four examples arising in different application areas including chemistry and biology.