Numerical Simulations with XPPAUT
As we noted at the end of the Preface of the book, we're huge fans of the freely available software program XPPAUT, which was developed by G. Bard Ermentrout of the University of Pittsburgh Department of Mathematics. Roughly speaking, XPPAUT consists of two main components: XPP is a tool for numerical solution of differential equations, difference equations, delay equations, functional equations, boundary value problems, and stochastic equations. AUTO is "software for continuation and bifurcation problems in ordinary differential equations".Installation and General Pointers: Visit the XPPAUT website to download XPPAUT for either Windows, Mac, or Linux and to see installation instructions. Although we are by no means equipped to provide technical support for XPPAUT, you may click HERE for some things we found helpful when installing XPPAUT for Windows. (Generally, we prefer to use the Linux version.) We'll also mention that XPPAUT is both powerful and quirky, and we recommend that you click here for some useful hints regarding syntax, conventions and quirks.
| Chapter and Section | Equation number | Description and Notes | XPPAUT code |
|---|---|---|---|
| 1.1.1 | (1.6) | Riccati equation | ch1-riccati.ode |
| 1.4.4, 4.4.4 | (1.33), (1.36) | van der Pol's equation | ch1-van-der-Pol.ode |
| 1.4.2 | (1.28) | Duffing's equation | ch1-duffing.ode |
| 1.6.2 | (1.41) | Augmented Lotka-Volterra equations | ch1-modified-LV.ode |
| 1.7.2 | (1.53) | Vertically-vibrated pendulum | ch1-pendulum.ode |
| 3.5.2 | (3.46) | Mathieu's equation | ch3-mathieu.ode |
| 4.3.2, 5.5.2 | (4.21), (5.22) | Chemostat model | ch4-chemostat.ode |
| 4.4.2, 5.6 | (4.30), (5.26) | Activator-inhibitor model | ch4-activator-inhibitor.ode |
| 4.4.3, 5.4 | (4.32), (5.17) | Sel'kov's model for glycolysis | ch4-selkov.ode |
| 4.4.5, 5.7 | (4.36), (5.35) | Michaelis-Menten kinetics | ch4-mm.ode |
| 6.3.2, 8.6.1 | (6.28), (8.60) | Turing instability | ch6-turing.ode |
| 6.6.4 | (6.1), (6.61) | Stable and Unstable Manifolds I: Duffing's equation | ch6-duffing.ode |
| 6.7.2 | (6.22) | Stable and Unstable Manifolds II: Activator-inhibitor equations | ch6-ai.ode |