A Basic Manual for AUTO-07p in Computing Bifurcation Diagrams of a Predator-Prey Model

Abstract

This is a beginner’s manual of AUTO-07p, a continuation and bifurcation software for ordinary differential equation (ODE). AUTO package is available for Windows, Mac OS, or UNIX/Linux platform. The directory auto/07p/demos has many tutorial demos for algebraic system, ODE and partial differential equation. We focus on the continuation of solutions of system of ODE. In this manual, we will learn the main tools in AUTO by doing cusp and pp2 demos step-by-step. In the first example, we will generate one- and two-parameter bifurcation diagrams. The second example is a 2D predator-prey model with the detection of a Hopf bifurcation. We plot some orbits and time series plot. We provide two options for running AUTO, i.e., by using Unix and Python commands.