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

  • Livia OwenEmail author
  • Eric Harjanto
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 295)

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.

Keywords

AUTO AUTO-07p Dynamical system Bifurcation diagram Hopf bifurcation Fold bifurcation 

Notes

Acknowledgements

We would like to express our sincere gratitude to SEAMS School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA) committee for offering us this opportunity. Livia Owen acknowledges the financial support from The Indonesian Education Scholarship Program (LPDP), Ministry of Finance of the Republic of Indonesia.

References

  1. 1.
    Doedel, E.J., Champneys, A.R., Dercole, F. et al.: AUTO-07P: continuation and bifurcation software for ordinary differential equations. California Institute of Technology, Pasadena, California (2008)Google Scholar
  2. 2.
    Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, vol. 112, 2nd edn. Springer, New York (1998)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Analysis and Geometry Group, Faculty of Mathematics and Natural SciencesInstitut Teknologi BandungBandungIndonesia

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