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Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems pp 85–113Cite as

Using Dynamical System Tools in Matlab

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 119))

Abstract

Numerical tools play an important role in analyzing dynamical systems. There are many numerical packages currently available for such problems as exploration of phase portraits, initial value problems, boundary value problems and bifurcation analysis. Although these packages provide substantial information about the dynamical systems, they do not inter-operate with one another easily. Each package has its own data type, model declaration, input/output structure. Frequently one has to duplicate information on the dynamical system in question to run separate packages.

The authors would like to thank the IMA and Geometry Center at the University of Minnesota for their hospitality and support. Research partially supported by the Air Force Office of Scientific Research, the National Science Foundation and the Department of Energy.

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References

  1. U. Ascher, J. Christiansen and R.D. Russell, Collocation software for boundary-value odes, ACM Trans. Math Software 7, (1981), 209–222.

    Article  MATH  Google Scholar 

  2. U. Ascher, R. Mattheij and R. Russell, Numerical Solution of Boundary Value Problems, Prentice Hall, (1988).

    Google Scholar 

  3. Doedel, Eusebius; Keller, Herbert B. Kernévez, Jean-Pierre, Numerical analysis and control of bifurcation problems, II, Bifurcation in infinite dimensions, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 1, (1991), 4, 745–772.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, (1983).

    Google Scholar 

  5. J. Guckenheimer and I. Labouriau, Bifurcation of the Hodgkin Huxley Equations: A New Twist, Bulletin of Math. Biol., 55, (1993), 937–952.

    MATH  Google Scholar 

  6. A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its applications to conduction and excitation in nerve, J. Physiology, 117, (1952), 500–544.

    Google Scholar 

  7. http://www.netlib.org/ode/colnew

  8. Khibnik, Alexander I. Kuznetsov, Yuri A.; Levitin, Victor V.; Nikolaev, Eugene V. Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps, Homoclinic chaos. Phys., D 62, (1993), 1-4, 360–371.

    MATH  Google Scholar 

  9. Lorenz, Edwardn, Deterministic nonperiodic flow, J. Atmos. Sci., 20, (1963), 130–141.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics POSTECH Pohang Korea Center for Applied Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Won Gyu Choe

  2. Mathematics Department, Cornell University, Ithaca, NY, 14853, USA

    J. Guckenheimer

Authors
  1. Won Gyu Choe
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  2. J. Guckenheimer
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Editor information

Editors and Affiliations

  1. Applied Math 217-50, California Institute of Technology, Pasadena, CA, 91125, USA

    Eusebius Doedel

  2. Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur (LIMSI), B.P. 133, 91403, Orsay, France

    Laurette S. Tuckerman

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© 2000 Springer Science+Business Media New York

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Choe, W.G., Guckenheimer, J. (2000). Using Dynamical System Tools in Matlab. In: Doedel, E., Tuckerman, L.S. (eds) Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems. The IMA Volumes in Mathematics and its Applications, vol 119. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1208-9_4

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  • DOI: https://doi.org/10.1007/978-1-4612-1208-9_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7044-7

  • Online ISBN: 978-1-4612-1208-9

  • eBook Packages: Springer Book Archive

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