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Practical Bifurcation Theory

Practical Bifurcation Theory. John J. Tyson Virginia Polytechnic Institute & Virginia Bioinformatics Institute. References. Strogatz, Nonlinear Dynamics and Chaos (Addison Wesley) Kuznetsov, Elements of Applied Bifurcation Theory (Springer) XPP-AUT www.math.pitt.edu/~bard/xpp

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Practical Bifurcation Theory

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  1. Practical Bifurcation Theory John J. Tyson Virginia Polytechnic Institute & Virginia Bioinformatics Institute Practical Bifurcation Theory

  2. References • Strogatz, Nonlinear Dynamics and Chaos (Addison Wesley) • Kuznetsov, Elements of Applied Bifurcation Theory (Springer) • XPP-AUT www.math.pitt.edu/~bard/xpp • Oscill8 http://oscill8.sourceforge.net Practical Bifurcation Theory

  3. Molec Genetics Biochemistry Cell Biology Molecular Mechanism The Dynamical Perspective Kinetic Equations The Curse of Parameter Space State Space, Vector Field Attractors, Transients, Repellors Bifurcation Diagrams Signal-Response Curves Practical Bifurcation Theory

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  5. Generic Bifurcations of Dynamical Systems • Saddle-Node • Hopf • Cyclic Fold • Saddle Loop • Saddle-Node Invariant Circle Rene Thom (1972), “Structural Stability and Morphogenesis” Practical Bifurcation Theory

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