practical bifurcation theory1 john j. tyson virginia polytechnic institute & virginia...
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Practical Bifurcation Theory 1
Practical Bifurcation Theory
John J. TysonVirginia Polytechnic Institute
& Virginia Bioinformatics Institute
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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
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Practical Bifurcation Theory 3
The Dynamical Perspective
Molec Genetics Biochemistry Cell Biology
Kinetic Equations
State Space, Vector Field
Attractors, Transients, Repellors
Bifurcation Diagrams
Molecular Mechanism
Signal-Response Curves
The Curse ofParameter
Space
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Practical Bifurcation Theory 4
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Practical Bifurcation Theory 5
Generic Bifurcations ofDynamical Systems
•Saddle-Node•Hopf•Cyclic Fold•Saddle Loop•Saddle-Node Invariant Circle
Rene Thom (1972), “StructuralStability and Morphogenesis”
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Practical Bifurcation Theory 6
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Torus
Heteroclinic
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Torus?
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Trajectories for the Fold-Hopf bifurcationsas illustrated in the Kuznetsov’s book.
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