Practical Bifurcation Theory1 John J. Tyson Virginia Polytechnic Institute & Virginia Bioinformatics Institute.

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Presentation transcript:

Practical Bifurcation Theory1 John J. Tyson Virginia Polytechnic Institute & Virginia Bioinformatics Institute

Practical Bifurcation Theory2 References Strogatz, Nonlinear Dynamics and Chaos (Addison Wesley) Kuznetsov, Elements of Applied Bifurcation Theory (Springer) XPP-AUT Oscill8

Practical Bifurcation Theory3 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 of Parameter Space

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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”

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Practical Bifurcation Theory55 Torus Heteroclinic

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Practical Bifurcation Theory57 Torus ?

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Practical Bifurcation Theory60 Trajectories for the Fold-Hopf bifurcations as illustrated in the Kuznetsov’s book.

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