Numerical Algorithms for Nonlinear Dynamics
&
Existing Program Implementations
Software for bifurcation analysis
Bifurcation analysis capabilities
Numerical Algorithms for Nonlinear Dynamics
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SGTND main : : Algorithms and Programms : : Software for bifurcation analysis : : Basic features |
(based on the table ftom the lecture slides by Yury A. Kuznetsov at Heidelberg)
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time-integration |
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Poincare maps |
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continuation of equilibria |
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detection of branch points and codim 1 bifurcations (limit and Hopf points) of equilibria |
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computation of normal forms for codim 1 bifurcations of equilibria |
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continuation of codim 1 bifurcations of equilibria |
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detection of codim 2 equilibrium bifurcations |
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continuation of limit cycles |
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detection of branch points and codim 1 bifurcations |
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continuation of codim 1 bifurcations of cycles |
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branch switching at equilibrium and cycle bifurcations |
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continuation of branching points of equilibria and cycles |
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computation of normal forms for codim 1 bifurcations of cycles |
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detection of codim 2 bifurcations of cycles |
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continuation of orbits homoclinic to equilibria |
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1)Normal forms are computed for simple bifurcations, e.g. folds and flip. For a fold it makes possible to distinguish cusps. For a flip the coefficient is computed defining the degeneracy condition, making possible to distinguish between subcritical and supercritical bifurcations.