From First Lyapunov Coefficients to Maximal Canards

@article{Kuehn2010FromFL,
  title={From First Lyapunov Coefficients to Maximal Canards},
  author={C. Kuehn},
  journal={Int. J. Bifurc. Chaos},
  year={2010},
  volume={20},
  pages={1467-1475}
}
  • C. Kuehn
  • Published 2010
  • Mathematics, Physics, Computer Science
  • Int. J. Bifurc. Chaos
  • Hopf bifurcations in fast–slow systems of ordinary differential equations can be associated with a surprisingly rapid growth of periodic orbits. This process is referred to as canard explosion. The key step in locating a canard explosion is to calculate the location of a special trajectory, called a maximal canard, in parameter space. A first-order asymptotic expansion of this location was found by Krupa and Szmolyan [2001a, 2001b, 2001c] in the framework of a "canard point"-normal-form for… CONTINUE READING
    From Hopf Bifurcation to Limit Cycles Control in Underactuated Mechanical Systems
    • 3
    • PDF
    A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications
    • C. Kuehn
    • Computer Science, Mathematics
    • 2013
    • 69
    • PDF
    Dynamical analysis of evolution equations in generalized models
    • 18
    • PDF
    On estimation of the global error of numerical solution on canard-cycles
    • 1
    Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs
    • 18
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 41 REFERENCES
    Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
    • 1,276
    • Highly Influential
    Singular Hopf Bifurcation in Systems with Fast and Slow Variables
    • 55
    Sungular hopf bifurcation to relaxation oscillations
    • 147
    When Shil'nikov Meets Hopf in Excitable Systems
    • 45
    • PDF
    Singular Hopf Bifurcation in Systems with Two Slow Variables
    • 107
    • PDF
    Relaxation Oscillation and Canard Explosion
    • 308
    Homoclinic Orbits of the FitzHugh-Nagumo Equation: Bifurcations in the Full System
    • 37
    • PDF
    HOMOCLINIC ORBITS OF THE FITZHUGH-NAGUMO EQUATION: THE SINGULAR-LIMIT
    • 41
    • Highly Influential
    • PDF
    Computing Slow Manifolds of Saddle Type
    • 64
    • PDF