A Taylor series-based continuation method for solutions of dynamical systems

Louis Guillot (1) , Bruno Cochelin (1) , Christophe Vergez (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

This paper describes a generic Taylor series based continuation method, the so-called Asymptotic Numerical Method, to compute the bifurcation diagrams of nonlinear systems. The key point of this approach is the quadratic recast of the equations as it allows to treat in the same way a wide range of dynamical systems and their solutions. Implicit Differential-Algebraic Equations, forced or autonomous, possibly with time-delay or fractional order derivatives are handled in the same framework. The static, periodic and quasi-periodic solutions can be continued as well as transient solutions.

Domaines: Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]; Analyse numérique [math.NA]

Louis Guillot, Bruno Cochelin, Christophe Vergez. A Taylor series-based continuation method for solutions of dynamical systems. Nonlinear Dynamics, 2019, ⟨10.1007/s11071-019-04989-5⟩. ⟨hal-02274968⟩