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

Abstract : 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.
Complete list of metadatas

Cited literature [43 references]  Display  Hide  Download

Contributor : Louis Guillot <>
Submitted on : Friday, August 30, 2019 - 1:25:50 PM
Last modification on : Tuesday, September 3, 2019 - 1:17:28 AM


 Restricted access
To satisfy the distribution rights of the publisher, the document is embargoed until : 2019-11-20

Please log in to resquest access to the document



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



Record views