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

摘要

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 and also transient solutions.