An algebraic procedure for the determination of periodic bifurcating solutions of quadratic ordinary differential equations

Abstract

The behavior of a considerable number of physical phenomena is described by periodic bifurcating solutions of quadratic Ordinary Differential Equations. The purpose of this paper is to present an algorithm consisting of a combination of Power series and Fourier Series (PES) which reduces the problem of solving the differential equations to a recursive sequence of linear algebraic ones. This algorithm is based on two theorems that, with easily verifiable algebraic conditions, ensure the existence of such solutions.

Keywords:

• ODE
• quadratic systems
• perturbation methods
• bifurcation

C. R. Categories:

• 5.15
• 5.17