Computation of focal values and stability analysis of 4-dimensional systems

Abstract

This article presents a recursive formula for computing the n-th singular point values of a class of 4-dimensional autonomous systems, and establishes the algebraic equivalence between focal values and singular point values. The formula is linear and then avoids complicated integrating operations, therefore the calculation can be carried out by computer algebra system such as Maple. As an application of the formula, bifurcation analysis is made for a quadratic system with a Hopf equilibrium, which can have three small limit cycles around an equilibrium point. The theory and methodology developed in this paper can be used for higher-dimensional systems.

Keywords

• Focal value
• limit cycle
• Hopf bifurcation