Hopf bifurcation of the sunflower equation

Abstract

In this paper, the problem of Hopf bifurcation of the sunflower equation is discussed on the basis of the newly proposed pseudo-oscillator analysis. The bifurcated periodic solution with different parameters is analyzed and compared with some results given in the literature by using the center manifold reduction and the Normal Form theory. It shows that the pseudo-oscillator analysis involves easier computation and yields better prediction on the bifurcated periodic solutions than the Norma Form theory.