Abstract

A nonlinear phenomenon in nature is often modeled by a system of differential equations with parameters. The bifurcation occurs when a parameter varies in such systems, causing a qualitative change in its solution. In this paper, we study one of the most exciting bifurcations, which is Hopf bifurcation. We use tools from algebraic topology to analyze and reveal supercritical and subcritical Hopf bifurcations.

Keywords: Supercritical Hopf bifurcation; subcritical Hopf bifurcation; stable limit cycle; unstable limit cycle; homological Conley index; Morse sets.

MSC: 55-08, 37B30, 37G15, 37M20

DOI: 10.57016/MV-rx451is8

Pages:  216$-$224     

Volume  75 ,  Issue  3 ,  2023