Hopf bifurcation analysis in a novel nonlinear system

The paper mainly focuses on a novel nonlinear system. More precisely, we study the stability of the equilibrium points and basic dynamic properties of the nonlinear system by means of nonlinear dynamics theory. The local stability of equilibrium is analyzed and existence of Hopf bifurcation is established. Moreover, formulas for determining the stability and direction of bifurcating periodic solutions are derived by center manifold theorem and normal form theory. Finally, numerical simulation is given to illustrate the theoretical analysis.