Dynamical analysis, feedback control and synchronization of Liu dynamical system (Q955630)

Subject of the paper is the Liu system of scalar ordinary differential equations \[ x'=a(x-y),\quad y'=bx-kxz, \quad z'=-cz+hx^2, \] where \(a,b,c,k,h\) are real parameters. The paper investigates the local dynamics in the vicinity of equilibria of this system. In particular, conditions for stability of equilibria and Hopf bifurcations are obtained. Using center manifold theory, criticality of the Hopf bifurcation is investigated (supercritical or subcritical). Linear feedback control is applied to stabilize and synchronize two Liu systems.