Qualitative Analysis Of An Extended Lorenz-type System

In1963, the American meteorologist E. N. Lorenz discovered accidentally thefrst chaotic attractor through numerical simulation. Since then, the study of chaosattracted wide attention in many areas. As the frst chaotic system, the Lorenz systemhasbecome the foundationfor the studyof the chaostheory in the nextseveral decades,which is hence considered as a milestone in this area.Later,peoplefoundmoreandmore3-dimensionchaoticdynamicalsystems,throughdiferent techniques. This phenomenon inspired naturally us to derive a more gener-alized Lorenz-type chaotic systems. Hua, Chen, Li and Ge proposed for the frst timean extended Lorenz-type system (ELTS for simplicity), preserving the basic qualitativeproperties of the Lorenz system while containing a large class of existing chaotic dy-namical systems. The main mission of this paper is devoted to the study of equilibriumof an extended Lorenz-type system, including the stability of equilibrium, bifurcationand other features. Finally, a sufcient condition for the globally asymptotic stabilityin such ELTS is derived with the aid of a generalisation of the Bendixson’s criterion tohigher dimensions.