Abstract
In this paper, the complex dynamics of a newly proposed 4D hyperchaotic Lorenz-type system are studied. The sufficient conditions of the emergence of periodic solutions and the stability of them at bifurcation points are obtained by averaging theory. The ultimate bound estimation of this hyperchaotic system is derived using the Lyapunov stability theory and the optimization idea, and relevant numerical simulations are given. Finally, a variable-order fractional network of this new 4D hyperchaotic Lorenz-type system is introduced and investigated.