Abstract
This paper introduces and analyzes new hyperchaotic complex Lorenz systems. These systems are 6-dimensional systems of real first order autonomous differential equations and their dynamics are very complicated and rich. In this study we extend the idea of adding state feedback control and introduce the complex periodic forces to generate hyperchaotic behaviors. The fractional Lyapunov dimension of the hyperchaotic attractors of these systems is calculated. Bifurcation analysis is used to demonstrate chaotic and hyperchaotic behaviors of our new systems. Dynamical systems where the main variables are complex appear in many important fields of physics and communications.