Complex dynamic behaviors of the complex Lorenz system

This study compares the dynamic behaviors of the Lorenz system with complex variables to that of the standard Lorenz system involving real variables. Different methodologies, including the Lyapunov Exponents spectrum, the bifurcation diagram, the first return map to the Poincaré section and topological entropy, were used to investigate and compare the behaviors of these two systems. The results show that expressing the Lorenz system in terms of complex variables leads to more distinguished behaviors, which could not be achieved in the Lorenz system with real variables, such as quasi-periodic and hyper-chaotic behaviors.