Mechanical Analyses of a Modified Lorenz System

Abstract

The paper analyzes the bifurcation diagram of a modified Lorenz system and presents a relationship between this system and Kolmogorov system. The transformation procedure of the Kolmogorov type of the chaotic system is illustrated in detail according to the bifurcation diagram through the system parameter change. Furthermore, the corresponding mechanics analyses about different modes under different torques are discussed, such as inertial, internal, dissipative torques and the combination. The conversions of energy analyses are also studied including Hamiltonian, kinetic and potential energies in order to verify the energy effect on the system dynamics.