Dynamics of a particular Lorenz type system - Testoni G.E.* (2010)
In this paper we analytically and numerically investigate the dynamics of a nonlinear three-dimensional autonomous first-order ordinary differential equation system, obtained from paradigmatic Lorenz system by suppressing the y variable in the right-hand side of the second equation. The RouthHurwitz criterion is used to decide on the stability of the nontrivial equilibrium points of the system, as a function of the parameters. The dynamics of the system is numerically characterized by using diagrams that associate colors to largest Lyapunov exponent values in the parameter-space. Additionally, phase-space plots and bifurcation diagrams are used to characterize periodic and chaotic attractors. © 2010 World Scientific Publishing Company.