Heteroclinic orbits in the T and the Lü systems

The present work is devoted to investigate the existence of heteroclinic orbits in two three-dimensional autonomous systems, more exactly in the Lü and the T systems. The two systems belong to the class of Lorenz systems, having the nonlinear terms of order two. We prove that, under some constraints for the parameters, the both systems have exactly two heteroclinic orbits which are symmetrical with respect to the z-axis. We register also results on closed and homoclinic orbits for the Lü system.