ON THE NATURE OF THE TORUS IN THE COMPLEX LORENZ EQUATIONS.

The complex Lorenz equations are a nonlinear fifth-order set of physically derived differential equations which exhibit an exact analytic limit cycle which subsequently bifurcates to a torus. The authors build upon previously derived results to examine a connection between this torus at high and low r//1 (bifurcation parameter) and between zero and nonzero r//2 (complexity parameter). In so doing they gain insight into the effect of the rotational invariance of the system, and into how extra weak dispersion (r//2 does not equal 0) affects the chaotic behavior of the real Lorenz system (which describes a weakly dissipative, dispersive instability).