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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. In this paper we build upon previously derived results to examine a connection between this torus at high and low r1 bifurcation parameter) and between zero and nonzero r2(complexity parameter); in so doing, we are able to gain insight on the effect of the rotational invariance of the system, and on how extra weak dispersion (r2 ≠ 0) affects the chaotic behavior of the real Lorenz system (which describes a weakly dissipative, dispersive instability).