C.8 Further Reading

E. N. Lorenz, "Deterministic Nonperiodic Flow," J. Atmos. Sei. 20, 130-41 (1963). Reprinted in [Cvitanovic, 1984]. The Lorenz model first appeared in this pioneering and quite readable paper.

B. Saltzman, "Finite Amplitude Free Convection as an Initial Value Problem-I." J. Atmos. Sei. 19, 329-41 (1962). The Lorenz model was an outgrowth of an earlier model of atmospheric convection introduced by Saltzman.

[Bergé, Pomeau, Vidal, 1984], Appendix D, contains a slightly different development of the Lorenz model equations, and in addition, provides more details on the how the dynamics evolve as the reduced Rayleigh number r changes.

[Sparrow, 1983] gives a detailed treatment of the Lorenz model and its behavior. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New
York, 1984). Chapter 11. A wide-ranging discussion of the physics and mathematics of Rayleigh-Benard convection along with many historical references.

H. Haken, "Analogy between Higher Instabilities in Fluids and Lasers," Phys. Lett. 53A, 77-78 (1975). Certain laser systems are modeled by equations that are identical in form to the Lorenz model equations.

R. Graham, "Onset of Self-Pulsing in Lasers and the Lorenz Model," Phys. Lett.
58A, 440-41 (1976).

C. O. Weiss and J. Brock, "Evidence for Lorenz-Type Chaos in a Laser," Phys.
Rev. Lett. 57, 2804-6 (1986).

C. O. Weiss, N. B. Abraham, and U. Hübmer. "Homoclinic and Heteroclinic
Chaos in a Single-Mode Laser," Phys. Rev. Lett. 61, 1587-90 (1988).