Analytical Solutions of the Lorenz System

    2015, Volume 20, Number 2, pp.  123-133

    Author(s): Kudryashov N. A.

    The Lorenz system is considered. The Painlevé test for the third-order equation corresponding to the Lorenz model at $\sigma \ne 0$ is presented. The integrable cases of the Lorenz system and the first integrals for the Lorenz system are discussed. The main result of the work is the classification of the elliptic solutions expressed via the Weierstrass function. It is shown that most of the elliptic solutions are degenerated and expressed via the trigonometric functions. However, two solutions of the Lorenz system can be expressed via the elliptic functions.
    Keywords: Lorenz system, Painlevé property, Painlevé test, analytical solutions, elliptic solutions
    Citation: Kudryashov N. A., Analytical Solutions of the Lorenz System, Regular and Chaotic Dynamics, 2015, Volume 20, Number 2, pp. 123-133

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