Dynamics of the stochastic Lorenz chaotic system with long memory effects

Journal Article · Tue Dec 15 00:00:00 EST 2015 · Chaos (Woodbury, N. Y.)

DOI:https://doi.org/10.1063/1.4937726· OSTI ID:22482300

Zeng, Caibin; Yang, Qigui ^[1]

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1. School of Mathematics, South China University of Technology, Guangzhou 510640 (China)

Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.

• OSTI ID: 22482300
• Journal Information: Chaos (Woodbury, N. Y.), Vol. 25, Issue 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAOS THEORY
FUNCTIONS
LYAPUNOV METHOD
NOISE
STANFORD LINEAR COLLIDER
STOCHASTIC PROCESSES