Effects of External Noise on Complexity in Two Dimensional Driven Damped Dynamical System

  • Jinqing Fang
Part of the NATO ASI Series book series (NSSB, volume 208)


We consider the following Langevin equation with two dimensional driven damped dynamical system (2-D DDDS)1
$$\begin{array}{*{20}{c}} {{{\dot X}_1} = {X_2}} \\ {{{\dot X}_2} = A\cos (2\pi {X_3}) + B{X_1} + CX_1^3 - (CX_1^2 - E){X_2} + {F_w}} \\ {{{\dot X}_3} = \omega /2\pi } \end{array}$$
where Fw is Gaussian white noise which has the properties
$$ < {F_{\text{w}}}(t) > = 0$$
$$ < {F_{\text{w}}}(t){F_w}(s) > = 2{D_F}\delta (t - s)$$
where DF, is diffusion coefficient, S the Dirac delta function. Eq.(2) and (3) completely determines all of its statistical feature.


White Noise Phase Portrait Noise Intensity Langevin Equation Dirac Delta Function 
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  1. 1.
    Fang Jinqing, Generalized Farey Organization and The Effects of White Noise on Complexity in 2-D DDDS, to be submitted to Phys. Rev. A, 1989.Google Scholar
  2. 2.
    U. Parlitz and W. Lanterbom, Period-doubling Cascades and Devil’s Staircases of the Driven Van Der Pol Oscillator, Phys. Rev. A, 36: 1428 (1987).Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • Jinqing Fang
    • 1
  1. 1.Center for Studies in Statistical MechanicsUniversity of Texas at AustinAustinUSA

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