Asymptotic Evaluation Methods of Nonlinear Differential Equations Near the Instability Point

  • Masuo Suzuki
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 75)


The purpose of this paper is to present a general method [Suzuki, 1976a, b, 1977a, b, c, 1978, 1980, in press, to be published] to evaluate asymptotically solutions of nonlinear stochastic differential equations or Langevin’s equations when the system is initially located at or near the unstable point. One of our keypoints is to notice the existence of the scaling regime in an intermediate time region, in which the temporal evolution of physical quantities is expressed by a certain scaling function of the so-called scaling variable τ = S(t, ɛ, …) of time t and the relevant smallness parameter ɛ. Namely, we divide the whole time region into three regimes, i.e., initial, second (scaling), and final regimes.


Nonlinear Differential Equation Nonlinear Transformation Transient Phenomenon Instability Point Final Regime 
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Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • Masuo Suzuki
    • 1
  1. 1.Department of PhysicsUniversity of TokyoHongo, Bunkyo-ku TokyoJapan

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