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1 results

  • Asymptotic analysis for interactive oscillators of the van der Pol type

  • Kiyomasa Narita
  • Journal:
    Advances in Applied Probability / Volume 19 / Issue 1 / March 1987
    Published online by Cambridge University Press:
    01 July 2016, pp. 44-80
    Print publication:
    March 1987

  • We consider the N-oscillator system of the van der Pol type, which contains a small positive parameter ε multiplying the non-linear damping and the random disturbance. For a formulation of the output we take the solution X(t) = (Xi(t))i=1···,N of the system of 2N-dimensional stochastic differential equations. Rotating each component Xi(t) about the origin of the plane by an angle t, we find that on time scales of order 1/ε together with sufficiently large N each Xi(t) behaves as the equi-ultimately bounded solution of an equation of the McKean type admitting a stationary probability distribution.