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Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations

Abstract

Systems of differential equations arising in the theory of nonlinear oscillations in resonance-related problems are considered. Of special interest are solutions whose amplitude increases without bound with time. Specifically, such solutions correspond to autoresonance. The stability of autoresonance solutions with respect to random perturbations is analyzed. The classes of admissible perturbations are described. The results rely on information on Lyapunov functions for the unperturbed equations.

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Correspondence to O. A. Sultanov.

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Original Russian Text © O.A. Sultanov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 1, pp. 65–79.

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Sultanov, O.A. Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations. Comput. Math. and Math. Phys. 54, 59–73 (2014). https://doi.org/10.1134/S0965542514010126

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Keywords

  • systems of nonlinear oscillation equations
  • autoresonance
  • random perturbations
  • stability of solutions
  • Lyapunov function method