WIAS Preprint No. 116, (1994)

Simulation of stochastic auto-oscillating systems through variable stepsize algorithms with small noise


  • Artemiev, Sergey S.
  • Averina, Tatjana A.
  • Schurz, Henri

2010 Mathematics Subject Classification

  • 60H10 65C20 65L20 65U05


  • Stochastic differential equations, auto-oscillating systems, limit cycle, strange attractor, bifurcation, numerical methods, mean square error, variable stepsize algorithm, simulation studies


The paper considers some questions of the numerical analysis of stochastic auto-oscillating systems and their simulation on computers. A low computer costs, variable stepsize algorithm based on local error estimation of stochastic Runge-Kutta- Fehlberg methods is stated for solving nonlinear stochastic differential equations. In particular, it turns out to be very efficient for dynamical systems with small noise intensity. Results of numerical experiments for a plenty of well-known examples from Physics, Chemistry, Biology and Ecology are illustrated with the help of the dialogue system 'Dynamics and Control'.

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