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Ryashko L. B. Quasi-potential method for 2-torus stochastic sensitivity analysis. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 1, pp. 38-54. DOI: 10.18500/0869-6632-2006-14-1-38-54

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Quasi-potential method for 2-torus stochastic sensitivity analysis

Ryashko Lev Borisovich, Ural Federal University named after the first President of Russia B.N.Yeltsin

On the basis of quasi-potential method the stationary distribution of random trajectories in a vicinity of toroidal manifolds of stochastically forced nonlinear systems is investigated. For the quasi-potential approximation the quadratic form defined by some matrix function is used. This function named stochastic sensitivity function characterizes the response of considered system on random disturbances. Construction of this function is reduced to the decision of a boundary problem for linear differential matrix equation. For 2-torus in three-dimensional space a constructive decision of this problem is given. Construction of stochastic sensitivity function is reduced to the decision of some functional equation. Efficiency of the presented results is shown on the example. 

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