A New Look at the Stochastic Linearization Technique for Hyperbolic Tangent Oscillator

Stochastic linearization technique is reconsidered for oscillator with restoring force in form of hyperbolic tangent. We show that a subtle error was made in the previously known procedure for derivation of the linearized system parameters. Two new error-free procedures, namely, those based on minimization of mean square difference between (a) restoring force or (b) potential energy of the original non-linear system and their linear counterparts, are suggested. The results of numerical analysis are shown.