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The noisy Pais-Uhlenbeck oscillator. (English) Zbl 1417.81130

Summary: In this paper, we include simultaneously additive and multiplicative noise to the Pais-Uhlenbeck oscillator (PUO). We construct an integral of motion of the PUO with a time-dependent coefficient. Viewing the PUO as two coupled harmonic oscillators, we add noise to the corresponding frequencies. The systems are solved with the fourth-order stochastic Runge-Kutta method. Some graphics of the solutions and integrals of motion are presented, and the average deviations are calculated in order to quantify the noise influence.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E03 Stochastic systems in control theory (general)
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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