Investigation of non-autonomous fourth order random oscillating systems in the case of complex roots of characteristic equation
Рік:
2017
Сторінок:
Р. 9-12
Тип документу:
Стаття
Головний документ:
Київський Вісник Київського національного університету імені Тараса Шевченка / Київський, університет імені національний; редкол.: голов. ред. Анісімов А.В. ; Хусаінов Д.Я., Arturs Medvids, Miklos Ronto [та ін.]. - Київ, 2017
Анотація:
The asymptotic behavior of non-autonomous oscillating system describing by di erential equation of fourth order with small non-linear periodical external perturbations of white noise, non-centered and centered Poisson noise types is studied. Every term of external perturbations has own order of small parameter ". If small parameter is equal to zero, then general solution of obtained non-stochastic fourth order di erential equation has an oscillating part. We consider given di erential equation with external stochastic perturbations as the system of stochastic di erential equations and study the limit behavior of its solution at the time moment t/[epsilon]k, as [epsilon] ["з… випливає" або "якщо…, то…"]0. The system of averaging stochastic di erential equations is derived and its dependence on the order of small parameter in every term of external perturbations is studied. The non-resonance and resonance cases under the conditions that characteristic equation has two conjugate complex roots and two conjugate pure imaginary roots are considered.
