Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Stochastic dynamics and denaturation of thermalized DNA.

In the first part of the paper, the stochastic dynamics of the Peyrard-Bishop-Dauxois (PBD) DNA model is studied. A one-dimensional averaged Itô stochastic differential equation governing the total energy of the system and the associated Fokker-Planck equation governing the transition probability density function of the total energy are derived from the Langevin equations for the base-pair (bp) separation of the PBD DNA model by using the stochastic averaging method for quasinonintegrable Hamiltonian systems. The stationary probability density function of the average energy and the mean square of the bp separation are obtained by solving the reduced Fokker-Planck equation.

Stationary motion of active Brownian particles.

The stationary motion of active Brownian particles is studied by using the stochastic averaging method for quasi-integrable Hamiltonian systems. First the stochastic averaging method for quasi-integrable Hamiltonian systems is briefly introduced. Then the stationary solution of the dynamic equations governing an active Brown particle in plane with the Rayleigh velocity-dependent friction model subject to Gaussian white noise excitations is obtained by using the stochastic averaging method.