This paper introduces
analytical and numerical solutions of the nonlinear Langevin’s equation under
square nonlinearity with stochastic non-homogeneity. The solution is obtained by using the Wiener-Hermite expansion with
perturbation (WHEP) technique, and the
results are compared with those of Picard iterations and the homotopy
perturbation method (HPM). The WHEP technique is used to obtain up to fourth
order approximation for different number of corrections. The mean and variance
of the solution are obtained and compared among the different methods, and some parametric studies are done by using Matlab.
In this paper, quadratic nonlinear oscillators under stochastic
excitation are considered. The Wiener-Hermite expansion with perturbation
(WHEP) method and the homotopy perturbation method (HPM) are used and compared.
Different approximation orders are considered and statistical moments are
computed in the two methods. The two methods show efficiency in estimating the
stochastic response of the nonlinear differential equations.
This paper presents a
comprehensive stability analysis of the dynamics of the damped cubic-quintic
Duffing oscillator. We employ the derivative expansion method to investigate
the slightly damped cubic-quintic Duffing oscillator obtaining a uniformly
valid solution. We obtain a uniformly valid solution of the un-damped
cubic-quintic Duffing oscillator as a special case of our solution. A phase
plane analysis of the damped cubic-quintic Duffing oscillator is undertaken
showing some chaotic dynamics which sends a signal that the oscillator may be
useful as model for prediction of earth- quake occurrence.