The stochastic interaction between plants (i.e. flexible plant grows only or in canopy and that it concerns the aquatic plants or terrestrial plants) and wind is subjected to turbulent air flow conditions and the effects of the stochastic white Gaussian noise (consider as standard Brownian motion) on the plant’s oscillations are analyzed. Using the stochastic multiple scales method, the amplitude and phase of the oscillations are derived so as to obtain the resonance and hysteresis behavior. The chaotic behavior is studied by direct numerical integration of the original governing equation. The Fokker-Planck equation is also applied to study the probability density of the system’s response. The relationship between the characteristics of the random excitation and nonlinear coefficient which is governed by the physical properties of the system is discussed. This relationship is then used to solve the probability density function of the original stochastic system at the stationary state.

stochastic force, multi-scale analysis, Fokker-Planck equations, chaotic behavior.