Stability and subcritical dynamics of structures with spatially disordered travelling parametric excitation

Homoclinic bifurcation and chaos in simple pendulum under bounded noise excitation

“…Thus, it can be a reasonable model for random excitation or response of engineering systems. This model has been used for a long time in electrical engineering but it was only recently used in mechanical and structural engineering [9][10][11][12].…”

Stationary response of strongly non-linear oscillator with fractional derivative damping under bounded noise excitation

“…For example, by adjusting its parameters, the Dryden and von Karman spectra of wind turbulence can be fit very well [15]. It can be a reasonable model for traveling loads and structures [16,17]. So far, the behavior of a variety of systems under bounded noise excitations has been studied, including the stochastic response [18][19][20], stability [18,21,22], chaotic motion [23][24][25], jump and bifurcation [26,27] of strongly non-linear oscillators.…”

Transitions in a Duffing oscillator excited by random noise

“…[3,[20][21][22][23][24]). We will show that the transitions take place also for this model but the deterministic parameter γ can promote them.…”