We consider differential equations of the form ~ + ~f(x, ~ ) + x = Eu, where E > 0 is supposed to be small. For piecewise continuous controls u(t), satisfying lu( t ) l -1 , we present sulIicient conditions for the existence of 2¢r-periodic solutions with a given amplitude. We present a method for determining the limiting behavior of controls fi, for which the equation has a 27r-periodic soluti...

We employ Chirikov’s overlap criterion to investigate interactions between subharmonic resonances of coherent structure solutions of the Gross–Pitaveskii (GP) equation governing the mean-field dynamics of cigar-shaped Bose–Einstein condensates in optical superlattices. We apply a standing wave ansatz to the GP equation to obtain a parametrically forced Duffing equation describing the BEC’s spat...

Due to great noise interference and strong signal attenuation in low voltage power line, two Duffing oscillator methods is proposed to detect QPSK carrier signal. At the same time, after analyzing the law of system solution of Duffing Oscillator, the algorithm of difference distribution of system solution is proposed to identify phase transition, which can greatly decrease calculation. The expe...

In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The four order RungeKutta method and ten order CFE-Euler methods are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on the system dynamics is investigated using phase diagrams, bifurcation diagrams and Poincare map. The bifurcation diagram is a...

We consider an abstract evolution equation with linear damping, a nonlinear term of Duffing type, and small forcing term. The problem is inspired by some models for damped oscillations beam subject to external loads or magnetic fields, shaken transversal force.The main feature that very natural choices the boundary conditions lead equations whose part involves two operators do not commute.We ex...