In this article, we consider the nonlinear Duffing-van der Pol-type oscillator system by means of the first integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly, we apply the Division Theorem for two variables in the comple...

Let λ denote the almost sure Lyapunov exponent obtained by linearizing the stochastic Duffing-van der Pol oscillator ẍ = −ωx + βẋ−Ax −Bxẋ + σxẆt at the origin x = ẋ = 0 in phase space. If λ > 0 then the process {(xt, ẋt) : t ≥ 0} is positive recurrent on R \ {(0, 0)} with stationary probability measure μ, say. For λ > 0 let λ̃ denote the almost sure Lyapunov exponent obtained by linearizing the ...

Integral boundary conditions for evolution problems have various applications in chemical engineering, thermoelasticity, underground water flow and population dynamics, see for example [16, 17, 24]. In fact, boundary value problems involving integral boundary conditions have received considerable attention, see for instance, [3, 10], [12]–[15], [18, 19, 26] and the references therein. In a rece...

The orbital free density functional theory and the single density equation approach are formally equivalent. An orbital free density based quantum dynamical strategy is used to study the quantum-classical correspondence in both weakly and strongly coupled van der Pol and Duffing oscillators in the presence of an external electric field in one dimension. The resulting quantum hydrodynamic equati...

The Lyapunov based approach for synchronizing and identifying the unknown parameters in the Duffing system is presented in this paper. The strategy consists of proposing a slave system which has to follow asymptotically the desired Duffing system. The gains of the slave system are adjusted continually according to a convenient adaptation control law, until the measurable output error converges ...

The paper proposed a new method for the detection of QPSK carrier signal that based on double duffing oscillator to solve the problems as high attenuation and strong noise interference in the QPSK carrier communication of low voltage power line. This method has making use of the different phase of QPSK carrier signal to stimulate the double duffing oscillators to enter different states and thro...