This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of it...

This paper studies time-delay synchronization of a periodically modulated Duffing Van der Pol (DVP) oscillator subjected to uncertainties with emphasis on complete synchronization. A robust adaptive response system is designed to synchronize with the uncertain drive periodically modulated DVP oscillator. Adaptation laws on the upper bounds of uncertainties are proposed to guarantee the boundedn...

This paper revisits the resonant behavior of a harmonically-forced Duffing oscillator with specific attention to phase resonance and its relation amplitude resonance. To this end, different families resonances, namely primary (1:1), superharmonic (k:1), subharmonic (1:ν) ultra-subharmonic (k:ν) resonances are carefully studied using first higher-order averaging. When lag is calculated between k...

We study mechanical amplification and noise squeezing in a nonlinear nanomechanical resonator driven by an intense pump near its dynamical bifurcation point, namely, the onset of Duffing bistability. Phase sensitive amplification is achieved by a homodyne detection scheme, where the displacement detector's output, which has a correlated spectrum around the pump frequency, is down-converted by m...

<p style='text-indent:20px;'>This paper analyzes conservation issues in the discretization of certain stochastic dynamical systems by means <inline-formula><tex-math id="M2">\begin{document}$ \vartheta $\end{document}</tex-math></inline-formula>-mehods. The analysis also takes into account effects estimation expected values Monte Carlo simulations. theoretical is s...

This paper studies the interaction between non-viscous damping and nonlinearities for nonlinear oscillators with reflection symmetry. The non-viscous damping function is an exponential damping model which adds a decaying memory property to the damping term of the oscillator. We consider the case of softening and hardening behaviour in the frequency response of the system. Numerical simulations ...

Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical dissipative chaotic Duffing oscillator. The similarities and differences from the classical oscillator are examined; in particular, a new concept of quantum maps is introduced, and alterations in the classical strange attractor due to the presence of scale-dependent quantu...

S. JEYAKUMARI, V. CHINNATHAMBI Department of Physics, Sri K.G.S. Arts College, Srivaikuntam 628 619, Tamilnadu, India., S. RAJASEKAR School of Physics, Bharathidasan University, Tiruchirapalli 620 024, Tamilnadu, India. [email protected], and M.A.F. SANJUAN Departamento de F́ısica, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain. [email protected] Abstract We ...

A two-dimensional Duffing oscillator which can produce stochastic resonance (SR) is studied in this paper. We introduce its SR mechanism and present a generalized parameter-adjusted SR (GPASR) model of this oscillator for the necessity of parameter adjustments. The Kramers rate is chosen as the theoretical basis to establish a judgmental function for judging the occurrence of SR in this model; ...