In this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the oscillator (I) (FDCDO (I)) FDCDO (II), investigated by using effective analytical numerical approaches. For approximation, models of FDCDOs reduced to decoupled standard (FDDOs). After that, both ansatz method Krylov–Bogoliubov–Mitropolsky (KBM) app...

In this introductory course we sketch the framework of quantum probability in order to discuss open quantum systems, in particular the damped harmonic oscillator.

Abstract The interrelationship between the non-Markovian stochastic Schrödinger equations and the corresponding non-Markovian master equations is investigated in the finite temperature regimes. We show that the general finite temperature non-Markovian trajectories can be used to derive the corresponding non-Markovian master equations. A simple, yet important solvable example is the well-known d...

In addition to the passive observation of a non­ linear oscillator and the description of the measured data with Lyapounow exponents [1, 2], fractal dimensions [3-5], entropies [6], etc. it is possible to charcterize a non-linear oscillator by an active method, namely by determining its response to specific perturbations. The resonances of harmonic systems which are brought about by a sinusoida...

Bioluminescence techniques allow accurate monitoring of the circadian clock in single cells. We have analyzed bioluminescence data of Per gene expression in mouse SCN neurons and fibroblasts. From these data, we extracted parameters such as damping rate and noise intensity using two simple mathematical models, one describing a damped oscillator driven by noise, and one describing a self-sustain...

Quantum mechanics of a damped harmonic oscillator investigated by its coupling with a Klein-Gordon field as environment. A new minimal coupling method introduced. Correct Heisenberg equation including a dissipative term proportional to velocity is obtained. Energy flow between oscillator and environment investigated by some transition probabilities.

In a single-degree-of-freedom weakly nonlinear oscillator subjected to periodic external excitation, a small-amplitude excitation may produce a relatively large-amplitude response under primary resonance conditions. Jump and hysteresis phenomena that result from saddle-node bifurcations may occur in the steady-state response of the forced nonlinear oscillator. A simple mass-spring-damper vibrat...