The paper deals with the problem of estimation of the topological entropy for non-autonomous systems of differential equations via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Lorenz system and Duffing oscillator.

The vagueness of the quantum-classical border in physics makes some physicists uncertain about the foundation of their science. Others, by contrast, feel that the accuracy of the verified predictions makes these foundations especially solid. This longtime state of affairs is changing in an interesting way. Recent progress in mesoscopic physics, and the so-called “new science of nanotechnology,”...

We present an analytical calculation of the response a driven Duffing oscillator to low-frequency fluctuations in resonance frequency and damping. find that these parameters manifest themselves distinctively, allowing them be distinguished. In strongly nonlinear regime, amplitude phase noise due damping are attenuated, while transduction into remains order $1$. show this can seen by comparing r...

The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the ⋆-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is investigated in greater detail. The constraints for rotationally symmetric solutions and the corresponding twodimensional harmonic oscillator are solved. The angular moment...

The bistablity onset due to the interaction of highto low-frequency oscillations in the Duffing oscillator is considered. It is shown that such interaction results in arising of additional bistable states, which has a lower threshold for bistability with respect to the forcing amplitude as compared to the harmonically forced oscillator. This phenomenon is illustrated by considering two examples...

Harmonic Balance is one of the most popular methods for computing periodic solutions nonlinear dynamical systems. In this work, we address two its major shortcomings: First, investigate to what extent computational burden stability analysis can be reduced by consistent use Chebyshev polynomials. Second, problem a rigorous error bound, which, authors' knowledge, has been ignored in all engineeri...

The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different (time-dependent) parameters can be related through unitary transformations. The existence of generalized coherent states for a simple harmonic oscillator can then be inte...