A detailed analytical study of irreversible energy transfer in an oscillatory system with time-dependent parameters has not been addressed thus far in the literature. This paper demonstrates a closed-form asymptotic solution of this problem for a system of two weakly coupled linear oscillators; the first oscillator with constant parameters is excited by an initial impulse, whereas the coupled o...

Exponential stability analysis and L2-gain analysis are developed for uncertain distributed parameter systems. Scalar heat processes and distributed mechanical oscillators, governed by semilinear partial differential equations of parabolic and, respectively, hyperbolic types, are chosen for treatment. Sufficient exponential stability conditions with a given decay rate are derived in the form of...

Nonlinear observers based on the well-known concept of minimum energy estimation are discussed. The approach relies an output injection operator determined by a Hamilton–Jacobi–Bellman equation whose solution is subsequently approximated neural network. A suitable optimization problem allowing to learn network parameters proposed and numerically investigated for linear nonlinear oscillators.

We study work fluctuation theorems for oscillators in non-Markovian heat baths. By calculating the work distribution function for a harmonic oscillator with motion described by the generalized Langevin equation, the Jarzynski equality (JE), transient fluctuation theorem (TFT), and Crooks' theorem (CT) are shown to be exact. In addition to this derivation, numerical simulations of anharmonic osc...

Image contrast enhancement is realised by using nonlinear oscillatory theory. Two different uncoupled networks based on nonlinear oscillators have been studied. Simulators for both networks are developed and tested with very low contrasted images. Results show a possible effective area of application of nonlinear oscillators for image processing tasks.

We study neuro-computational properties of non-linear oscillatory systems. Since we use the canonical phase models approach, our results do not depend on the physical nature of each oscillator or the detailed form of mathematical equations that describe its dynamics. In particular, we show that anything that can oscillate can also compute, the only problem is how to couple the oscillators. We a...

The existence of several small planar traveling waves with arbitrary direction of propagation is shown for two-dimensional cubic networks of oscillators with linear nearest-neighbor coupling. The analysis is based on a spatial dynamics reformulation of the relevant advance-delay equation. Whereas important aspects of the analysis are discontinuous in the direction of travel, continuity of the t...