A relaxation oscillator model of neural spiking dynamics is applied to the task of finding downbeats in rhythmical patterns. The importance of downbeat discovery or 'beat induction' is discussed, and the relaxation oscillator model is compared to other oscillator models. In a set of computer simulations the model is tested on 35 rhythmical patterns. The model performs well, making good predicti...

An investigation of the nonlinear dynamics of a heart model is presented. The model compartmentalizes the heart into one part that beats autonomously (the x oscillator), representing the pacemaker or SA node, and a second part that beats only if excited by a signal originating outside itself (the y oscillator), representing typical cardiac tissue. Both oscillators are modeled by piecewise linea...

 In this work, time domain analysis is used to solve Adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. Mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked LC and Ring oscillators considering their time-varying nature. Then, the analysis is verifie...

Spectral line shapes in a condensed phase contain information from various dynamic processes that modulate the transition energy, such as microscopic dynamics, inter- and intramolecular couplings, and solvent dynamics. Because nonlinear response functions are sensitive to the complex dynamics of chemical processes, multidimensional vibrational spectroscopies can separate these processes. In mul...

The literature on quantum mechanics in a finite-dimensional Hilbert space is substantial. This paper is devoted to an algebraic model for a quantum oscillator allowing finite-dimensional representations, thus leading to a finite oscillator model. The canonical one-dimensional quantum oscillator (in the convention m = ω = ~ = 1) is described by a position operator q̂, a momentum operator p̂ and a ...