Related papers: Analyzing Oscillators using Describing Functions

We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This…

The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation…

In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…

Many combinatorial optimization problems can be mapped to finding the ground states of the corresponding Ising Hamiltonians. The physical systems that can solve optimization problems in this way, namely Ising machines, have been attracting…

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed…

The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…

We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…

Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…

An analog of the describing function method is developed using square waves rather than sinusoids. Static nonlinearities map square waves to square waves, and their behavior is characterized by their response to square waves of varying…

An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…

In this paper, we discuss the definition of Q factor for nonlinear oscillators. While available definitions of Q are often limited to linear resonators or oscillators with specific topologies, our definition is applicable to any oscillator…

A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…

The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…

Properties of the response functions for a two-dimensional quartic oscillator are studied based on the diagonalization of the Hamiltonian in a large model space. In particular, response functions corresponding to a given momentum transfer…

There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…

In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…

Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…

The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…

The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…