We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips, frequency suppression, multiple periodic states and chaos. Such phenomena are frequently observed in the collective behavior of a large number of coupled limit cycle...

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relat...

The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that an otherwise linear oscillator can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting ...

A good initial guess and an appropriate homotopy equation are two main factors in applications of the perturbation method. For a nonlinear oscillator, cosine function is used guess. This article recommends general approach to construction equation. Duffing oscillator adopted as example elucidate effectiveness

‎Rough extreme learning machines (RELMs) are rough-neural networks with one hidden layer where the parameters between the inputs and hidden neurons are arbitrarily chosen and never updated‎. ‎In this paper‎, ‎we propose RELMs with a stable online learning algorithm for the identification of continuous-time nonlinear systems in the presence of noises and uncertainties‎, ‎and we prove the global ...

The current paper presents the first treatment to obtain solution of a complex Helmholtz–Duffing oscillator. This model has described elevation surface waves in fluid mechanics. non-perturbative approach is used convert nonlinear oscillator linear derive opened path for new way study more waves.

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy ...

The fractal Toda oscillator with an exponentially nonlinear term is extremely difficult to solve; Elias-Zuniga et al. (2020) suggested the equivalent power-form method. In this paper, first, variational theory used show basic property of oscillator, and a new form obtained free exponential term, which similar Jerk oscillator. homotopy perturbation method solve analytical solution examined using...

This paper proposes a modi ed model of the oscillator network, LEGION, suitable for VLSI implementation. The model performs gray-level real image segmentation using nonlinear analog dynamics. Because of the limited calculation precision in VLSI implementation, it is important to estimate the calculation precision required for proper operations in the modi ed model. By using numerical simulation...

We study the steady-state behavior of a damped, driven nonlinear LRC oscillator, where the nonlinearity arises due to voltage-dependent capacitance. The driving or input signal is assumed to be a pure tone. Using an iterative, perturbative solution technique combinedwith an energy conservation argument, we show that the oscillator transfers energy from the fundamental to higher harmonics. We de...