Related papers: Frequency stabilization by synchronization of Duff…
The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force $f$ and its frequency $\Omega$. We first examine the stability of the steady state…
We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
Dynamics of the Duffing--Van der Pol driven oscillator is investigated. Periodic steady-state solutions of the corresponding equation are computed within the Krylov-Bogoliubov-Mitropolsky approach to yield dependence of amplitude $A$ on…
This paper considers nonlinear dynamics of polarization oscillations when some materials when they are subjected to the action of an electromagnetic wave modeled by multifrequency forced Duffing equation. Multiresonance and chaotic behavior…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and…
We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…
When simulating resistive-capacitive circuits or electroquasistatic problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
This work is a theoretical investigation of the stability of the non-linear behavior of an oscillating tip-cantilever system used in dynamic force microscopy. Stability criterions are derived that may help to a better understanding of the…
A class of modified Duffing oscillator differential equations, having nonlinear damping forces, are shown to have finite time dynamics, i.e., the solutions oscillate with only a finite number of cycles, and, thereafter, the motion is zero.…
We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched random frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically…
In the work a nonlinear Duffing oscillator is considered under impulse excitation with two ways of introduction of the random additive term simulating noise, - with help of amplitude modulation and modulation of period of impulses sequence.…
Synchronization of coupled oscillators is a paradigm for complexity in many areas of science and engineering. Any realistic network model should include noise effects. We present a description in terms of phase and amplitude deviation for…
Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…