Vibratory control of a linear system by addition of a chain of nonlinear oscillators
Sign Up to like & getrecommendations! Published in 2017 at "Acta Mechanica"
DOI: 10.1007/s00707-017-1867-7
Abstract: An N-degree-of-freedom model consisting of a single-degree-of-freedom linear system coupled to a chain of $$(N-1)$$(N-1) light nonlinear oscillators is studied. The connection between the chain and the single-degree-of-freedom system is supposed to be linear. Time… read more here.
Keywords: linear system; chain; system; nonlinear oscillators ... See more keywords
On the Asymptotic Stability for Nonlinear Oscillators with Time-Dependent Damping
Sign Up to like & getrecommendations! Published in 2018 at "Qualitative Theory of Dynamical Systems"
DOI: 10.1007/s12346-018-0294-z
Abstract: The equation $$\begin{aligned} x''+h(t,x,x')x'+f(x)=0 \qquad (x\in \mathbb {R},\ xf(x)\ge 0,\ t\in [0,\infty )) \end{aligned}$$x′′+h(t,x,x′)x′+f(x)=0(x∈R,xf(x)≥0,t∈[0,∞))is considered, where the damping coefficient h allows an estimate $$\begin{aligned} a(t)|x'|^\alpha w(x,x')\le h(t,x,x')\le b(t) W(x,x'). \end{aligned}$$a(t)|x′|αw(x,x′)≤h(t,x,x′)≤b(t)W(x,x′).Sufficient conditions on the lower and… read more here.
Keywords: stability nonlinear; oscillators time; nonlinear oscillators; asymptotic stability ... See more keywords
Approximate limit cycles of coupled nonlinear oscillators with fractional derivatives
Sign Up to like & getrecommendations! Published in 2020 at "Applied Mathematical Modelling"
DOI: 10.1016/j.apm.2019.08.028
Abstract: Abstract In this paper, the homotopy analysis method (HAM) is presented to establish the accurate approximate analytical solutions for multi-degree-of-freedom (MDOF) coupled nonlinear oscillators with fractional derivatives. Approximate limit cycles (LCs) of two systems of… read more here.
Keywords: limit cycles; nonlinear oscillators; approximate limit; oscillators fractional ... See more keywords
Generalization of the modified Lindstedt-Poincare method for solving some strong nonlinear oscillators
Sign Up to like & getrecommendations! Published in 2019 at "Ain Shams Engineering Journal"
DOI: 10.1016/j.asej.2018.08.007
Abstract: Abstract The modified Lindstedt-Poincare method has been generalized for solving strongly nonlinear oscillators. The original formula (presented by Cheung et al.) covers a class of nonlinear problems. So, it requires another formula to cover the… read more here.
Keywords: lindstedt poincare; nonlinear oscillators; poincare method; modified lindstedt ... See more keywords
On the design of external excitations in order to make nonlinear oscillators respond as free oscillators of the same or different type
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Non-linear Mechanics"
DOI: 10.1016/j.ijnonlinmec.2016.06.012
Abstract: This study deals with nonlinear oscillators whose restoring force has a polynomial nonlinearity of the cubic or quadratic type. Conservative unforced oscillators with such a restoring force have closed-form exact solutions in terms of Jacobi… read more here.
Keywords: different type; oscillators different; nonlinear oscillators; respond free ... See more keywords
The simplest approach to nonlinear oscillators
Sign Up to like & getrecommendations! Published in 2019 at "Results in physics"
DOI: 10.1016/j.rinp.2019.102546
Abstract: Abstract This paper gives the simplest approach to the cubic-quintic Duffing equation (M.S.H. Chowdhury et al., Results in Physics 7(2017): 3962–3967), providing an extremely fast and relatively accurate estimation of the frequency of a nonlinear… read more here.
Keywords: simplest approach; nonlinear oscillators; physics; approach nonlinear ... See more keywords
Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators
Sign Up to like & getrecommendations! Published in 2018 at "Scientific Reports"
DOI: 10.1038/s41598-018-25492-8
Abstract: A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine… read more here.
Keywords: nonlinear oscillators; sampling ising; quantum heating; coupled nonlinear ... See more keywords
A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint.
Sign Up to like & getrecommendations! Published in 2022 at "Chaos"
DOI: 10.1063/5.0088559
Abstract: We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but… read more here.
Keywords: quantum nonlinear; nonlinear oscillators; asymptotic phase; phase quantum ... See more keywords
Transition from inhomogeneous limit cycles to oscillation death in nonlinear oscillators with similarity-dependent coupling.
Sign Up to like & getrecommendations! Published in 2022 at "Chaos"
DOI: 10.1063/5.0100595
Abstract: We consider a system of coupled nonlinear oscillators in which the interaction is modulated by a measure of the similarity between the oscillators. Such a coupling is common in treating spatially mobile dynamical systems where… read more here.
Keywords: nonlinear oscillators; similarity; inhomogeneous limit; oscillation death ... See more keywords
Discrete Vortices in Systems of Coupled Nonlinear Oscillators: Numerical Results for an Electric Model
Sign Up to like & getrecommendations! Published in 2020 at "JETP Letters"
DOI: 10.1134/s0021364020070097
Abstract: Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by relatively weak capacitances has been… read more here.
Keywords: nonlinear oscillators; discrete vortices; vortices systems; systems coupled ... See more keywords
Nonintegrability of Parametrically Forced Nonlinear Oscillators
Sign Up to like & getrecommendations! Published in 2018 at "Regular and Chaotic Dynamics"
DOI: 10.1134/s156035471803005x
Abstract: We discuss nonintegrability of parametrically forced nonlinear oscillators which are represented by second-order homogeneous differential equations with trigonometric coefficients and contain the Duffing and van der Pol oscillators as special cases. Specifically, we give sufficient… read more here.
Keywords: nonintegrability; nonintegrability parametrically; nonlinear oscillators; forced nonlinear ... See more keywords