Coupled Oscillator Model for Nonlinear Gravitational Perturbations
Yang, Huan; Green, Stephen R; Lehner, Luis
2015-01-01
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although borne out of the gravity/fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, w...
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...
Entanglement Dynamics of Quantum Oscillators Nonlinearly Coupled to Thermal Environments
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2014-01-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing and coupling strength, is compared to results for systems with linear system-reservoir coupling. We fin...
Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2015-07-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators
Directory of Open Access Journals (Sweden)
R. Naz
2011-01-01
Full Text Available We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations. The difference arises in the gauge terms due to Lagrangians being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian. We have illustrated it here for nonlinear Duffing oscillators.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Experiments on oscillator ensemble with global nonlinear coupling
Rosenblum, Michael; Temirbayev, Amirkhan; Zhanabaev, Zeinulla; Tarasov, Stanislav; Ponomarenko, Vladimir
2012-02-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a linear or nonlinear phase-shifting unit in the global feedback loop. With linear unit we observe, with increase of the coupling strength, a standard Kuramoto-like transition to a fully synchronous state; the threshold of the transition depends on the phase shift. In case of nonlinear global coupling we first observe a transition to a state when approximately half of the population forms a synchronous cluster. With further increase of the coupling strength we observe destruction of this cluster and formation of a self-organized quasiperiodic state, predicted in [M. Rosenblum and A. Pikovsky, PRL, 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. The transition is characterized by a non-monotonic dependence of the order parameter on the coupling strength. We demonstrate a good correspondence between theory and experiment.
Experiments on oscillator ensembles with global nonlinear coupling
Temirbayev, Amirkhan A.; Zhanabaev, Zeinulla Zh.; Tarasov, Stanislav B.; Ponomarenko, Vladimir I.; Rosenblum, Michael
2012-01-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.064101 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
Senthilkumar, D. V.; Muruganandam, P.; Lakshmanan, M.; Kurths, J.
2010-01-01
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by siz...
Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling.
Rosenblum, Michael; Pikovsky, Arkady
2007-02-09
We describe a transition from fully synchronous periodic oscillations to partially synchronous quasiperiodic dynamics in ensembles of identical oscillators with all-to-all coupling that nonlinearly depends on the generalized order parameters. We present an analytically solvable model that predicts a regime where the mean field does not entrain individual oscillators, but has a frequency incommensurate to theirs. The self-organized onset of quasiperiodicity is illustrated with Landau-Stuart oscillators and a Josephson junction array with a nonlinear coupling.
Time-varying interaction leads to amplitude death in coupled nonlinear oscillators
Indian Academy of Sciences (India)
Awadhesh Prasad
2013-09-01
A new form of time-varying interaction in coupled oscillators is introduced. In this interaction, each individual oscillator has always time-independent self-feedback while its interaction with other oscillators are modulated with time-varying function. This interaction gives rise to a phenomenon called amplitude death even in diffusively coupled identical oscillators. The nonlinear variation of the locus of bifurcation point is shown. Results are illustrated with Landau–Stuart (LS) and Rössler oscillators.
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate ap...... accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators
Institute of Scientific and Technical Information of China (English)
CHEN Hai-Ling; YANG Jun-Zhong
2009-01-01
In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearit...
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Pikovsky, Arkady [Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Potsdam (Germany); Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
PT-symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
Avinash Khare
2015-11-01
We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry, i.e., one of them has gain and the other an equal and opposite amount of loss. We first discuss various symmetries of the model. We show that both the linear system as well as a special case of the nonlinear system can be derived from a Hamiltonian, whose structure is similar to the Pais–Uhlenbeck Hamiltonian. Exact solutions are obtained in a few special cases. We show that the system is a superintegrable system within the rotating wave approximation (RWA). We also obtain several exact solutions of these RWA equations. Further, we point out a novel superposition in the context of periodic solutions in terms of Jacobi elliptic functions that we obtain in this problem. Finally, we briefly mention numerical results about the stability of some of the solutions.
Komech, A I; Stuart, D
2008-01-01
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Vierheilig, Carmen; Grifoni, Milena
2010-01-01
We consider a qubit coupled to a nonlinear quantum oscillator, the latter coupled to an Ohmic bath, and investigate the qubit dynamics. This composed system can be mapped onto that of a qubit coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum oscillator. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, the problem of the quantum Duffing oscillator within linear response theory in the driving amplitude. Knowing the effective spectral density, the qubit dynamics is investigated. In particular, an analytic formula for the qubit's population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the...
Oscillation death in coupled oscillators
Institute of Scientific and Technical Information of China (English)
Wei ZOU; Xin-gang WANG; Qi ZHAO; Meng ZHAN
2009-01-01
We study dynamical behaviors in coupled nonlinear oscillators and find that under certain condi- tions, a whole coupled oscillator system can cease oscil- lation and transfer to a globally nonuniform stationary state [I.e., the so-called oscillation death (OD) state], and this phenomenon can be generally observed. This OD state depends on coupling strengths and is clearly differ- ent from previously studied amplitude death (AD) state, which refers to the phenomenon where the whole system is trapped into homogeneously steady state of a fixed point, which already exists but is unstable in the ab- sence of coupling. For larger systems, very rich pattern structures of global death states are observed. These Turing-like patterns may share some essential features with the classical Turing pattern.
Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
Energy Technology Data Exchange (ETDEWEB)
Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br [Associate Laboratory for Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE (Brazil); Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de [Department of Physics and Astronomy, University of Potsdam, Germany and Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2015-04-15
We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.
Experimental observation of multifrequency patterns in arrays of coupled nonlinear oscillators.
In, Visarath; Kho, Andy; Neff, Joseph D; Palacios, Antonio; Longhini, Patrick; Meadows, Brian K
2003-12-12
Frequency-related oscillations in coupled oscillator systems, in which one or more oscillators oscillate at different frequencies than the other oscillators, have been studied using group theoretical methods by Armbruster and Chossat [Phys. Lett. A 254, 269 (1999)] and more recently by Golubitsky and Stewart [in Geometry, Mechanics, and Dynamics, edited by P. Newton, P. Holmes, and A. Weinstein (Springer, New York, 2002), p. 243]. We demonstrate, experimentally, via electronic circuits, the existence of frequency-related oscillations in a network of two arrays of N oscillators, per array, coupled to one another. Under certain conditions, one of the arrays can be induced to oscillate at N times the frequency of the other array. This type of behavior is different from the one observed in a driven system because it is dictated mainly by the symmetry of the coupled system.
Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators
Zhou, Brian B.; Roy, Rajarshi
2007-02-01
We propose a basic mechanism for isochronal synchrony and communication with mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators, mutually coupled with a propagation delay, synchronize isochronally when both are symmetrically driven by a third Ikeda oscillator. This synchronous operation, unstable in the two delay-coupled oscillators alone, facilitates simultaneous, bidirectional communication of messages with chaotic carrier wave forms. This approach to combine both bidirectional and unidirectional coupling represents an application of generalized synchronization using a mediating drive signal for a spatially distributed and internally synchronized multicomponent system.
Energy Technology Data Exchange (ETDEWEB)
Macias-Diaz, J.E. [Departamento de Matematicas y Fisica, Universidad Autonoma de Aguascalientes, Aguascalientes, Ags. 20100 (Mexico) and Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)]. E-mail: jemacias@correo.uaa.mx; Puri, A. [Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)]. E-mail: apuri@uno.edu
2007-07-02
In the present Letter, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear supratransmission. Our numerical results-which are based on a brand-new computational technique with energy-invariant properties-show an efficient and reliable transmission of information.
Array-induced collective transport in the Brownian motion of coupled nonlinear oscillator systems
Zheng, Zhigang; Hu, Bambi; Hu, Gang
1998-01-01
Brownian motion of an array of harmonically coupled particles subject to a periodic substrate potential and driven by an external bias is investigated. In the linear response limit (small bias), the coupling between particles may enhance the diffusion process, depending on the competition between the harmonic chain and the substrate potential. An analytical formula of the diffusion rate for the single-particle case is also obtained. In the nonlinear response regime, the moving kink may become...
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
Murrell, J K J
2001-01-01
previously unexplored regions of parameter space. We show that these calculations predict a range of previously unreported dynamical I-V characterises for SQUID rings in the strongly hysteretic regime. Finally, we present the successful realisation of a novel experimental technique that permits the weak link of a SQUID to be probed independently of the associated ring structure by mechanically opening and closing the ring. We demonstrate that this process can be completed during the same experimental run without the need for warming and re-cooling of the sample. This thesis is concerned with the investigation of the non-linear behaviour of a Superconducting Quantum Interference Device (SQUID) coupled to a RF tank circuit. We consider two regimes, one where the underlying SQUID behaviour is non-hysteretic with respect to an externally applied magnetic flux, and the other where hysteretic (dissipative) behaviour is observed. We show that, by following non-linearities induced in the tank circuit response, the un...
Noise Effects on Synchronized Globally Coupled Oscillators
Moro, Esteban; Sánchez, Angel
1998-01-01
The synchronized phase of globally coupled identical nonlinear oscillators subject to noise fluctuations is studied by means of a new analytical approach able to tackle general couplings, nonlinearities, and noise temporal correlations. Our results show that the interplay between coupling and noise modi es the e ective frequency of the system in a nontrivial way. Whereas for linear couplings the e ect of noise is always to increase the e ective frequency, for nonlinear coupling...
Bachelard, Nicolas; Sebbah, Patrick; Vanneste, Christian
2014-01-01
We use time-domain numerical simulations of a two-dimensional (2D) scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a small electric field intensity, we observe the strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a larger intensity induces non-linear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in non-linear Rabi oscillations. The transition between both regimes is observed and an analytical model is proposed which accurately describes our numerical observations.
Nonlinear Oscillators in Space Physics
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
Linearization of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E; Pascual, I [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-03-11
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for the complete range of oscillation amplitudes. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of the technique.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Energetics of Synchronization in Coupled Oscillators
Izumida, Yuki; Seifert, Udo
2016-01-01
We formulate the energetics of synchronization in coupled oscillators by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. We derive a concise and universal expression of the energy dissipation rate using nonlinear-dynamics quantities characterizing synchronization, and elucidate how synchronization/desynchronization between the oscillators affects it. We apply our theory to hydrodynamically-coupled Stokes spheres rotating on circular trajectories that may be interpreted as the simplest model of synchronization of coupled oscillators in a biological system, revealing that the oscillators gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Parametrically Driven Nonlinear Oscillators with an Impurity
Institute of Scientific and Technical Information of China (English)
张卓; 唐翌
2002-01-01
By virtue of the method of multiple scales, we study a chain of parametrically driven nonlinear oscillators with a mass impurity. An equation is presented to describe the nonlinear wave of small amplitude in the chain.In our derivation, the equation is applicable to any eigenmode of coupled pendulum. Our result shows that a nonpropagation soliton emerges as the lowest or highest eigenmode of coupled pendulum is excited, and the impurity tends to pin the nonpropagation soliton excitation.
An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions
Dodonov, V. V.; Klimov, A. B.
1993-01-01
We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.
Coupled oscillators with parity-time symmetry
Tsoy, Eduard N.
2017-02-01
Different models of coupled oscillators with parity-time (PT) symmetry are studied. Hamiltonian functions for two and three linear oscillators coupled via coordinates and accelerations are derived. Regions of stable dynamics for two coupled oscillators are obtained. It is found that in some cases, an increase of the gain-loss parameter can stabilize the system. A family of Hamiltonians for two coupled nonlinear oscillators with PT-symmetry is obtained. An extension to high-dimensional PT-symmetric systems is discussed.
Nonlinear oscillations of a coupled autoparametrical system with ideal and nonideal sources of power
Directory of Open Access Journals (Sweden)
Sado Danuta
2006-01-01
Full Text Available An ideal and nonideal autoparametrical system excited by DC motor with unbalanced mass is presented in this work. The system consists of the body of mass M which is hung on a nonlinear spring with a nonlinear damper, and a pendulum of the length l and mass m mounted to the body of mass M. It is assumed that the motion of the pendulum is damped by nonlinear resistive forces. Vibrations of both models (ideal and nonideal are researched. Solutions for the system response are presented for specific values of the parameters of system and the energy transfer between modes of vibrations is studied. Next excited vibrations for both models have been examined analytically and numerically. Except different kinds of periodic vibrations, there may also appear chaotic vibrations.
Cubication of Conservative Nonlinear Oscillators
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Lin Xiao-Gang; Liu Wen-Jun; Lei Ming
2016-03-01
Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota’s bilinear method. The bilinear forms and analytic soliton solutions are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.
Institute of Scientific and Technical Information of China (English)
GU Ji-jun; AN Chen; LEVI Carlos; SU Jian
2012-01-01
The Generalized Integral Transform Technique (GITT) was applied to predict dynamic response of Vortex-Induced Vibration (VIV) of a long flexible cylinder.A nonlinear wake oscillator model was used to represent the cross-flow force acting on the cylinder,leading to a coupled system of second-order Partial Differential Equations (PDEs) in temporal variable.The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs),which was numerically solved by using the Adams-Moulton and Gear method (DIVPAG) developed by the International Mathematics and Statistics Library (IMSL).Numerical results were presented for comparison to those given by the finite difference method and experimental results,allowing a critical evaluation of the technique performance.The influence of variation of mean axial tension induced by elongation of flexible cylinder was evaluated,which was shown to be not negligible in numerical simulation of VIV of a long flexible cylinder.
Yuan, L. H.; Wang, C. N.; Zhang, Z. Z.
2016-10-01
Based on the Lyapunov stability theory, an improved Lyapunov function scheme is used to understand the complete synchronization of hyperchaotic systems by imposing pulse linear coupling on the response system. According to this scheme, the controller begins to control the response system in a period when the output error variables are increasing; otherwise, the controller turns off. The distribution of conditional Lyapunov exponent versus coupling intensity, and the synchronization cost (averaged power consumption of controller) is calculated, respectively. By designing an exponential type of Lyapunov function, it is found that complete synchronization could be realized between two Chen hyperchaotic systems and two 4-dimensional LC hyperchaotic systems. Our numerical results are consistent with the previous theoretical discussion.
Coalescence in coupled Duffing oscillators
Institute of Scientific and Technical Information of China (English)
YANG Jun-Zhong
2009-01-01
The forced Duffing oscillator has a pair of symmetrical attractors in a proper parameter regime. When a lot of Duffing oscillators are coupled linearly, the system tends to form clusters in which the neighboring oscillators fall onto the same attractor. When the coupling strength is strong, all of the oscillators fall onto one attractor. In this work, we investigate coalescence in the coupled forced Duffing oscillators. Some phenomena are found and explanations are presented.
Autoresonance versus localization in weakly coupled oscillators
Kovaleva, Agnessa; Manevitch, Leonid I.
2016-04-01
We study formation of autoresonance (AR) in a two-degree of freedom oscillator array including a nonlinear (Duffing) oscillator (the actuator) weakly coupled to a linear attachment. Two classes of systems are studied. In the first class of systems, a periodic force with constant (resonance) frequency is applied to a nonlinear oscillator (actuator) with slowly time-decreasing stiffness. In the systems of the second class a nonlinear time-invariant oscillator is subjected to an excitation with slowly increasing frequency. In both cases, the attached linear oscillator and linear coupling are time-invariant, and the system is initially engaged in resonance. This paper demonstrates that in the systems of the first type AR in the nonlinear actuator entails oscillations with growing amplitudes in the linear attachment while in the system of the second type energy transfer from the nonlinear actuator is insufficient to excite high-energy oscillations of the attachment. It is also shown that a slow change of stiffness may enhance the response of the actuator and make it sufficient to support oscillations with growing energy in the attachment even beyond the linear resonance. Explicit asymptotic approximations of the solutions are obtained. Close proximity of the derived approximations to exact (numerical) results is demonstrated.
Modeling of Coupled Chaotic Oscillators
Energy Technology Data Exchange (ETDEWEB)
Lai, Y. [Departments of Physics and Astronomy and of Mathematics, University of Kansas, Lawrence, Kansas 66045 (United States); Grebogi, C. [Institute for Plasma Research, Department of Mathematics, Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)
1999-06-01
Chaotic dynamics may impose severe limits to deterministic modeling by dynamical equations of natural systems. We give theoretical argument that severe modeling difficulties may occur for high-dimensional chaotic systems in the sense that no model is able to produce reasonably long solutions that are realized by nature. We make these ideas concrete by investigating systems of coupled chaotic oscillators. They arise in many situations of physical and biological interests, and they also arise from discretization of nonlinear partial differential equations. {copyright} {ital 1999} {ital The American Physical Society}
Cubication of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-09-15
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
Akbarzade, M.; Langari, J.
2011-02-01
In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, comparisons with other results are presented to show the effectiveness of this method. The validity of the method is independent of whether or not there exist small or large parameters in the considered nonlinear equations; the obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. At the end we compare our procedure with the optimal homotopy perturbation method.
Institute of Scientific and Technical Information of China (English)
黄思训; 项杰; 韩威
2004-01-01
The troposphere and ocean mixed layer were considered as two components of a dynamic system operated by solar radiation as the constant source of energy, where upon an air-sea coupling selfexited coupling oscillation model was based with the aid of a locally averaged thermodynamic climate model, resulting mathematically in a closed self-governed dynamic system, a so-called El Nino-Southern Oscillation (ENSO) system. With the limit cycle solution of the system. It is shown that the essential physics of the coupled system can be described by the ENSO system. Compared with the observations, the theoretical limit cycle orbit matches the observed phase loop qualitatively. The ENSO system provides a useful theoretical framework for study of interannual variation of the tropical climate system.
Nonlinear harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Calogero, F [Dipartimento di Fisica, Universita di Roma ' La Sapienza' (Italy); Inozemtsev, V I [Joint Institute for Nuclear Research, Dubna (Russian Federation)
2002-12-06
The existence is noted of assemblies of an arbitrary number of complex oscillators, or equivalently, of an arbitrary even number of real oscillators, characterized by Newtonian equations of motion ('acceleration equal force') with one-body velocity-dependent linear forces and many-body velocity-independent cubic forces, all the nonsingular solutions of which are isochronous (completely periodic with the same period). As for the singular solutions, as usual they emerge, in the context of the initial-value problem, from a closed domain in phase space having lower dimensionality.
Pakhomov, A V; Babushkin, I V; Arkhipov, M V; Tolmachev, Yu A; Rosanov, N N
2016-01-01
We study the optical response of a resonant medium possessing the nonlinear coupling to external field under excitation by few-cycle pump pulses. A theoretical approach is developed, allowing to analyze unipolar half-cycle pulse generation in such a geometry. Our approach is applicable for the arbitrary coupling functions as well as arbitrarily curved pump pulse wavefronts and defines a general framework to produce unipolar pulses of desired form.
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... that at resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Synchronization of Nonlinear Oscillators Over Networks with Dynamic Links
De Persis, Claudio
2015-01-01
In this paper we investigate the problem of synchronization of homogeneous nonlinear oscillators coupled by dynamic links. The output of the nonlinear oscillators is the input to the dynamic links, while the output of these dynamics links is the quantity available to the distributed controllers at t
Chembo Kouomou, Y; Woafo, P
2003-04-01
We study the spatiotemporal dynamics of a ring of diffusely coupled single-well Duffing oscillators. The transitions from spatiotemporal chaos to cluster and complete synchronization states are particularly investigated, as well as the Hopf bifurcations to instability. It is found that the underlying mechanism of these transitions relies on the motion of the representative points corresponding to the system's nondegenerated spatial transverse Fourier modes in the parametric Strutt diagram. A scaling law is used to demonstrate that the compact interval of the scalar coupling parameter values leading to cluster synchronization broadens in a square-power-like fashion as the number of oscillators is increased. The analytical approach is confirmed by numerical simulations.
Covariant harmonic oscillators and coupled harmonic oscillators
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
1995-01-01
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
Variable order variable stepsize algorithm for solving nonlinear Duffing oscillator
Fadly Nurullah Rasedee, Ahmad; Ishak, Norizarina; Raihana Hamzah, Siti; Ijam, Hazizah Mohd; Suleiman, Mohamed; Bibi Ibrahim, Zarina; Sathar, Mohammad Hasan Abdul; Ainna Ramli, Nur; Shuhada Kamaruddin, Nur
2017-09-01
Nonlinear phenomena in science and engineering such as a periodically forced oscillator with nonlinear elasticity are often modeled by the Duffing oscillator (Duffing equation). The Duffling oscillator is a type of nonlinear higher order differential equation. In this research, a numerical approximation for solving the Duffing oscillator directly is introduced using a variable order stepsize (VOS) algorithm coupled with a backward difference formulation. By selecting the appropriate restrictions, the VOS algorithm provides a cost efficient computational code without affecting its accuracy. Numerical results have demonstrated the advantages of a variable order stepsize algorithm over conventional methods in terms of total steps and accuracy.
Coupled oscillators on evolving networks
Singh, R. K.; Bagarti, Trilochan
2016-12-01
In this work we study coupled oscillators on evolving networks. We find that the steady state behavior of the system is governed by the relative values of the spread in natural frequencies and the global coupling strength. For coupling strong in comparison to the spread in frequencies, the system of oscillators synchronize and when coupling strength and spread in frequencies are large, a phenomenon similar to amplitude death is observed. The network evolution provides a mechanism to build inter-oscillator connections and once a dynamic equilibrium is achieved, oscillators evolve according to their local interactions. We also find that the steady state properties change by the presence of additional time scales. We demonstrate these results based on numerical calculations studying dynamical evolution of limit-cycle and van der Pol oscillators.
On the nonlinear modeling of ring oscillators
Elwakil, Ahmed S.
2009-06-01
We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.
Hyperchaos in coupled Colpitts oscillators
DEFF Research Database (Denmark)
Cenys, Antanas; Tamasevicius, Arunas; Baziliauskas, Antanas
2003-01-01
The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R-k. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual...
Monlinear fish-scale metamaterial via coupled duffing oscillators
Kochetov, Bogdan; Tuz, Vladimir; Mladyonov, Pavel; Prosvirnin, Sergey; Kochetova, Lyudmila
2012-01-01
The dynamic system of two coupled Duffing oscillators is considered in order to predict the optical response of the nonlinear planar fish-scale metamaterial. The direct numerical calculation of meta material response confirms the correctness of the proposed model
Chaos in nonlinear oscillations controlling and synchronization
Lakshamanan, M
1996-01-01
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
A simple approach to nonlinear oscillators
Ren, Zhong-Fu; He, Ji-Huan
2009-10-01
A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
FORCED OSCILLATIONS IN NONLINEAR FEEDBACK CONTROL SYSTEM
Since a nonlinear feedback control system may possess more than one type of forced oscillations, it is highly desirable to investigate the type of...method for finding the existence of forced oscillations and response curve characteristics of a nonlinear feedback control system by means of finding the...second order feedback control system are investigated; the fundamental frequency forced oscillation for a higher order system and the jump resonance
Zalian, Cyrus
2016-01-01
Context. The Blazhko effect, in RR Lyrae type stars, is a century old mystery. Dozens of theory exists, but none have been able to entirely reproduce the observational facts associated to this modulation phenomenon. Existing theory all rely on the usual continuous modelization of the star. Aims. We present a new paradigm which will not only explain the Blazhko effect, but at the same time, will give us alternative explanations to the red limit of the instability strip, the synchronization of layers, the mode selection and the existence of a limit cycle for radially pulsating stars. Methods. We describe the RR Lyrae type pulsating stars as a system of coupled nonlinear oscillators. Considering a spatial discretisation of the star, supposing a spherical symmetry, we develop the equation of motion and energy up to the third order in the radial and adiabatic case. Then, we include the influence of the ionization region as a relaxation oscillator by including elements from synchronisation theory. Results. This dis...
Hydrodynamic synchronization of nonlinear oscillators at low Reynolds number.
Leoni, M; Liverpool, T B
2012-04-01
We introduce a generic model of a weakly nonlinear self-sustained oscillator as a simplified tool to study synchronization in a fluid at low Reynolds number. By averaging over the fast degrees of freedom, we examine the effect of hydrodynamic interactions on the slow dynamics of two oscillators and show that they can lead to synchronization. Furthermore, we find that synchronization is strongly enhanced when the oscillators are nonisochronous, which on the limit cycle means the oscillations have an amplitude-dependent frequency. Nonisochronity is determined by a nonlinear coupling α being nonzero. We find that its (α) sign determines if they synchronize in phase or antiphase. We then study an infinite array of oscillators in the long-wavelength limit, in the presence of noise. For α>0, hydrodynamic interactions can lead to a homogeneous synchronized state. Numerical simulations for a finite number of oscillators confirm this and, when α<0, show the propagation of waves, reminiscent of metachronal coordination.
Nonlinear analysis of ring oscillator circuits
Ge, Xiaoqing
2010-06-01
Using nonlinear systems techniques, we analyze the stability properties and synchronization conditions for ring oscillator circuits, which are essential building blocks in digital systems. By making use of its cyclic structure, we investigate local and global stability properties of an n-stage ring oscillator. We present a sufficient condition for global asymptotic stability of the origin and obtain necessity if the ring oscillator consists of identical inverter elements. We then give a synchronization condition for identical interconnected ring oscillators.
Magnetically Coupled Magnet-Spring Oscillators
Donoso, G.; Ladera, C. L.; Martin, P.
2010-01-01
A system of two magnets hung from two vertical springs and oscillating in the hollows of a pair of coils connected in series is a new, interesting and useful example of coupled oscillators. The electromagnetically coupled oscillations of these oscillators are experimentally and theoretically studied. Its coupling is electromagnetic instead of…
Direct observation of coherent energy transfer in nonlinear micromechanical oscillators
Chen, Changyao; Zanette, Damián H.; Czaplewski, David A.; Shaw, Steven; López, Daniel
2017-05-01
Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. The fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.
Direct observation of coherent energy transfer in nonlinear micromechanical oscillators.
Chen, Changyao; Zanette, Damián H; Czaplewski, David A; Shaw, Steven; López, Daniel
2017-05-26
Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. The fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.
The Dynamics of Coupled Oscillator Phase Control
Pogorzelski, R. J.; Maccarini, P. F.; York, R. A.
1998-01-01
Arrays of coupled oscillators have been proposed as means of realizing high power rf sources via coherent spatial power combining. In such applications, a uniform phase distribution over the aperture is usually desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Of particular interest among those achievable are linear phase distributions because these result in steering of the output rf beam away from the broadside direction. The theory describing the behavior of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. However, a simplified theory has been developed which facilitates intuitive understanding. This simplified theory is based on a "continuum model" in which the aperture phase is represented by a continuous function of the aperture coordinates. A challenging aspect of the development of this theory is the derivation of appropriate boundary conditions at the edges or ends of the array.
A single-ion nonlinear mechanical oscillator
Akerman, Nitzan; Glickamn, Yinnon; Dallal, Yehonatan; Keselman, Anna; Ozeri, Roee
2010-01-01
We study the steady state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser-cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate a unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the cooling laser parameters. Our observations open a way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.
Self-synchronization in an ensemble of nonlinear oscillators
Ostrovsky, L. A.; Galperin, Y. V.; Skirta, E. A.
2016-06-01
The paper describes the results of study of a system of coupled nonlinear, Duffing-type oscillators, from the viewpoint of their self-synchronization, i.e., generation of a coherent field (order parameter) via instability of an incoherent (random-phase) initial state. We consider both the cases of dissipative coupling (e.g., via the joint radiation) and reactive coupling in a Hamiltonian system.
Non- Markovian Quantum Stochastic Equation For Two Coupled Oscillators
Alpomishev, E X
2016-01-01
The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical expressions for transport coefficients was found. Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of linear couplings in the coordinate between the collective two coupled harmonic oscillators and heat bath.
Resurgence of oscillation in coupled oscillators under delayed cyclic interaction
Bera, Bidesh K.; Majhi, Soumen; Ghosh, Dibakar
2017-07-01
This paper investigates the emergence of amplitude death and revival of oscillations from the suppression states in a system of coupled dynamical units interacting through delayed cyclic mode. In order to resurrect the oscillation from amplitude death state, we introduce asymmetry and feedback parameter in the cyclic coupling forms as a result of which the death region shrinks due to higher asymmetry and lower feedback parameter values for coupled oscillatory systems. Some analytical conditions are derived for amplitude death and revival of oscillations in two coupled limit cycle oscillators and corresponding numerical simulations confirm the obtained theoretical results. We also report that the death state and revival of oscillations from quenched state are possible in the network of identical coupled oscillators. The proposed mechanism has also been examined using chaotic Lorenz oscillator.
Phase reduction approach to synchronisation of nonlinear oscillators
Nakao, Hiroya
2016-04-01
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 often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.
Steady-state negative Wigner functions of nonlinear nanomechanical oscillators
Rips, Simon; Wilson-Rae, Ignacio; Hartmann, Michael J
2011-01-01
We propose a scheme to prepare nanomechanical oscillators in non-classical steady states, characterized by a pronounced negative Wigner function. In our optomechanical approach, the mechanical oscillator couples to multiple laser driven resonances of an optical cavity. By lowering the resonant frequency of the oscillator via an inhomogeneous electrostatic field, we significantly enhance its intrinsic geometric nonlinearity per phonon. This causes the motional sidebands to split into separate spectral lines for each phonon number and transitions between individual phonon Fock states can be selectively addressed. We show that this enables preparation of the nanomechanical oscillator in a single phonon Fock state. Our scheme can for example be implemented with a carbon nanotube dispersively coupled to the evanescent field of a state of the art whispering gallery mode microcavity.
Transmitting information by controlling nonlinear oscillators
Tôrres, Leonardo A. B.; Aguirre, Luis A.
2004-09-01
The transmission of information relying on the perturbation of nonlinear oscillators vector fields can be approached in a unified manner. This can be accomplished by making use of the Information Transmission Via Control principle, which is stated and proved in the present work. In short, this principle establishes that any controller used to identically synchronize pairs of nonlinear oscillators, including chaotic ones as a special case, can be actually employed as demodulator/decoder in the process of information recovery. Other theoretical results related to the practical realization of the ITVC principle are presented and experimental data is provided showing a good agreement with the proposed theory.
Low dimensional behavior of large systems of globally coupled oscillators
Ott, Edward; Antonsen, Thomas M.
2008-09-01
It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered.
Basin stability measure of different steady states in coupled oscillators.
Rakshit, Sarbendu; Bera, Bidesh K; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-04-05
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.
Basin stability measure of different steady states in coupled oscillators
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-01-01
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis. PMID:28378760
A Simplified Theory of Coupled Oscillator Array Phase Control
Pogorzelski, R. J.; York, R. A.
1997-01-01
Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining. In such - applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Notable among these are linear phase distributions resulting in steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simpl!fied theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.
Chaotic synchronization of two complex nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Gamal M. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)], E-mail: gmahmoud@aun.edu.eg; Mahmoud, Emad E. [Department of Mathematics, Faculty of Science, Sohag University (Egypt)], E-mail: emad_eluan@yahoo.com; Farghaly, Ahmed A. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)], E-mail: ahmed_1_66@yahoo.com; Aly, Shaban A. [Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511 (Egypt)], E-mail: shhaly12@yahoo.com
2009-12-15
Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.
Revoking amplitude and oscillation deaths by low-pass filter in coupled oscillators
Zou, Wei; Zhan, Meng; Kurths, Jürgen
2017-06-01
When in an ensemble of oscillatory units the interaction occurs through a diffusion-like manner, the intrinsic oscillations can be quenched through two structurally different scenarios: amplitude death (AD) and oscillation death (OD). Unveiling the underlying principles of stable rhythmic activity against AD and OD is a challenging issue of substantial practical significance. Here, by developing a low-pass filter (LPF) to track the output signals of the local system in the coupling, we show that it can revoke both AD and OD, and even the AD to OD transition, thereby giving rise to oscillations in coupled nonlinear oscillators under diverse death scenarios. The effectiveness of the local LPF is proven to be valid in an arbitrary network of coupled oscillators with distributed propagation delays. The constructive role of the local LPF in revoking deaths provides a potential dynamic mechanism of sustaining a reliable rhythmicity in real-world systems.
Synchronization in a coupled architecture of microelectromechanical oscillators
Agrawal, Deepak K.; Woodhouse, Jim; Seshia, Ashwin A.
2014-04-01
There has been much recent interest in engineering the phenomenon of synchronization in coupled micro-/nano-scale oscillators for applications ranging from precision time and frequency references to new approaches to information processing. This paper presents descriptive modelling detail and further experimental validation of the phenomenon of mutual synchronization in coupled MEMS oscillators building upon recent experimental validation of this concept by the present authors. In particular, the underlying dependence of the observation of synchronization on system parameters is studied through numerical and analytical modelling while considering essential nonlinearities in both the resonator and circuit domain. Experimental results demonstrating synchronized response are elaborated based on the realization of electrically coupled MEMS resonator based square-wave oscillators. The experimental results on frequency entrainment are found to be in general agreement with results obtained through analytical modeling and numerical simulation. The concept presented here is scalable and could be used to investigate the dynamics of large-arrays of coupled MEMS oscillators.
Fourier series expansion for nonlinear Hamiltonian oscillators.
Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac
2010-06-01
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 relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.
Energy Technology Data Exchange (ETDEWEB)
Lim, C.W. [Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong (China)], E-mail: bccwlim@cityu.edu.hk; Lai, S.K. [Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong (China)
2007-08-20
This Letter deals with a research subject in nonlinear mechanics and applied mathematics. It develops (i) accurate higher-order approximate analytical nonlinear oscillator system with negative dissipation, and (ii) analogy to long Josephson junction. Particular emphasis has been placed on the weakly damped nonlinear oscillating system with negative dissipation with respect to a transformed temporal variable derived from the weak link of the simplified Josephson junction model. Nevertheless, the system response is shown to be stable with positive dissipation with respect to the physical time at a specific location. The analysis forms an innovative extension of the harmonic balancing method commonly used in nonlinear oscillation and vibration systems such as the Duffing oscillator and van der Pol oscillator. Besides introducing coupling of linearized governing equation and harmonic balancing method, the method of averaging is also employed to obtain accurate higher-order analytical approximate solutions. Unlike the classical harmonic balance method without analytical solution, the approach not only considers energy dissipation but also presents simple linear algebraic approximate solutions. In addition, general approximate analytical expressions for the dispersion relations are also established. The presence of a small perturbed parameter is not required.
Chaotic coupling synchronization of hyperchaotic oscillators
Institute of Scientific and Technical Information of China (English)
Zou Yan-Li; Zhu Jie; Chen Guan-Rong
2005-01-01
In this paper, two kinds of chaotic coupling synchronization schemes are presented. The synchronizability of the coupled hyperchaotic oscillators is proved mathematically and the numerical simulation is also carried out. The numerical calculation of the largest conditional Lyapunov exponent shows that in a given range of coupling strengths,chaotic-coupling synchronization is quicker than the typical continuous-coupling synchronization.
Capture into resonance of coupled Duffing oscillators.
Kovaleva, Agnessa
2015-08-01
In this paper we investigate capture into resonance of a pair of coupled Duffing oscillators, one of which is excited by periodic forcing with a slowly varying frequency. Previous studies have shown that, under certain conditions, a single oscillator can be captured into persistent resonance with a permanently growing amplitude of oscillations (autoresonance). This paper demonstrates that the emergence of autoresonance in the forced oscillator may be insufficient to generate oscillations with increasing amplitude in the attachment. A parametric domain, in which both oscillators can be captured into resonance, is determined. The quasisteady states determining the growth of amplitudes are found. An agreement between the theoretical and numerical results is demonstrated.
Asymptotic solution for EI Nino-southern oscillation of nonlinear model
Institute of Scientific and Technical Information of China (English)
MO Jia-qi; LIN Wan-tao
2008-01-01
A class of nonlinear coupled system for E1 Nino-Southern Oscillation (ENSO) model is considered. Using the asymptotic theory and method of variational iteration, the asymptotic expansion of the solution for ENSO models is obtained.
Averaged Behaviour of Nonconservative Coupled Oscillators
Bakri, T.
2007-01-01
In this Thesis we study the dynamics of systems of two and three coupled oscillators by efficiently applying Normal Form theory. The subject of Coupled oscillators plays an important part in dynamical systems. It has a wide range of applications in various fields like physics, biology, economics and
Diverse routes to oscillation death in a coupled oscillator system
Suárez-Vargas, José J.; González, Jorge A.; Stefanovska, Aneta; McClintock, Peter V. E.
2010-01-01
We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparameter-sensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory. PMID:20823952
Heteroclinic Bifurcation of Strongly Nonlinear Oscillator
Institute of Scientific and Technical Information of China (English)
ZHANG Qi-Chang; WANG Wei; LI Wei-Yi
2008-01-01
Analytical prediction of heteroclinic bifurcation of the strongly nonlinear oscillator is presented by using the extended normal form method.We consider the approximate periodic solution of the system subject to the quintic nonlinearity by introducing the undetermined fundamental frequency.For the occurrence of heteroclinicity,the bifurcation criterion is accomplished.It depends on the contact of the limit cycle with the saddle equilibrium.As is illustrated,the explicit application shows that the new results coincide very well with the results of numerical simulation when disturbing parameter is of arbitrary magnitude.PACS: 82.40.Bj,47.20.Ky,02.30.Hq
Analytical solution of strongly nonlinear Duffing oscillators
Directory of Open Access Journals (Sweden)
A.M. El-Naggar
2016-06-01
Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.
Phase reduction theory for hybrid nonlinear oscillators
Shirasaka, Sho; Kurebayashi, Wataru; Nakao, Hiroya
2017-01-01
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of limit-cycle oscillations in rhythmic systems, has mostly been restricted to smooth dynamical systems. Here we develop a general phase reduction theory for weakly perturbed limit cycles in hybrid dynamical systems that facilitates analysis, control, and optimization of nonlinear oscillators whose smooth models are unavailable or intractable. On the basis of the generalized theory, we analyze injection locking of hybrid limit-cycle oscillators by periodic forcing and reveal their characteristic synchronization properties, such as ultrafast and robust entrainment to the periodic forcing and logarithmic scaling at the synchronization transition. We also illustrate the theory by analyzing the synchronization dynamics of a simple physical model of biped locomotion.
Suppression and revival of oscillation in indirectly coupled limit cycle oscillators
Energy Technology Data Exchange (ETDEWEB)
Sharma, P.R.; Kamal, N.K.; Verma, U.K. [Department of Physics, Central University of Rajasthan, Ajmer 305 817, Rajasthan (India); Suresh, K. [Department of Physics, Anjalai Ammal-Engineering College, Koyilvenni 614 403, Tamil Nadu (India); Thamilmaran, K. [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu (India); Shrimali, M.D., E-mail: shrimali@curaj.ac.in [Department of Physics, Central University of Rajasthan, Ajmer 305 817, Rajasthan (India)
2016-09-16
Highlights: • The phenomena of suppression and revival of oscillations are studied in indirectly coupled nonlinear oscillators. • The decay parameter and a feedback factor play a crucial role in emergent dynamical behavior of oscillators. • The critical curves for different dynamical regions are obtained analytically using linear stability analysis. • Electronic circuit experiments demonstrate these emergent dynamical states. - Abstract: We study the phenomena of suppression and revival of oscillations in a system of limit cycle oscillators coupled indirectly via a dynamic local environment. The dynamics of the environment is assumed to decay exponentially with time. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). We also show that introducing a feedback factor in the diffusion term revives the oscillations in this system. The critical curves for the regions of different emergent states as a function of coupling strength, decay parameter of the environment and feedback factor in the coupling are obtained analytically using linear stability analysis. These results are found to be consistent with the numerics and are also observed experimentally.
Raman-Suppressing Coupling for Optical Parametric Oscillator
Savchenkov, Anatoliy; Maleki, Lute; Matsko, Andrey; Rubiola, Enrico
2007-01-01
A Raman-scattering-suppressing input/ output coupling scheme has been devised for a whispering-gallery-mode optical resonator that is used as a four-wave-mixing device to effect an all-optical parametric oscillator. Raman scattering is undesired in such a device because (1) it is a nonlinear process that competes with the desired nonlinear four-wave conversion process involved in optical parametric oscillation and (2) as such, it reduces the power of the desired oscillation and contributes to output noise. The essence of the present input/output coupling scheme is to reduce output loading of the desired resonator modes while increasing output loading of the undesired ones.
Nonlinear oscillations in coriolis based gyroscopes
Directory of Open Access Journals (Sweden)
Dag Kristiansen
1999-01-01
Full Text Available In this paper we model and analyze nonlinear oscillations which are known to exist in some Coriolis based gyroscopes due to large amplitude excitation in the drive loop. A detailed derivation of a dynamic model for a cylinder gyroscope which includes geometric nonlinearities is given, and energy transfer between the system's modes are analyzed using perturbation theory and by proposing a simplified model. The model is also simulated, and the results are shown to give an accurate description of the experimental results. This work is done in order to gain a better understanding of the gyroscope's dynamics, and is intended to be a starting point for designing nonlinear observers and vibration controllers for the gyroscope in order to increase the performance.
Dynamics of Coupled Quantum-Classical Oscillators
Institute of Scientific and Technical Information of China (English)
HE Wei-Zhong; XU Liu-Su; ZOU Feng-Wu
2004-01-01
@@ The dynamics of systems consisting of coupled quantum-classical oscillators is numerically investigated. It is shown that, under certain conditions, the quantum oscillator exhibits chaos. When the mass of the classical oscillator increases, the chaos will be suppressed; if the energy of the system and/or the coupling strength between the two oscillators increases, chaotic behaviour of the system appears. This result will be helpful to understand the probability of the emergence of quantum chaos and may be applied to explain the spectra of complex atoms qualitatively.
Institute of Scientific and Technical Information of China (English)
吴勇峰; 张世平
2011-01-01
Considering the huge computation and long time calculation in phase transition identification of weak signal detection based on single Duffing oscillator,a unidirectional driving nonlinear coupled Duffing oscillator system is established.System synchronization state from chaotic state to large-scale periodic state is analyzed according to transverse Lyapunov exponent,and a novel method for phase transition identification based on synchronization error is proposed.Experiment simulation shows that this coupled Duffing oscillator system can quickly detect weak signal in strong noise.%针对单个Duffing振子检测微弱信号时相交判别计算量大、时间长、不易把握等问题,建立了一个单向驱动非线性耦合Duffing振子系统.根据横向Lyapunov指数分析了系统在混沌态到大尺度周期态时振子间运动轨迹的同步演化特性,提出了利用同步误差来判别相变的新方法.实验仿真表明,在强噪声背景下该耦合系统仍能够正确快速地检测出微弱信号.
Control of coupled oscillator networks with application to microgrid technologies.
Skardal, Per Sebastian; Arenas, Alex
2015-08-01
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
Complex behavior in chains of nonlinear oscillators
Alonso, Leandro M.
2017-06-01
This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.
Parameters Approach Applied on Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Najeeb Alam Khan
2014-01-01
Full Text Available We applied an approach to obtain the natural frequency of the generalized Duffing oscillator u¨ + u + α3u3 + α5u5 + α7u7 + ⋯ + αnun=0 and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection u¨+αu|u|n−1=0. This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of n, the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain.
Phase Multistability in Coupled Oscillator Systems
DEFF Research Database (Denmark)
Mosekilde, Erik; Postnov, D.E.; Sosnovtseva, Olga
2003-01-01
The phenomenon of phase multistability arises in connection with the synchronization of coupled oscillator systems when the systems individually display complex wave forms associated, for instance, with the presence of subharmonic components or with significant variations of the phase velocity...
Resonance phenomena for asymmetric weakly nonlinear oscillator
Institute of Scientific and Technical Information of China (English)
钱定边
2002-01-01
We establish the coexistence of periodic solution and unbounded solution, the infinity of largeamplitude subharmonics for asymmetric weakly nonlinear oscillator x" + a2x+ - b2x- + h(x) = p(t) with h(±∞) - 0 and xh(x) → +∞(x →∞), assuming that M(τ ) has zeros which are all simple and M(τ ) 0respectively, where M(τ ) is a function related to the piecewise linear equation x" + a2x+ - b2x- = p(t).``
Multistability in nonlinearly coupled ring of Duffing systems
Jaros, P.; Kapitaniak, T.; Perlikowski, P.
2016-11-01
In this paper we consider dynamics of three unidirectionally coupled Duffing oscillators with nonlinear coupling function in the form of third degree polynomial. We focus on the influence of the coupling on the occurrence of different bifurcation's scenarios. The stability of equilibria, using Routh-Hurwitz criterion, is investigated. Moreover, we check how coefficients of the nonlinear coupling influence an appearance of different types of periodic solutions. The stable periodic solutions are computed using path-following. Finally, we show the two parameters' bifurcation diagrams with marked areas where one can observe the coexistence of solutions.
Pulse-coupled BZ oscillators with unequal coupling strengths.
Horvath, Viktor; Kutner, Daniel J; Chavis, John T; Epstein, Irving R
2015-02-14
Coupled chemical oscillators are usually studied with symmetric coupling, either between identical oscillators or between oscillators whose frequencies differ. Asymmetric connectivity is important in neuroscience, where synaptic strength inequality in neural networks commonly occurs. While the properties of the individual oscillators in some coupled chemical systems may be readily changed, enforcing inequality between the connection strengths in a reciprocal coupling is more challenging. We recently demonstrated a novel way of coupling chemical oscillators, which allows for manipulation of individual connection strengths. Here we study two identical, pulse-coupled Belousov-Zhabotinsky (BZ) oscillators with unequal connection strengths. When the pulse perturbations contain KBr (inhibitor), this system exhibits simple out-of-phase and complex oscillations, oscillatory-suppressed states as well as temporally periodic patterns (N : M) in which the two oscillators exhibit different numbers of peaks per cycle. The N : M patterns emerge due to the long-term effect of the inhibitory pulse-perturbations, a feature that has not been considered in earlier works. Time delay was previously shown to have a profound effect on the system's behaviour when pulse coupling was inhibitory and the coupling strengths were equal. When the coupling is asymmetric, however, delay produces no qualitative change in behaviour, though the 1 : 2 temporal pattern becomes more robust. Asymmetry in instantaneous excitatory coupling via AgNO3 injection produces a previously unseen temporal pattern (1 : N patterns starting with a double peak) with time delay and high [AgNO3]. Numerical simulations of the behaviour agree well with theoretical predictions in asymmetrical pulse-coupled systems.
Arrays of coupled chemical oscillators
Forrester, Derek Michael
2016-01-01
Oscillating chemical reactions result from complex periodic changes in the concentration of the reactants. In spatially ordered ensembles of candle flame oscillators the fluctuations in the ratio of oxygen atoms with respect to that of carbon, hydrogen and nitrogen produces an oscillation in the visible part of the flame related to the energy released per unit mass of oxygen. Thus, the products of the reaction vary in concentration as a function of time, giving rise to an oscillation in the amount of soot and radiative emission. Synchronisation of interacting dynamical sub-systems occurs as arrays of flames that act as master and slave oscillators, with groups of candles numbering greater than two, creating a synchronised motion in three-dimensions. In a ring of candles the visible parts of each flame move together, up and down and back and forth, in a manner that appears like a "worship". Here this effect is shown for rings of flames which collectively empower a central flame to pulse to greater heights. In ...
Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators
Directory of Open Access Journals (Sweden)
Gerold Baier
1997-01-01
Full Text Available We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. The systems involved are: (a a two-variable oscillator with two consecutive autocatalytic reactions derived from the Lotka–Volterra scheme; (b a minimal two-variable oscillator with one first-order autocatalytic reaction; (c a three-variable oscillator with first-order feedback lacking autocatalysis. The dynamics of a finite number of coupled biochemical oscillators may account for complex patterns in compartmentalized living systems like cells or tissue, and may be tested experimentally in coupled microreactors.
Synchronization of coupled Boolean phase oscillators
Rosin, David P.; Rontani, Damien; Gauthier, Daniel J.
2014-04-01
We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bidirectional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of the large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.
Intense energy transfer and superharmonic resonance in a system of two coupled oscillators.
Kovaleva, Agnessa; Manevitch, Leonid; Manevitch, Elina
2010-05-01
The paper presents the analytic study of energy exchange in a system of coupled nonlinear oscillators subject to superharmonic resonance. The attention is given to complete irreversible energy transfer that occurs in a system with definite initial conditions corresponding to a so-called limiting phase trajectory (LPT). We show that the energy imparted in the system is partitioned among the principal and superharmonic modes but energy exchange can be due to superharmonic oscillations. Using the LPT concept, we construct approximate analytic solutions describing intense irreversible energy transfer in a harmonically excited Duffing oscillator and a system of two nonlinearly coupled oscillators. Numerical simulations confirm the accuracy of the analytic approximations.
Amplitude envelope synchronization in coupled chaotic oscillators.
Gonzalez-Miranda, J M
2002-03-01
A peculiar type of synchronization has been found when two Van der Pol-Duffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.
Coupling among three chemical oscillators: Synchronization, phase death, and frustration
Yoshimoto, Minoru; Yoshikawa, Kenichi; Mori, Yoshihito
1993-02-01
Various modes in three coupled chemical oscillators in a triangular arrangement were observed. As a well-defined nonlinear oscillator, the Belousov-Zhabotinsky reaction was studied in a continuous-flow stirred tank reactor (CSTR). Coupling among CSTR's was performed by mass exchange. The coupling strength was quantitatively controlled by changing the flow rate of reacting solutions among the three CSTR's using peristaltic pumps between each pair of the reactors. As a key parameter to control the model of coupling, we changed the symmetry of the interaction between the oscillators. In the case of the symmetric coupling, a quasiperiodic state or a biperiodic mode, an all-death mode and two kinds of synchronized modes appeared, depending on the coupling strength. On the other hand, under the asymmetric coupling, a quasiperiodic state or a biperiodic mode, an all death mode and four kinds of synchronized modes appeared. Those modes have been discussed in relation to the idea of ``frustration'' in the Ising spin system, where the three-phase mode appears as a transition from the Ising spin system to the XY spin system.
Analytical Solutions to Non-linear Mechanical Oscillation Problems
DEFF Research Database (Denmark)
Kaliji, H. D.; Ghadimi, M.; Barari, Amin
2011-01-01
In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...
Oscillator death induced by amplitude-dependent coupling in repulsively coupled oscillators
Liu, Weiqing; Xiao, Guibao; Zhu, Yun; Zhan, Meng; Xiao, Jinghua; Kurths, Jürgen
2015-05-01
The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression.
Nonlinear oscillations in a unijunction transistor (UJT) circuit
Zielinski, John
2005-10-01
Phenomena such as plasma wavesootnotetextT Tsuru, Nonlinear resonance phenomena of elect. plasma oscillations by beam modulation, J. Phys. Soc. Japan, 40, 548, 1976. and oscillations in electric circuits which employ a plasma componentootnotetextM Wendt, I Axnas, S Torven, Amplitude collapse of nonlinear double-layer oscillations, Phys. Rev. E, 57, 4638, 1998. can be described by a differential equation with nonlinear dissipative and restoring force terms. The UJT oscillator circuit developed by Koepke and HartleyootnotetextME Koepke, DM Hartley, Experimental verification of periodic pulling in a nonlinear electronic oscillator, Phys. Rev. A, 44, 6877, 1991 is also described by a similar equation. During the past year efforts have been made to understand the following aspects of this circuit's operation: 1) Determining conditions which lead to oscillation onset and termination (amplitude collapse). 2) Analytic and numerical modeling. 3) Characterizing the capacitances associated with the emitter-base junctions. 4) Exploring the relationship between this circuit and astable multivibrators.
Coupling ultracold atoms to mechanical oscillators
Hunger, David; Korppi, Maria; Jöckel, Andreas; Hänsch, Theodor W; Treutlein, Philipp
2011-01-01
In this article we discuss and compare different ways to engineer an interface between ultracold atoms and micro- and nanomechanical oscillators. We start by analyzing a direct mechanical coupling of a single atom or ion to a mechanical oscillator and show that the very different masses of the two systems place a limit on the achievable coupling constant in this scheme. We then discuss several promising strategies for enhancing the coupling: collective enhancement by using a large number of atoms in an optical lattice in free space, coupling schemes based on high-finesse optical cavities, and coupling to atomic internal states. Throughout the manuscript we discuss both theoretical proposals and first experimental implementations.
Coupled Oscillator Systems Having Partial PT Symmetry
Beygi, Alireza; Bender, Carl M
2015-01-01
This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\\leq j\\leq N$) has the natural frequency $\\omega_j$ and is described by the Hamiltonian $\\frac{1}{2}p_j^2+\\frac{1}{2}\\omega_j^2x_j^2$. The oscillators are coupled adjacently with coupling constants that are purely imaginary; the coupling of the $j$th oscillator to the $(j+1)$st oscillator has the bilinear form $i\\gamma x_jx_{j+1}$ ($\\gamma$ real). The complex Hamiltonians for these systems exhibit {\\it partial} $\\mathcal{PT}$ symmetry; that is, they are invariant under $i\\to-i$ (time reversal), $x_j\\to-x_j$ ($j$ odd), and $x_j\\to x_j$ ($j$ even). [They are also invariant under $i\\to-i$, $x_j\\to x_j$ ($j$ odd), and $x_j\\to- x_j$ ($j$ even).] For all $N$ the quantum energy levels of these systems are calculated exactly and it is shown that the ground-state energy is real. When $\\omega_j=1$ for all $j$, the full spectrum consists of a real energy spectrum embedded in a complex one; the eigenfunctions correspondi...
Mode interaction in horses, tea, and other nonlinear oscillators: the universal role of symmetry
Weele, van der Jacobus P.; Banning, Erik J.
2001-01-01
This paper is about mode interaction in systems of coupled nonlinear oscillators. The main ideas are demonstrated by means of a model consisting of two coupled, parametrically driven pendulums. On the basis of this we also discuss mode interaction in the Faraday experiment (as observed by Ciliberto
Building better oscillators using nonlinear dynamics and pattern formation
Indian Academy of Sciences (India)
M C Cross; Eyal Kenig; John-Mark A Allen
2015-03-01
Frequency and time references play an essential role in modern technology and in living systems. The precision of self-sustained oscillations is limited by the effects of noise, which becomes evermore important as the sizes of the devices become smaller. In this paper, we review our recent theoretical results on using nonlinear dynamics and pattern formation to reduce the effects of noise and improve the frequency precision of oscillators, with particular reference to ongoing experiments on oscillators based on nanomechanical resonators. We discuss using resonator nonlinearity, novel oscillator architectures and the synchronization of arrays of oscillators, to improve the frequency precision.
Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators
Institute of Scientific and Technical Information of China (English)
王雪红; 郭军义; 李艳
2012-01-01
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
Susceptibility of large populations of coupled oscillators
Daido, Hiroaki
2015-01-01
It is an important and interesting problem to elucidate how the degree of phase order in a large population of coupled oscillators responds to a synchronizing periodic force from the outside. Here this problem is studied analytically as well as numerically by introducing the concept of susceptibility for globally coupled phase oscillators with either nonrandom or random interactions. It is shown that the susceptibility diverges at the critical point in the nonrandom case with Widom's equality satisfied, while it exhibits a cusp in the most random case.
Chaos Synchronization in Two Coupled Duffing Oscillators
Institute of Scientific and Technical Information of China (English)
方见树; 荣曼生; 方焯; 刘小娟
2001-01-01
We have obtained two general unstable periodic solutions near the homoclinic orbits of two coupled Duffing oscillators with weak periodic perturbations by using the direct perturbation technique. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding numerical results show that the phase portraits in the (x, u) and (y, v) planes are identical and are synchronized when the parameters of the two coupled oscillators are identical, but they are different and asynchronized when there is any difference between these parameters. It has been shown that the system parameters play a very important role in chaos control and synchronization.
Limiting Phase Trajectories and Resonance Energy Transfer in a System of Two Coupled Oscillators
Directory of Open Access Journals (Sweden)
L. I. Manevitch
2010-01-01
Full Text Available We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories (LPTs. The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an LPT and examine the convergence to stationary oscillations for a Duffing oscillator subjected to resonance harmonic excitation. As a second example, we treat resonance oscillations in a system of two nonlinearly coupled oscillators. We demonstrate the reduction of the equations of motion to an equation of a single oscillator. It is shown that the most intense energy exchange and beating arise when motion of the equivalent oscillator is close to an LPT. Damped beating and the convergence to rest in a system with dissipation are demonstrated.
Mode coupling in spin torque oscillators
Energy Technology Data Exchange (ETDEWEB)
Zhang, Steven S.-L., E-mail: ZhangShule@missouri.edu [Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211 (United States); Zhou, Yan, E-mail: yanzhou@hku.hk [Department of Physics, The University of Hong Kong, Hong Kong (China); Center of Theoretical and Computational Physics, University of Hong Kong, Hong Kong (China); Li, Dong, E-mail: geodesic.ld@gmail.com [Department of Physics, Centre for Nonlinear Studies, and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China); Heinonen, Olle, E-mail: heinonen@anl.gov [Material Science Division, Argonne National Laboratory, Lemont, IL 60439 (United States); Northwestern-Argonne Institute of Science and Technology, 2145 Sheridan Road, Evanston, IL 60208 (United States); Computation Institute, The Unversity of Chicago, 5735 S Ellis Avenue, Chicago, IL 60637 (United States)
2016-09-15
A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature. - Highlights: • Deriving equations for coupled modes in spin torque oscillators. • Including Hamiltonian formalism and elimination of three–magnon processes. • Thermal bath of magnons central to mode coupling. • Numerical examples of circular and elliptical devices.
Synchronization in Coupled Oscillators with Two Coexisting Attractors
Institute of Scientific and Technical Information of China (English)
ZHU Han-Han; YANG Jun-Zhong
2008-01-01
Dynamics in coupled Duffing oscillators with two coexisting symmetrical attractors is investigated. For a pair of Dutffng oscillators coupled linearly, the transition to the synchronization generally consists of two steps: Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions.
Energy Method to Obtain Approximate Solutions of Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion.
Projective synchronization of chaotic systems with bidirectional nonlinear coupling
Indian Academy of Sciences (India)
Mohammada Ali Khan; Swarup Poria
2013-09-01
This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.
On Synchronization of Coupled Hopf-Kuramoto Oscillators with Phase Delays
Chung, Soon-Jo
2010-01-01
This paper presents new methods and results on almost global synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any positive coupling gain is proven to induce almost global asymptotic synchronization, and a threshold value for truly global exponential synchronization is also computed. Furthermore, a hierarchical connection between coupled Hopf oscillators and Kuramoto oscillators is identified. Finally, a new result on the synchronization of Kuramoto oscillators with arbitrary time-varying heterogeneous frequencies and delays is derived.
On the Critical Coupling for Kuramoto Oscillators
Dorfler, Florian
2010-01-01
The celebrated Kuramoto model captures various synchronization phenomena in biological and man-made dynamical systems of coupled oscillators. It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency to synchronization occurs. This paper features three contributions. First, we characterize and distinguish the different notions of synchronization used throughout the literature and formally introduce the concept of phase cohesiveness as an analysis tool and performance index for synchronization. Second, we review the vast literature providing necessary, sufficient, implicit, and explicit estimates of the critical coupling strength in the finite and infinite-dimensional case. Finally, we present the first explicit necessary and sufficient condition on the critical coupling strength to achieve synchronization in the finite-dimensional Kuramoto model for an arbitrary distribution of the natural frequencies. The multiplicative gap in the synch...
Paradoxical stabilization of forced oscillations by strong nonlinear friction
Esirkepov, Timur Zh.; Bulanov, Sergei V.
2017-08-01
In a dissipative dynamic system driven by an oscillating force, a strong nonlinear highly oscillatory friction force can create a quasi-steady tug, which is always directed opposite to the ponderomotive force induced due to a spatial inhomogeneity of oscillations. When the friction-induced tug exceeds the ponderomotive force, the friction stabilizes the system oscillations near the maxima of the oscillation spatial amplitude of the driving force.
Investigation of coupled optical parametric oscillators for novel applications
Ding, Yujie J.
2016-03-01
In this proceedings article, we summarize our previous results on the novel applications using the coupled optical parametric oscillators (OPO's). In a conventional OPO, a single pump wavelength is capable of generating a pair of the signal and idler beams by placing a bulk nonlinear crystal inside an OPO cavity. When a nonlinear crystal composite consisting of periodically-inverted KTiOPO4 (KTP) plates bonded together by the adhesive-free-bonded (AFB) technique is used instead of the bulk nonlinear crystal, the optical parametric oscillation takes place at two sets of the new wavelengths for the signal and idler beams due to the phase shifts occurring at the interfaces of the adjacent domains making up the composite. These two sets of the signal and idler waves are effectively generated by the two OPO's being coupled to each other. These signals and idlers exhibit ultrastability in terms of their frequency separation. We review the progress made by us on the applications being realized by using such coupled OPO's such as THz generation and restoration of the blurred images after propagating through a distortion plate and a phase plate simulating atmospheric turbulence.
Energy Technology Data Exchange (ETDEWEB)
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere, E-mail: kyandoghere.kyamakya@uni-klu.ac.a, E-mail: jean.chedjou@uni-klu.ac.a [Transportation Informatics Group, Institute of Smart Systems Technologies, University of Klagenfurt (Austria)
2010-10-15
It is well known that a machine vision-based analysis of a dynamic scene, for example in the context of advanced driver assistance systems (ADAS), does require real-time processing capabilities. Therefore, the system used must be capable of performing both robust and ultrafast analyses. Machine vision in ADAS must fulfil the above requirements when dealing with a dynamically changing visual context (i.e. driving in darkness or in a foggy environment, etc). Among the various challenges related to the analysis of a dynamic scene, this paper focuses on contrast enhancement, which is a well-known basic operation to improve the visual quality of an image (dynamic or static) suffering from poor illumination. The key objective is to develop a systematic and fundamental concept for image contrast enhancement that should be robust despite a dynamic environment and that should fulfil the real-time constraints by ensuring an ultrafast analysis. It is demonstrated that the new approach developed in this paper is capable of fulfilling the expected requirements. The proposed approach combines the good features of the 'coupled oscillators'-based signal processing paradigm with the good features of the 'cellular neural network (CNN)'-based one. The first paradigm in this combination is the 'master system' and consists of a set of coupled nonlinear ordinary differential equations (ODEs) that are (a) the so-called 'van der Pol oscillator' and (b) the so-called 'Duffing oscillator'. It is then implemented or realized on top of a 'slave system' platform consisting of a CNN-processors platform. An offline bifurcation analysis is used to find out, a priori, the windows of parameter settings in which the coupled oscillator system exhibits the best and most appropriate behaviours of interest for an optimal resulting image processing quality. In the frame of the extensive bifurcation analysis carried out, analytical formulae have
Nonlinear Oscillations in Biology and Chemistry
1986-01-01
This volume contains the proceedings of a meeting entitled 'Nonlinear Oscillations in Biology and Chemistry', which was held at the University of Utah May 9-11,1985. The papers fall into four major categories: (i) those that deal with biological problems, particularly problems arising in cell biology, (ii) those that deal with chemical systems, (iii) those that treat problems which arise in neurophysiology, and (iv), those whose primary emphasis is on more general models and the mathematical techniques involved in their analysis. Except for the paper by Auchmuty, all are based on talks given at the meeting. The diversity of papers gives some indication of the scope of the meeting, but the printed word conveys neither the degree of interaction between the participants nor the intellectual sparks generated by that interaction. The meeting was made possible by the financial support of the Department of Mathe matics of the University of Utah. I am indebted to Ms. Toni Bunker of the Department of Mathematics for...
Synchronization Dynamics of Coupled Chemical Oscillators
Tompkins, Nathan
The synchronization dynamics of complex networks have been extensively studied over the past few decades due to their ubiquity in the natural world. Prominent examples include cardiac rhythms, circadian rhythms, the flashing of fireflies, predator/prey population dynamics, mammalian gait, human applause, pendulum clocks, the electrical grid, and of the course the brain. Detailed experiments have been done to map the topology of many of these systems and significant advances have been made to describe the mathematics of these networks. Compared to these bodies of work relatively little has been done to directly test the role of topology in the synchronization dynamics of coupled oscillators. This Dissertation develops technology to examine the dynamics due to topology within networks of discrete oscillatory components. The oscillatory system used here consists of the photo-inhibitable Belousov-Zhabotinsky (BZ) reaction water-in-oil emulsion where the oscillatory drops are diffusively coupled to one another and the topology is defined by the geometry of the diffusive connections. Ring networks are created from a close-packed 2D array of drops using the Programmable Illumination Microscope (PIM) in order to test Turing's theory of morphogenesis directly. Further technology is developed to create custom planar networks of BZ drops in more complicated topologies which can be individually perturbed using illumination from the PIM. The work presented here establishes the validity of using the BZ emulsion system with a PIM to study the topology induced effects on the synchronization dynamics of coupled chemical oscillators, tests the successes and limitations of Turing's theory of morphogenesis, and develops new technology to further probe the effects of network topology on a system of coupled oscillators. Finally, this Dissertation concludes by describing ongoing experiments which utilize this new technology to examine topology induced transitions of synchronization
Scleronomic Holonomic Constraints and Conservative Nonlinear Oscillators
Munoz, R.; Gonzalez-Garcia, G.; Izquierdo-De La Cruz, E.; Fernandez-Anaya, G.
2011-01-01
A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present…
OSCILLATION OF NONLINEAR IMPULSIVE PARABOLIC DIFFERENTIAL EQUATIONS WITH SEVERAL DELAYS
Institute of Scientific and Technical Information of China (English)
CuiChenpei; ZouMin; LiuAnping; XiaoLi
2005-01-01
In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.
Trade-off between phase-noise and signal quadrature in unilaterally coupled oscillators
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
We present a comprehensive nonlinear analysis of coupled oscillators and examine the trade-off between phase-noise of the oscillator and the quadrature precision. We show that asymmetry gives rise to amplitude and phase imbalance which are proportional to the inverse and inverse square......, respectively, of the relative coupling strength. It is shown that the level of AM-PM is determined by the nonlinearity of the coupling transconductance. The 3dB noise reduction in close-to-carrier phase-noise in quadrature oscillators due to mutual coupling is lost to the extra AM-PM noise for large coupling...... strengths. The additional contribution of the internal noise sources in the coupling circuit together with the AM-PM noise contribution explains why the 3dB noise reduction is rarely seen in measurements of this particular circuit....
An open plus nonlinear closed loop control of chaotic oscillators
Institute of Scientific and Technical Information of China (English)
陈立群
2002-01-01
An open plus nonlinear closed loop control law is presented for chaotic oscillations described by a set of non-autonomous second-order ordinary differential equations. It is proven that the basins of entrainment are global whenthe right-hand sides of the equations are given by arbitrary polynomial functions. The forced Duffing oscillator and theforced van der Pol oscillator are treated as numerical examples to demonstrate the applications of the method.
Nonlinear Oscillations of Microscale Piezoelectric Resonators and Resonator Arrays
2006-06-30
linear characteristics [2-5]. These characteristics include DUffing oscillator like response during resonance excitations [6], temporal harmonics in the...model is used with a single-mode approximation to produce a forced Duffing oscillator . Nonlinear analysis is used to obtain the frequency-response...backward this procedure, the simplified model takes the form of a forced frequency sweeps, only the forward sweep data are used in Duffing oscillator , shown
Oscillation death in a coupled van der Pol–Mathieu system
Indian Academy of Sciences (India)
Madhurjya P Bora; Dipak Sarmah
2013-10-01
We report an investigation of the oscillation death (OD) of a parametrically excited coupled van der Pol–Mathieu (vdPM) system. The system can be considered as a pair of harmonically forced van der Pol oscillators under a double-well potential. The two oscillators are coupled with a cubic nonlinearity. We have shown that the system arrives at an OD regime when coupling strength crosses a threshold value at which the system undergoes saddle-node bifurcation and two limit cycles coalesce onto a fixed point of the system. We have further shown that this nonautonomous system possesses a centre manifold corresponding to the OD regime.
Scleronomic holonomic constraints and conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Munoz, R; Gonzalez-Garcia, G; Izquierdo-De La Cruz, E Izquierdo-De La [Universidad Autonoma de la Ciudad de Mexico, Centro Historico, Fray Servando Teresa de Mier 92, Col Centro, Del Cuauhtemoc, Mexico DF, CP 06080 (Mexico); Fernandez-Anaya, G, E-mail: rodrigo.munoz@uacm.edu.mx, E-mail: gggharper@gmail.com, E-mail: erickidc@gmail.com, E-mail: guillermo.fernandez@uia.mx [Universidad Iberoamericana, Departamento de Fisica y Matematicas, Prolongacon Paseo de de la Reforma 880, Col Lomas de Santa Fe, Del Alvaro Obregn, Mexico DF, CP 01219 (Mexico)
2011-05-15
A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present cases in which the effective potential acting on the bead is not analytical around a minimum. The small oscillation approximation cannot be applied to such pathological cases. Nonetheless, these latter instances are studied with other standard techniques.
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
Nonlinear self-excited oscillations of a ducted flame
Dowling, A. P.
1997-09-01
Self-excited oscillations of a confined flame, burning in the wake of a bluff-body flame-holder, are considered. These oscillations occur due to interaction between unsteady combustion and acoustic waves. According to linear theory, flow disturbances grow exponentially with time. A theory for nonlinear oscillations is developed, exploiting the fact that the main nonlinearity is in the heat release rate, which essentially ‘saturates’. The amplitudes of the pressure fluctuations are sufficiently small that the acoustic waves remain linear. The time evolution of the oscillations is determined by numerical integration and inclusion of nonlinear effects is found to lead to limit cycles of finite amplitude. The predicted limit cycles are compared with results from experiments and from linear theory. The amplitudes and spectra of the limit-cycle oscillations are in reasonable agreement with experiment. Linear theory is found to predict the frequency and mode shape of the nonlinear oscillations remarkably well. Moreover, we find that, for this type of nonlinearity, describing function analysis enables a good estimate of the limit-cycle amplitude to be obtained from linear theory.
An Analytical Approximation Method for Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Wang Shimin
2012-01-01
Full Text Available An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.
Coupled oscillators and Feynman's three papers
Kim, Y. S.
2007-05-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the "rest of the universe" contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.
Interactive optomechanical coupling with nonlinear polaritonic systems
Bobrovska, N; Liew, T C H; Kyriienko, O
2016-01-01
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effective optical nonlinearity terms of high order, being quartic in the polariton number. We consider particular systems of exciton-polaritons and dipolaritons, and show that the induced effective optical nonlinearity due to the interactive coupling can exceed in magnitude the strength of Kerr nonlinear terms, such as those arising from polariton-polariton interactions. As applications, we show that the higher order terms give...
Escaff, Daniel; Harbola, Upendra; Lindenberg, Katja
2012-07-01
We present a model of identical coupled two-state stochastic units, each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition.
High-Order Energy Balance Method to Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Seher Durmaz
2012-01-01
Full Text Available Energy balance method (EBM is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.
Analytical approximations for a conservative nonlinear singular oscillator in plasma physics
Directory of Open Access Journals (Sweden)
A. Mirzabeigy
2012-10-01
Full Text Available A modified variational approach and the coupled homotopy perturbation method with variational formulation are exerted to obtain periodic solutions of a conservative nonlinear singular oscillator in plasma physics. The frequency–amplitude relations for the oscillator which the restoring force is inversely proportional to the dependent variable are achieved analytically. The approximate frequency obtained using the coupled method is more accurate than the modified variational approach and ones obtained using other approximate methods and the discrepancy between the approximate frequency using this coupled method and the exact one is lower than 0.31% for the whole range of values of oscillation amplitude. The coupled method provides a very good accuracy and is a promising technique to a lot of practical engineering and physical problems.
Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators
Hoff, Anderson; Manchein, Cesar; Albuquerque, Holokx A
2015-01-01
The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of two coupled FitzHugh-Nagumo oscillators. We consider unidirectional and bidirectional couplings, for which Lyapunov and isoperiodic diagrams were constructed calculating the Lyapunov exponents and the number of the local maxima of a variable in one period interval of the time-series, respectively. By numerical continuation method the bifurcation curves are also obtained for both couplings. The dynamics of the networks here investigated are presented in terms of the variation between the coupling strength of the oscillators and other parameters of the system. For the network of two oscillators unidirectionally coupled, the results show the existence of Arnold tongues, self-organized sequentially in a branch of a Stern-Brocot tree and ...
Stimulated scattering in strongly coupled nanolasers induced by Rabi oscillations
Marconi, Mathias; Raineri, Fabrice; Levenson, Ariel; Yacomotti, Alejandro M
2016-01-01
Two coupled-cavity systems, or "photonic dimers", are efficient test-beds for both fundamental optics -the realization of quantum correlated states, Josephson physics, and so forth-, and applications such as optical flip-flop memories. In this work we report on the first observation of nonlinear mode interaction in a photonic dimer formed by two semiconductor photonic crystal coupled nanolasers. For this, we investigate energy transfer between hybrid modes, which manifests as a switching from the blue-detuned (bonding) to the red-detuned (anti-bonding) modes. An mean-field model allows us to explain this phenomenon as stimulated scattering due to carrier population oscillations in the cavities at the Rabi frequency. Such asymmetrical mode interaction is universal in semiconductor laser photonic molecules, and unveils the origin of cross-correlation dips in the statistics of mode fluctuations.
Synchronization and entrainment of coupled circadian oscillators
Komin, Niko; Hernandez-Garcia, Emilio; Toral, Raul
2010-01-01
Circadian rhythms in mammals are controlled by the neurons located in the suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the system of neurons is very efficiently entrained by the 24-hour light-dark cycle. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light dark cycle in neuronal synchronization. Nevertheless, heterogeneity as a natural and permanent ingredient of these cellular interactions is seemingly to play a major role in these biochemical processes. In this paper we use a model that considers the neurons of the suprachiasmatic nucleus as chemically-coupled modified Goodwin oscillators, and introduce non-negligible heterogeneity in the periods of all neurons in the form of quenched noise. The system response to the light-dark cycle periodicity is studied as a function of the interneuronal coupling strength, external forcing amplitude and neuronal heterogeneity. Our results indicate that the right amount of heterogeneity hel...
Chimera states in a population of identical oscillators under planar cross-coupling
Indian Academy of Sciences (India)
C R Hens; A Mishra; P K Roy; A Sen; S K Dana
2015-02-01
We report the existence of chimera states in an assembly of identical nonlinear oscillators that are globally linked to each other in a simple planar cross-coupled form. The rotational symmetry breaking of the coupling term appears to be responsible for the emergence of these collective states that display a characteristic coexistence of coherent and incoherent behaviour. The finding, observed in both a collection of van der Pol oscillators and chaotic Rössler oscillators, further simplifies the existence criterion for chimeras, thereby broadens the range of their applicability to real-world situations.
A simple harmonic balance method for solving strongly nonlinear oscillators
Directory of Open Access Journals (Sweden)
Md. Abdur Razzak
2016-10-01
Full Text Available In this paper, a simple harmonic balance method (HBM is proposed to obtain higher-order approximate periodic solutions of strongly nonlinear oscillator systems having a rational and an irrational force. With the proposed procedure, the approximate frequencies and the corresponding periodic solutions can be easily determined. It gives high accuracy for both small and large amplitudes of oscillations and better result than those obtained by other existing results. The main advantage of the present method is that its simplicity and the second-order approximate solutions almost coincide with the corresponding numerical solutions (considered to be exact. The method is illustrated by examples. The present method is very effective and convenient method for solving strongly nonlinear oscillator systems arising in nonlinear science and engineering.
Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation
Moon, Songky; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon
2015-01-01
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of $0.41\\dot{6}\\eta^2$ for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of $\\eta$ much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained...
Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation
Fiori, Simone
2017-06-01
Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of complex nonlinear phenomena, as well as in engineering, being able to generate repeating (i.e., periodic) or non-repeating (i.e., chaotic) reference signals. The state of the classical oscillators known from the literature evolves in the space Rn , typically with n = 1 (e.g., the famous van der Pol vacuum-tube model), n = 2 (e.g., the FitzHugh-Nagumo model of spiking neurons) or n = 3 (e.g., the Lorenz simplified model of turbulence). The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.
Nonlinear Dynamics of A Damped Magnetic Oscillator
Kim, S Y
1999-01-01
We consider a damped magnetic oscillator, consisting of a permanent magnet in a periodically oscillating magnetic field. A detailed investigation of the dynamics of this dissipative magnetic system is made by varying the field amplitude $A$. As $A$ is increased, the damped magnetic oscillator, albeit simple looking, exhibits rich dynamical behaviors such as symmetry-breaking pitchfork bifurcations, period-doubling transitions to chaos, symmetry-restoring attractor-merging crises, and saddle-node bifurcations giving rise to new periodic attractors. Besides these familiar behaviors, a cascade of ``resurrections'' (i.e., an infinite sequence of alternating restabilizations and destabilizations) of the stationary points also occurs. It is found that the stationary points restabilize (destabilize) through alternating subcritical (supercritical) period-doubling and pitchfork bifurcations. We also discuss the critical behaviors in the period-doubling cascades.
Oscillation criteria for nonlinear fractional differential equation with damping term
Directory of Open Access Journals (Sweden)
Bayram Mustafa
2016-01-01
Full Text Available In this paper, we study the oscillation of solutions to a non-linear fractional differential equation with damping term. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a generalized Riccati transformation, inequalities, and integration average techniquewe establish new oscillation criteria for the fractional differential equation. Several illustrative examples are also given.
Bifurcations of a parametrically excited oscillator with strong nonlinearity
Institute of Scientific and Technical Information of China (English)
唐驾时; 符文彬; 李克安
2002-01-01
A parametrically excited oscillator with strong nonlinearity, including van der Poi and Duffing types, is studied for static bifurcations. The applicable range of the modified Lindstedt-Poincaré method is extended to 1/2 subharmonic resonance systems. The bifurcation equation of a strongly nonlinear oscillator, which is transformed into a small parameter system, is determined by the multiple scales method. On the basis of the singularity theory, the transition set and the bifurcation diagram in various regions of the parameter plane are analysed.
High-Order Energy Balance Method to Nonlinear Oscillators
Seher Durmaz; Metin Orhan Kaya
2012-01-01
Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated fo...
Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach
Directory of Open Access Journals (Sweden)
Ricardo Aguilar-López
2014-01-01
Full Text Available The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.
Optimal operating points of oscillators using nonlinear resonators.
Kenig, Eyal; Cross, M C; Villanueva, L G; Karabalin, R B; Matheny, M H; Lifshitz, Ron; Roukes, M L
2012-11-01
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources.
Synchronization using environmental coupling in mercury beating heart oscillators
Singla, Tanu; Montoya, Fernando; Rivera, M.; Tajima, Shunsuke; Nakabayashi, Seiichiro; Parmananda, P.
2016-06-01
We report synchronization of Mercury Beating Heart (MBH) oscillators using the environmental coupling mechanism. This mechanism involves interaction of the oscillators with a common medium/environment such that the oscillators do not interact among themselves. In the present work, we chose a modified MBH system as the common environment. In the absence of coupling, this modified system does not exhibit self sustained oscillations. It was observed that, as a result of the coupling of the MBH oscillators with this common environment, the electrical and the mechanical activities of both the oscillators synchronized simultaneously. Experimental results indicate the emergence of both lag and the complete synchronization in the MBH oscillators. Simulations of the phase oscillators were carried out in order to better understand the experimental observations.
Nonlinear dynamics of self-oscillating polymer gels
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Self-oscillating polymer gels driven by Belousov-Zhabotinsky (BZ) chemical reaction are a new class of functional gels that have a wide range of potential applications (e.g., autonomously functioning membranes, actuate artificial muscles). However, the precise control of these gels has been an issue due to limited investigations of the influences of key system parameters on the characteristics of BZ gels. To address this deficiency, we studied the self-oscillating behavior of BZ gels using the nonline-ar dynamics theory and an Oregonator-like model, with focus placed upon the influences of various system parameters. The analysis of the oscillation phase indicated that the dynamic response of BZ gels represents the classical limit cycle oscillation. We then investigated the characteristics of the limit cycle oscillation and quantified the influences of key parameters (i.e., ini-tial reactant concentration, oxidation and reduction rate of catalyst, and response coefficient) on the self-oscillating behavior of BZ gels. The results demonstrated that sustained limit cycle oscillation of BZ gels can be achieved only when these key pa-rameters meet certain requirements, and that the pattern, period and amplitude of the oscillation are significantly influenced by these parameters. The results obtained in this study could enable the controlled self-oscillation of BZ gels system. This has several potential applications such as controlled drug delivery, miniature peristaltic pumps and microactuators.
Optimal Parametric Feedback Excitation of Nonlinear Oscillators
Braun, David J.
2016-01-01
An optimal parametric feedback excitation principle is sought, found, and investigated. The principle is shown to provide an adaptive resonance condition that enables unprecedentedly robust movement generation in a large class of oscillatory dynamical systems. Experimental demonstration of the theory is provided by a nonlinear electronic circuit that realizes self-adaptive parametric excitation without model information, signal processing, and control computation. The observed behavior dramatically differs from the one achievable using classical parametric modulation, which is fundamentally limited by uncertainties in model information and nonlinear effects inevitably present in real world applications.
Periodic Solutions for Highly Nonlinear Oscillation Systems
DEFF Research Database (Denmark)
Ghadimi, M; Barari, Amin; Kaliji, H.D
2012-01-01
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...
Coupled oscillators and Feynman's three papers
Kim, Y S
2006-01-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the ``rest of the universe'' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be c...
Nonlinear oscillation system of mass with serial linear and nonlinear springs
DEFF Research Database (Denmark)
Seyedalizadeh Ganji,, S.R; Barari, Amin; Karimpour, S;
2013-01-01
In this paper, two powerful methods called Max–Min and parameter expansion have been applied for the determination of the periodic solutions of the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities. It is found that these methods introduce two...
Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
Santo, Daniele; Lannes, David
2017-01-01
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Raghavan, S.; Smerzi, A.; Fantoni, S.; Shenoy, S. R.
1999-01-01
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to π (π-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of 3He-B and the internal Josephson effect in 3He-A are also discussed.
Comparison of alternative improved perturbative methods for nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico)]. E-mail: paolo@ucol.mx; Raya, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2005-06-06
We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt-Poincare technique. As illustrative examples we choose one-dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.
Nonlinear dynamics of a microelectromechanical oscillator with delayed feedback
Van Leeuwen, R.; Karabacak, D.M.; Van der Zant, H.S.J.; Venstra, W.J.
2013-01-01
We study the dynamics of a nonlinear electromechanical oscillator with delayed feedback. Compared to their linear counterparts, we find that the dynamics is dramatically different. The well-known Barkhausen stability criterion ceases to exist, and two modes of operation emerge: one characterized by
Quantifying Poincare’s Continuation Method for Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Daniel Núñez
2015-01-01
Full Text Available In the sixties, Loud obtained interesting results of continuation on periodic solutions in driven nonlinear oscillators with small parameter (Loud, 1964. In this paper Loud’s results are extended out for periodically driven Duffing equations with odd symmetry quantifying the continuation parameter for a periodic odd solution which is elliptic and emanates from the equilibrium of the nonperturbed problem.
Oscillation criteria for first-order forced nonlinear difference equations
Grace Said R; Agarwal Ravi P.; Smith Tim
2006-01-01
Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form Δx(n)+q1(n)xμ(n+1) = q2(n)xλ(n+1)+e(n), where λ, μ are the ratios of positive odd integers 0 <μ < 1 and λ > 1, are established.
Front spreading with nonlinear sorption for oscillating flow
Cirkel, D.G.; Zee, van der S.E.A.T.M.; Meeussen, J.C.L.
2015-01-01
In this paper, we consider dispersive and chromatographic mixing at an interface, under alternating flow conditions. In case of a nonreactive or linearly sorbing solute, mixing is in complete analogy with classical dispersion theory. For nonlinear exchange, however, oscillating convective flow leads
Oscillation Theorems for Nonlinear Second Order Elliptic Equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
Some oscillation theorems are given for the nonlinear second order elliptic equation N ∑i,j=1 Di[aij(x)Ψ(y)||(△)y||p-2Djy]+c(x)f(y)=0. The results are extensions of modified Riccati techniques and include recent results of Usami.
Nonlinear Oscillations and Bifurcations in Silicon Photonic Microresonators
Abrams, Daniel M; Srinivasan, Kartik
2013-01-01
Silicon microdisks are optical resonators that can exhibit surprising nonlinear behavior. We present a new analysis of the dynamics of these resonators, elucidating the mathematical origin of spontaneous oscillations and deriving predictions for observed phenomena such as a frequency comb spectrum with MHz-scale repetition rate. We test predictions through laboratory experiment and numerical simulation.
Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes
Kirkendall, Christopher R.; Kwon, Jae W.
2016-03-01
Nonlinear modal interactions have recently become the focus of intense research in micro- and nanoscale resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. However, our understanding of modal coupling is largely restricted to clamped-clamped beams, and lacking in systems with both geometric and material nonlinearities. Here we report multistable energy transfer between internally resonant modes of an electroelastic crystal plate and use a mixed analytical-numerical approach to provide new insight into these complex interactions. Our results reveal a rich bifurcation structure marked by nested regions of multistability. Even the simple case of two coupled modes generates a host of topologically distinct dynamics over the parameter space, ranging from the usual Duffing bistability to complex multistable behaviour and quasiperiodic motion.
Non-linear shape oscillations of rising drops and bubbles: Experiments and simulations
Lalanne, Benjamin; Abi Chebel, Nicolas; Vejražka, Jiří; Tanguy, Sébastien; Masbernat, Olivier; Risso, Frédéric
2015-12-01
This paper focuses on shape-oscillations of a gas bubble or a liquid drop rising in another liquid. The bubble/drop is initially attached to a capillary and is released by a sudden motion of that capillary, resulting in the rise of the bubble/drop along with the oscillations of its shape. Such experimental conditions make difficult the interpretation of the oscillation dynamics with regard to the standard linear theory of oscillation because (i) amplitude of deformation is large enough to induce nonlinearities, (ii) the rising motion may be coupled with the oscillation dynamics, and (iii) clean conditions without residual surfactants may not be achieved. These differences with the theory are addressed by comparing experimental observation with numerical simulation. Simulations are carried out using Level-Set and Ghost-Fluid methods with clean interfaces. The effect of the rising motion is investigated by performing simulations under different gravity conditions. Using a decomposition of the bubble/drop shape into a series of spherical harmonics, experimental and numerical time evolutions of their amplitudes are compared. Due to large oscillation amplitude, non-linear couplings between the modes are evidenced from both experimental and numerical signals; modes of lower frequency influence modes of higher frequency, whereas the reverse is not observed. Nevertheless, the dominant frequency and overall damping rate of the first five modes are in good agreement with the linear theory. Effect of the rising motion on the oscillations is globally negligible, provided the mean shape of the oscillation remains close to a sphere. In the drop case, despite the residual interface contamination evidenced by a reduction in the terminal velocity, the oscillation dynamics is shown to be unaltered compared to that of a clean drop.
An exactly solvable three-dimensional nonlinear quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Morris, J. R. [Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2013-11-15
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
Linearized oscillation theory for a nonlinear delay impulsive equation
Berezansky, Leonid; Braverman, Elena
2003-12-01
For a scalar nonlinear impulsive delay differential equationwith rk(t)≥0,hk(t)≤t, limj-->∞ τj=∞, such an auxiliary linear impulsive delay differential equationis constructed that oscillation (nonoscillation) of the nonlinear equation can be deduced from the corresponding properties of the linear equation. Coefficients rk(t) and delays are not assumed to be continuous. Explicit oscillation and nonoscillation conditions are established for some nonlinear impulsive models of population dynamics, such as the impulsive logistic equation and the impulsive generalized Lasota-Wazewska equation which describes the survival of red blood cells. It is noted that unlike nonimpulsive delay logistic equations a solution of a delay impulsive logistic equation may become negative.
Renewal Approach to the Analysis of the Asynchronous State for Coupled Noisy Oscillators
Farkhooi, Farzad
2015-01-01
We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of inter-event density allows for a self-consistent calculation that determines the asynchronous state and its stability. This framework, can readily be extended to the analysis of systems with more state variables. To exhibit this, we study a nonlinear pulse-coupled system, where couplings are dynamic and activity dependent. We investigate stability of this system and we show it undergoes a super-critical Hopf bifurcation to collective synchronization.
Primordial fluctuations from nonlinear couplings
Calzetta, E A; Calzetta, Esteban A.; Gonorazky, Sonia
1997-01-01
We study the spectrum of primordial fluctuations in theories where the inflaton field is coupled to massless fields and/or to itself. Conformally invariant theories generically predict a scale invariant spectrum. Scales entering the theory through infrared divergences cause logarithmic corrections to the spectrum, tiltilng it towards the blue. We discuss in some detail wether these fluctuations are quantum or classical in nature.
Leiser, Randolph J.; Rotstein, Horacio G.
2017-08-01
Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.
Optimal Variational Method for Truly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Vasile Marinca
2013-01-01
Full Text Available The Optimal Variational Method (OVM is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”. The main advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. This approach does not depend upon any small or large parameters. A very good agreement was found between approximate and numerical solution, which proves that OVM is very efficient and accurate.
Quorum Sensing and Synchronization in Populations of Coupled Chemical Oscillators
Taylor, Annette F.; Tinsley, Mark R.; Showalter, Kenneth
2013-12-01
Experiments and simulations of populations of coupled chemical oscillators, consisting of catalytic particles suspended in solution, provide insights into density-dependent dynamics displayed by many cellular organisms. Gradual synchronization transitions, the "switching on" of activity above a threshold number of oscillators (quorum sensing) and the formation of synchronized groups (clusters) of oscillators have been characterized. Collective behavior is driven by the response of the oscillators to chemicals emitted into the surrounding solution.
Tiberkevich, V. S.; Slavin, A. N.; Kim, Joo-Von
2008-01-01
The temperature dependence of the generation linewidth for an auto-oscillator with a nonlinear frequency shift is calculated. It is shown that the frequency nonlinearity creates a finite correlation time, tau, for the phase fluctuations. In the low-temperature limit in which the spectral linewidth is smaller than 1/tau, the line shape is approximately Lorentzian and the linewidth is linear in temperature. In the opposite high-temperature limit in which the linewidth is larger than 1/tau, the ...
Burioni, Raffaella; di Santo, Serena; di Volo, Matteo; Vezzani, Alessandro
2014-10-01
Self-organized quasiperiodicity is one of the most puzzling dynamical phases observed in systems of nonlinear coupled oscillators. The single dynamical units are not locked to the periodic mean field they produce, but they still feature a coherent behavior, through an unexplained complex form of correlation. We consider a class of leaky integrate-and-fire oscillators on random sparse and massive networks with dynamical synapses, featuring self-organized quasiperiodicity, and we show how complex collective oscillations arise from constructive interference of microscopic dynamics. In particular, we find a simple quantitative relationship between two relevant microscopic dynamical time scales and the macroscopic time scale of the global signal. We show that the proposed relation is a general property of collective oscillations, common to all the partially synchronous dynamical phases analyzed. We argue that an analogous mechanism could be at the origin of similar network dynamics.
Surprises of the Transformer as a Coupled Oscillator System
Silva, J. P.; Silvestre, A. J.
2008-01-01
We study a system of two RLC oscillators coupled through a variable mutual inductance. The system is interesting because it exhibits some peculiar features of coupled oscillators: (i) there are two natural frequencies; (ii) in general, the resonant frequencies do not coincide with the natural frequencies; (iii) the resonant frequencies of both…
Nonlinear magnetotransport theory and Hall induced resistance oscillations in graphene.
Gutiérrez-Jáuregui, R; Torres, M
2014-06-11
The quantum oscillations of nonlinear magnetoresistance in graphene that occur in response to a dc current bias are investigated. We present a theoretical model for the nonlinear magnetotransport of graphene carriers. The model is based on the exact solution of the effective Dirac equation in crossed electric and magnetic fields, while the effects of randomly distributed impurities are perturbatively added. To compute the nonlinear current effects, we develop a covariant formulation of the migration center theory. The current is calculated for short- and large-range scatterers. The analysis of the differential resistivity in the large magnetic field region, shows that the extrema of the Shubnikov de Hass oscillations invert when the dc currents exceed a threshold value. These results are in good agreement with experimental observations. In the small magnetic field regime, corresponding to large filling factors, the existence of Hall induced resistance oscillations are predicted for ultra clean graphene samples. These oscillations originate from Landau-Zener tunneling between Landau levels, that are tilted by the strong electric Hall field.
Coherent oscillations of electrons in tunnel-coupled wells under ultrafast intersubband excitation
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Cabrera, A [Departamento de FIsica Basica, Universidad de La Laguna, La Laguna 38206-Tenerife, Canary Islands (Spain); Aceituno, P [Departamento de FIsica Basica, Universidad de La Laguna, La Laguna 38206-Tenerife, Canary Islands (Spain); Vasko, F T [Institute of Semiconductor Physics, NAS of Ukraine, Kiev, 252650 (Ukraine)
2004-07-28
Ultrafast intersubband excitation of electrons in tunnel-coupled wells is studied in respect of its dependence on the structure parameters, the duration of the infrared pump and the detuning frequency. The temporal dependences of the photoinduced carrier concentration and dipole moment are obtained for two cases of transitions: from the single ground state to the tunnel-coupled excited states and from the tunnel-coupled states to the single excited state. The peculiarities of dephasing and population relaxation processes are also taken into account. The nonlinear regime of the response is also considered when the splitting energy between the tunnel-coupled levels is renormalized by the photoexcited electron concentration. The dependences of the period and the amplitude of oscillations on the excitation pulse are presented with a description of the damping of the nonlinear oscillations.
RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios
Tang, Zhi-Ling; Li, Si-Min; Yu, Li-Juan
2016-01-01
Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC) to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unidirectionally coupled, overdamped nonlinear oscillator ring is proposed. First, the numerical model of such a system is established based on the circuit of the nonlinear oscillator. Through numerical analysis of the model, the critical condition of the system’s starting oscillation is determined, and the simulation results of the system’s response to Gaussian white noise and periodic signal are presented. The results show that once the radio signal is input into the system, it starts oscillating when in the critical region, and the oscillating frequency of each element is fo/N, where fo is the frequency of the radio signal and N is the number of elements in the ring. The oscillation indicates that the spectrum resources at fo are occupied. At the same time, the sampling rate required for an ADC is reduced to the original value, 1/N. A prototypical circuit to verify the functionality of the system is designed, and the sensing bandwidth of the system is measured. PMID:27294928
Effects of noise on the phase dynamics of nonlinear oscillators
Daffertshofer, A.
1998-07-01
Various properties of human rhythmic movements have been successfully modeled using nonlinear oscillators. However, despite some extensions towards stochastical differential equations, these models do not comprise different statistical features that can be explained by nondynamical statistics. For instance, one observes certain lag one serial correlation functions for consecutive periods during periodic motion. This work aims at an extension of dynamical descriptions in terms of stochastically forced nonlinear oscillators such as ξ¨+ω20ξ=n(ξ,ξ˙)+q(ξ,ξ˙)Ψ(t), where the nonlinear function n(ξ,ξ˙) generates a limit cycle and Ψ(t) denotes colored noise that is multiplied via q(ξ,ξ˙). Nonlinear self-excited systems have been frequently investigated, particularly emphasizing stability properties and amplitude evolution. Thus, one can focus on the effects of noise on the frequency or phase dynamics that can be analyzed by use of time-dependent Fokker-Planck equations. It can be shown that noise multiplied via polynoms of arbitrary finite order cannot generate the desired period correlation but predominantly results in phase diffusion. The system is extended in terms of forced oscillators in order to find a minimal model producing the required error correction.
Analysis and design of coupled-oscillator arrays for microwave systems
Moussounda, Renaud
The concept of synchronized nonlinear coupled oscillators is applied to microwave and antenna engineering for the analysis and design of wireless communication and sensing systems operating at the microwave and/or millimeter (mm)-wave frequencies. The significance of such approach is justified from the potential gain in efficiency, weight, cost and functionality although technical challenges stand in the way. Unlike typical phased array systems, which are currently used to construct such systems, coupled-oscillator systems present additional challenges that mainly arise from maintaining stability and synchronization as the the coupled nonlinear system is operated. Linear systems do not present such stability issues and are consequently faster since they do not rely on any gradual synchronization mechanism in order to function. However, at significantly higher frequencies in the quasi-optical domain, coupled-oscillator systems can make up for the speed difference and present significant efficiency advantages over typical phased array architectures. In addition, coupled nonlinear systems possess inherent analog properties that can be used for a multitude of functions. This dissertation advances the topic of coupled-oscillator arrays by 1) developing an alternative set of techniques for designing the oscillating unit cells called active integrated antennas (AIAs) at microwave or mm-wave frequencies, 2) developing a more accurate description of the dynamics of the array, 3) developing and implementing a new topology for a coupling network that is able to extend stability, 4) implementing a fully non-reciprocally coupled array able to produce large scan angle without loss of stability, 5) proposing an architecture based on a single phase-locked loop (PLL) and containing a self-calibration mechanism, and finally 6) implementing a phase-boosting mechanism using simple circuits to amplify the phase difference between adjacent radiating antennas in order to increase
Frequency analysis of nonlinear oscillations via the global error minimization
Kalami Yazdi, M.; Hosseini Tehrani, P.
2016-06-01
The capacity and effectiveness of a modified variational approach, namely global error minimization (GEM) is illustrated in this study. For this purpose, the free oscillations of a rod rocking on a cylindrical surface and the Duffing-harmonic oscillator are treated. In order to validate and exhibit the merit of the method, the obtained result is compared with both of the exact frequency and the outcome of other well-known analytical methods. The corollary reveals that the first order approximation leads to an acceptable relative error, specially for large initial conditions. The procedure can be promisingly exerted to the conservative nonlinear problems.
The energy balance to nonlinear oscillations via Jacobi collocation method
Directory of Open Access Journals (Sweden)
M.K. Yazdi
2015-06-01
Full Text Available This study develops the energy balance based on Jacobi collocation method for accurate prediction of conservative nonlinear oscillator models with a single collocation point. The node points are taken as the roots of Jacobi orthogonal polynomials. Several examples are included to demonstrate the applicability and accuracy of the proposed algorithm, and some comparisons are made with the existing results. The method is suitable and the approximate frequencies are valid for small as well as large amplitudes of oscillation. Excellent agreement with exact ones is presented for the first order approximation.
Discrete oscillator design linear, nonlinear, transient, and noise domains
Rhea, Randall W
2014-01-01
Oscillators are an essential part of all spread spectrum, RF, and wireless systems, and today's engineers in the field need to have a firm grasp on how they are designed. Presenting an easy-to-understand, unified view of the subject, this authoritative resource covers the practical design of high-frequency oscillators with lumped, distributed, dielectric and piezoelectric resonators. Including numerous examples, the book details important linear, nonlinear harmonic balance, transient and noise analysis techniques. Moreover, the book shows you how to apply these techniques to a wide range of os
Hyperpolarizabilities of Chiral Molecules Based on Three-Coupled-Oscillator Model
Institute of Scientific and Technical Information of China (English)
WANG Xiao-Ou; LI Jun-Qing; LI Chun-Fei
2004-01-01
@@ A chiral molecular model of three coupled oscillators is established. A set of coupling equations and hyperpolarizabilities for the chiral molecules with the tripod structure are presented. The expression of second-order nonlinear susceptibility is derived for an isotropic molecular system. The calculated hyperpolarizabilities of NPAN and NPP chiral molecules are consistent with the experimental results and the applicability of this model is validated.
Schmidt, Lennart; Krischer, Katharina
2015-06-01
We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking transition towards a related chimera state. We demonstrate that the diffusional coupling is non-essential for these complex dynamics. Furthermore, we investigate localized turbulence and discuss whether it can be categorized as a chimera state.
Kuwahara, Jun; Miyata, Hajime; Konno, Hidetoshi
2017-09-01
Recently, complex dynamics of globally coupled oscillators have been attracting many researcher's attentions. In spite of their numerous studies, their features of nonlinear oscillator systems with global and local couplings in two-dimension (2D) are not understood fully. The paper focuses on 2D states of coherent, clustered and chaotic oscillation especially under the effect of negative global coupling (NGC) in 2D Alief-Panfilov model. It is found that the tuning NGC can cause various new coupling-parameter dependency on the features of oscillations. Then quantitative characterization of various states of oscillations (so called spiral wave turbulence) is examined by using the pragmatic information (PI) which have been utilized in analyzing multimode laser, solar activity and neuronal systems. It is demonstrated that the dynamics of the PI for various oscillations can be characterized successfully by the Hyper-Gamma stochastic process.
Miwadinou, C H; Monwanou, A V; Orou, J B Chabi
2013-01-01
This paper considers nonlinear dynamics of plasma oscillations modeled by a forced modified Van der Pol-Duffing oscillator. These plasma oscillations are described by a nonlinear differential equation of the form $ \\ddot{x}+ \\epsilon (1 +{x}^{2}){\\dot{x}} + x+ \\alpha \\epsilon{x}{\\dot{x}} + {\\beta}x^{2}+\\gamma x^{3}= F\\cos{\\Omega t}.$ The amplitudes of the forced harmonic, superharmonic and subharmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales methods. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth order Runge- Kutta scheme. The influences of the differents parameters and of amplitude of external forced have been found.
NONLINEAR FLUID DAMPING IN STRUCTURE-WAKE OSCILLATORS IN MODELING VORTEX-INDUCED VIBRATIONS
Institute of Scientific and Technical Information of China (English)
LIN Li-ming; LING Guo-can; WU Ying-xiang; ZENG Xiao-hui
2009-01-01
A Nonlinear Fluid Damping(NFD)in the form of the square-velocity is applied in the response analysis of Vortex-Induced Vibrations(VIV).Its nonlinear hydrodynamic effects on the coupled wake and structure oscillators are investigated.A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics,such as the amplification of body displacement at lock-in and frequency lock-in,both at high and low mass ratios.Particularly,the predicted peak amplitude of the body in the Griffin plot is in good agreement with experimental data and empirical equation,indicating the significant effect of the NFD on the structure motion.
The Duffing Equation Nonlinear Oscillators and their Behaviour
Kovacic, Ivana
2011-01-01
The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical
High-codimensional static bifurcations of strongly nonlinear oscillator
Institute of Scientific and Technical Information of China (English)
Zhang Qi-Chang; Wang Wei; Liu Fu-Hao
2008-01-01
The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied.We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form.To discuss the static bifurcation,the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory.The transition set and bifurcation diagrams for the singularity are presented,while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.
Symbolic Dynamics and Chaotic Synchronization in Coupled Duffing Oscillators
Gracio, Clara; Caneco, Acilina; Rocha, José
2008-01-01
In this work we discuss the complete synchronization of two identical double-well Duffing oscillators unidirectionally coupled, from the point of view of symbolic dynamics. Working with Poincar´e cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized. We obtained analytically the threshold value of the coupling parameter for the synchronization of two unimodal and two bimodal piecewise linea...
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators
Villanueva, L. G.; Kenig, E.; Karabalin, R. B.; Matheny, M. H.; Lifshitz, Ron; Cross, M. C.; Roukes, M. L.
2013-01-01
In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonator’s anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nano-electromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillator’s phase noise, as predicted by our model. PMID:23679770
A Review of the Nonlinear Dynamics of Intraseasonal Oscillations
Institute of Scientific and Technical Information of China (English)
ZHAO Qiang; CHEN Jian-Zhou
2011-01-01
In recent years, significant progress has been made regarding theories of intraseasonal oscillations （ISOs） （also known as the Madden-Julian oscillation （MJO） in the tropics）. This short review introduces the latest advances in ISO theories with an emphasis particularly on theoretical paradigms involving nonlinear dynamics in the following aspects： （1） the basic ideas and limitations of the previous and current theories and hypotheses regarding the MJO, （2） the new multi-scale theory of the MJO based on the intraseasonal planetary equatorial synoptic dynamics （IPESD） framework, and （3） nonlinear dynamics of ISOs in the extratropics based on the resonant triads of Rossby-Haurwitz waves.
Phase-selective entrainment of nonlinear oscillator ensembles
Zlotnik, Anatoly; Nagao, Raphael; Kiss, István Z.; Li-Shin, Jr.
2016-03-01
The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.
Damping of nonlinear standing kink oscillations: a numerical study
Magyar, N
2016-01-01
We aim to study the standing fundamental kink mode of coronal loops in the nonlinear regime, investigating the changes in energy evolution in the cross-section and oscillation amplitude of the loop which are related to nonlinear effects, in particular to the development of the Kelvin-Helmholtz instability (KHI). We run idea, high-resolution three-dimensional (3D) magnetohydrodynamics (MHD) simulations, studying the influence of the initial velocity amplitude and the inhomogeneous layer thickness. We model the coronal loop as a straight, homogeneous magnetic flux tube with an outer inhomogeneous layer, embedded in a straight, homogeneous magnetic field. We find that, for low amplitudes which do not allow for the KHI to develop during the simulated time, the damping time agrees with the theory of resonant absorption. However, for higher amplitudes, the presence of KHI around the oscillating loop can alter the loop's evolution, resulting in a significantly faster damping than predicted by the linear theory in so...
Nonlinear magnetoplasmons in strongly coupled Yukawa plasmas
Bonitz, M; Ott, T; Kaehlert, H; Hartmann, P
2010-01-01
The existence of plasma oscillations at multiples of the magnetoplasmon frequency in a strongly coupled two-dimensional magnetized Yukawa plasma is reported, based on extensive molecular dynamics simulations. These modes are the analogues of Bernstein modes which are renormalized by strong interparticle correlations. Their properties are theoretically explained by a dielectric function incorporating the combined effect of a magnetic field, strong correlations and finite temperature.
Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications
Li, Jibin; Feng, Zhaosheng
We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.
Closed-loop suppression of chaos in nonlinear driven oscillators
Aguirre, L. A.; Billings, S. A.
1995-05-01
This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.
Experimental Observation of Bohr’s Nonlinear Fluidic Surface Oscillation
Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon
2016-01-01
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η2 for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr’s hydrodynamic theory.
Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation.
Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon
2016-01-25
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η(2) for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr's hydrodynamic theory.
Jayaprasad, N; Bhalerao, M; Sengupta, Anand S; Majumder, Barun
2013-01-01
We design a low-cost, electromagnetically coupled, simple harmonic oscillator and demonstrate free, damped and forced oscillations in an under-graduate (UG) Physics laboratory. It consists of a spring-magnet system that can oscillate inside a cylinder around which copper coils are wound. Such demonstrations can compliment the traditional way in which a Waves & Oscillations course is taught and offers a richer pedagogical experience for students. We also show that with minimal modifications, it can be used to probe the magnitude of viscous damping forces in liquids by analyzing the oscillations of an immersed magnet. Finally, we propose some student activities to explore non-linear damping effects and their characterization using this apparatus.
Freezing of nonlinear Bloch oscillations in the generalized discrete nonlinear Schrödinger equation.
Cao, F J
2004-09-01
The dynamics in a nonlinear Schrödinger chain in a homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster frequencies in their dynamics. These phenomena are studied by direct numerical integration and through an adiabatic approximation. The adiabatic approximation allows a description in terms of an effective potential that greatly clarifies the phenomena.
Internal stochastic resonance in two coupled chemical oscil-lators
Institute of Scientific and Technical Information of China (English)
ZHONG; Shi
2001-01-01
［1］Sears, T. J., The calculation of the energy levels of an asymmetric top free radical in a magnetic field, Comput. Phys. Rep., 1984, 2: 1..［2］Davies, P. B., Liu, Y., Liu, Z., Far infrared LMR spectra of monobromomethyl radicals, Chem. Phys. Lett., 1993, 214: 305.［3］Nolte, J., Wagner, H. G., Sears, T. J. et al., The far-infrared laser magnetic resonance spectrum of CH2F, J. Mol. Spec-trosc., 1999, 195: 43.［4］Sears, T. J., ASYTOP--A program for detailed analysis of gas phase magnetic resonance spectra of asymmetric top molecules, Comput. Phys. Commun., 1984, 34: 123.［5］Papousek, D., Aliev, M. R., Molecular Vibrational Rotational Spectra, Prague: Academia, 1982, 72.［6］Matsushima, F., Nagase, H., Nakauchi, T. et al., Frequency measurement of pure rotational transitions of H2O, J. Mol. Spectrosc., 1999, 193: 217.［7］Bowater, I. C., Brown, J. M., Carrington, A., Microwave spectroscopy of nonlinear free radicals, Proc. R. Soc. Lond. A, 1973, 333: 265.［8］Castellano, S., Bothner-by, A. A., Analysis of NMR spectra by least squares, J. Chem. Phys., 1964, 41: 3863.［9］Bird, G. R., Microwave spectrum of NO2, J. Chem. Phys., 1956, 25: 1040.［10］Bird, G. R., Baird, J. C., Jache, A. W. et al., Microwave spectrum of NO2: fine structure and magnetic coupling, J. Chem. Phys., 1964, 40: 3378.［11］Lees, R. M., Curl, R. F., Baker, J. G., Millimeter-wavelength microwave spectrum of nitrogen dioxide, J. Chem. Phys., 1966, 45: 2037.［12］Baron, P. A., Godfrey, P. D., Harris, D. O., Microwave spectrum of NO2 at 70 GHz, J. Chem. Phys., 1974, 60: 3723.［13］Bowman, W. C., De Lucia, F. C., The millimeter and submillimeter spectrum of NO2, J. Chem. Phys., 1982, 77: 92.［14］Semmoud-Monnanteuil, N., Colmont, J. M., Perrin, A. et al., New measurements in the millimeter-wave spectrum of NO2, J. Mol. Spectrosc., 1989, 134: 176.［15］Baskakov, O. I., Moskienko, M. V., Dyubko, S. F., Submillimeter rotational spectrum of nitrogen dioxide, Opt
PERFORMANCE IMPROVEMENT OF A CHEMICAL REACTOR BY NONLINEAR NATURAL OSCILLATIONS
RAY, AK
1995-01-01
The dynamic behaviour of two coupled continuous stirred tank reactors in sequence is studied when the first reactor is being operated under limit cycle regimes producing self-sustained natural oscillations. The periodic output from the first reactor is then used as a forced input into the second rea
Synchronization and basin bifurcations in mutually coupled oscillators
Indian Academy of Sciences (India)
U E Vincent; A N Njah; O Akinlade
2007-05-01
Synchronization behaviour of two mutually coupled double-well Duffig oscillators exhibiting cross-well chaos is examined. Synchronization of the subsystems was observed for coupling strength > 0.4. It is found that when the oscillators are operated in the regime for which two attractors coexist in phase space, basin bifurcation sequences occur leading to + 1, ≥ 2 basins as the coupling is varied – a signature of Wada structure and ﬁnal-state sensitivity. However, in the region of complete synchronization, the basins structure is identical with that of the single oscillators and retains its essential features including fractal basin boundaries.
Statistics of Lyapunov exponent spectrum in randomly coupled Kuramoto oscillators.
Patra, Soumen K; Ghosh, Anandamohan
2016-03-01
Characterization of spatiotemporal dynamics of coupled oscillatory systems can be done by computing the Lyapunov exponents. We study the spatiotemporal dynamics of randomly coupled network of Kuramoto oscillators and find that the spectral statistics obtained from the Lyapunov exponent spectrum show interesting sensitivity to the coupling matrix. Our results indicate that in the weak coupling limit the gap distribution of the Lyapunov spectrum is Poissonian, while in the limit of strong coupling the gap distribution shows level repulsion. Moreover, the oscillators settle to an inhomogeneous oscillatory state, and it is also possible to infer the random network properties from the Lyapunov exponent spectrum.
Han, Wenchen; Cheng, Hongyan; Dai, Qionglin; Li, Haihong; Ju, Ping; Yang, Junzhong
2016-10-01
In this work, we investigate the dynamics in a ring of identical Stuart-Landau oscillators with conjugate coupling systematically. We analyze the stability of the amplitude death and find the stability independent of the number of oscillators. When the amplitude death state is unstable, a large number of states such as homogeneous oscillation death, heterogeneous oscillation death, homogeneous oscillation, and wave propagations are found and they may coexist. We also find that all of these states are related to the unstable spatial modes to the amplitude death state.
The effect of process delay on dynamical behaviors in a self-feedback nonlinear oscillator
Yao, Chenggui; Ma, Jun; Li, Chuan; He, Zhiwei
2016-10-01
The delayed feedback loops play a crucial role in the stability of dynamical systems. The effect of process delay in feedback is studied numerically and theoretically in the delayed feedback nonlinear systems including the neural model, periodic system and chaotic oscillator. The process delay is of key importance in determining the evolution of systems, and the rich dynamical phenomena are observed. By introducing a process delay, we find that it can induce bursting electric activities in the neural model. We demonstrate that this novel regime of amplitude death also exists in the parameter space of feedback strength and process delay for the periodic system and chaotic oscillator. Our results extend the effect of process delay in the paper of Zou et al.(2013) where the process delay can eliminate the amplitude death of the coupled nonlinear systems.
Asymmetry in pulse-coupled oscillators with delay.
Zeitler, M.; Daffertshofer, A.; Gielen, C.C.A.M.
2009-01-01
We studied the dynamics of synchronization in asymmetrically coupled neural oscillators with time delay. Stability analysis revealed that symmetric excitatory coupling results in synchrony at multiple phase relations. Asymmetry yields two saddle-node bifurcations of the stable states when coupling i
Asymmetry in pulse-coupled oscillators with delay.
Zeitler, M.; Daffertshofer, A.; Gielen, C.C.A.M.
2009-01-01
We studied the dynamics of synchronization in asymmetrically coupled neural oscillators with time delay. Stability analysis revealed that symmetric excitatory coupling results in synchrony at multiple phase relations. Asymmetry yields two saddle-node bifurcations of the stable states when coupling i
Quantifying phase-amplitude coupling in neuronal network oscillations.
Onslow, Angela C E; Bogacz, Rafal; Jones, Matthew W
2011-03-01
Neuroscience time series data from a range of techniques and species reveal complex, non-linear interactions between different frequencies of neuronal network oscillations within and across brain regions. Here, we briefly review the evidence that these nested, cross-frequency interactions act in concert with linearly covariant (within-frequency) activity to dynamically coordinate functionally related neuronal ensembles during behaviour. Such studies depend upon reliable quantification of cross-frequency coordination, and we compare the properties of three techniques used to measure phase-amplitude coupling (PAC)--Envelope-to-Signal Correlation (ESC), the Modulation Index (MI) and Cross-Frequency Coherence (CFC)--by standardizing their filtering algorithms and systematically assessing their robustness to noise and signal amplitude using artificial signals. Importantly, we also introduce a freely-downloadable method for estimating statistical significance of PAC, a step overlooked in the majority of published studies. We find that varying data length and noise levels leads to the three measures differentially detecting false positives or correctly identifying frequency bands of interaction; these conditions should therefore be taken into careful consideration when selecting PAC analyses. Finally, we demonstrate the utility of the three measures in quantifying PAC in local field potential data simultaneously recorded from rat hippocampus and prefrontal cortex, revealing a novel finding of prefrontal cortical theta phase modulating hippocampal gamma power. Future adaptations that allow detection of time-variant PAC should prove essential in deciphering the roles of cross-frequency coupling in mediating or reflecting nervous system function.
Classification of attractors for systems of identical coupled Kuramoto oscillators
Energy Technology Data Exchange (ETDEWEB)
Engelbrecht, Jan R. [Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467 (United States); Mirollo, Renato [Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467 (United States)
2014-03-15
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For N≠3 oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Classification of attractors for systems of identical coupled Kuramoto oscillators.
Engelbrecht, Jan R; Mirollo, Renato
2014-03-01
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Multiwave nonlinear couplings in elastic structures
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This short contribution considers the essentials of nonlinear wave properties in typical mechanical systems such as an infinite straight bar, a circular ring, and a flat plate. It is found that nonlinear resonance is experienced in all the systems exhibiting continuous and discrete spectra, respectively. Multiwave interactions and the stability of coupled modes with respect to small perturbations are discussed. The emphasis is placed on mechanical phenomena, for example, stress amplification, although some analogies with some nonlinear optical systems are also obvious. The nonlinear resonance coupling in a plate within the Kirchhoff-Love approximation is selected as a two-dimensional example exhibiting a rich range of resonant wave phenomena. This is originally examined by use of Whitham's averaged Lagrangian method. In particular, the existence of three basic resonant triads between longitudinal, shear, and bending modes is shown. Some of these necessarily enter cascade wave processes related to the instability of some mode components of the triad under small perturbations.
Transverse coupling and dynamics of patterns in a photorefractive oscillator
Institute of Scientific and Technical Information of China (English)
XU; Jiong(徐炯); ZHUANG; Jun(庄军); ZHAO; Li(赵利); LI; Yufen(李郁芬); LI; Fuming(李富铭)
2003-01-01
The effect of transverse coupling in a photorefractive oscillator is studied. From the study the condition for stable optical patterns of multimode oscillation is given analytically and verified by numerical simulation. Under the stable condition, the period-doubling route to spatiotemporal chaos is observed.
Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity
DEFF Research Database (Denmark)
Sfahania, M. G.; Ganji, S. S.; Barari, Amin
2010-01-01
This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...
Quantifying the dynamics of coupled networks of switches and oscillators.
Directory of Open Access Journals (Sweden)
Matthew R Francis
Full Text Available Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's evolution. We, therefore, introduce a new modeling framework that describes the dynamics of networks composed of both oscillators and switches. Both oscillator synchronization and switch stability are preserved in these heterogeneous, coupled networks. Furthermore, this model recapitulates the qualitative dynamics for the yeast cell cycle consistent with the hypothesized dynamics resulting from decomposition of the regulatory network into dynamic motifs. Introducing feedback into the cell-cycle network induces qualitative dynamics analogous to limitless replicative potential that is a hallmark of cancer. As a result, the proposed model of switch and oscillator coupling provides the ability to incorporate mechanisms that underlie the synchronized stimulus response ubiquitous in biochemical systems.
Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators
Hramov, Alexander E.; ALEXEY A. KORONOVSKII
2005-01-01
A new behavior type of unidirectionally coupled chaotic oscillators near the generalized synchronization transition has been detected. It has been shown that the generalized synchronization appearance is preceded by the intermitted behavior: close to threshold parameter value the coupled chaotic systems demonstrate the generalized synchronization most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous bursts. This type of th...
Transport for Stochastic System with Infinite Locally Coupled Oscillators
Institute of Scientific and Technical Information of China (English)
ZHAO Ying-Kui; LI Jing-Hui; ZHAO Xian-Geng
2003-01-01
We consider the transport of particles for spatially periodic system with infinite locally coupled oscillatorsdriven by additive and multiplicative noises. A formula of the probability current derived by us shows that the couplingamong the infinite oscillators is an ingredient for transport. This coupling of the oscillators can induce transport ofparticles in the absence of the correlation of the additive and multiplicative noises, even without the multiplicative noise.
Zhang, Zhen; Koroleva, I.; Manevitch, L. I.; Bergman, L. A.; Vakakis, A. F.
2016-09-01
We study the dynamics and acoustics of a nonlinear lattice with fixed boundary conditions composed of a finite number of particles coupled by linear springs, undergoing in-plane oscillations. The source of the strongly nonlinearity of this lattice is geometric effects generated by the in-plane stretching of the coupling linear springs. It has been shown that in the limit of low energy the lattice gives rise to a strongly nonlinear acoustic vacuum, which is a medium with zero speed of sound as defined in classical acoustics. The acoustic vacuum possesses strongly nonlocal coupling effects and an orthogonal set of nonlinear standing waves [or nonlinear normal modes (NNMs)] with mode shapes identical to those of the corresponding linear lattice; in contrast to the linear case, however, all NNMs except the one with the highest wavelength are unstable. In addition, the lattice supports two types of waves, namely, nearly linear sound waves (termed "L waves") corresponding to predominantly axial oscillations of the particles and strongly nonlinear localized propagating pulses (termed "N L pulses") corresponding to predominantly transverse oscillating wave packets of the particles with localized envelopes. We show the existence of nonlinear nonreciprocity phenomena in the dynamics and acoustics of the lattice. Two opposite cases are examined in the limit of low energy. The first gives rise to nonreciprocal dynamics and corresponds to collective, spatially extended transverse loading of the lattice leading to the excitation of individual, predominantly transverse NNMs, whereas the second case gives rise to nonreciprocal acoutics by considering the response of the lattice to spatially localized, transverse impulse or displacement excitations. We demonstrate intense and recurring energy exchanges between a directly excited NNM and other NNMs with higher wave numbers, so that nonreciprocal energy exchanges from small-to-large wave numbers are established. Moreover, we show the
Coupling of radial and nonradial oscillations of relativistic stars: Gauge-invariant formalism
Passamonti, Andrea; Bruni, Marco; Gualtieri, Leonardo; Sopuerta, Carlos F.
2005-01-01
Linear perturbation theory is appropriate to describe small oscillations of stars, while a mild nonlinearity is still tractable perturbatively but requires one to consider mode coupling, i.e., to take into account second order effects. It is natural to start to look at this problem by considering the coupling between linear radial and nonradial modes. A radial pulsation may be thought of as an important component of an overall mildly nonlinear oscillation, e.g., of a protoneutron star. Radial pulsations of spherical compact objects do not per se emit gravitational waves but, if the coupling between the existing first order radial and nonradial modes is efficient in driving and possibly amplifying the nonradial oscillations, one may expect the appearance of nonlinear harmonics, and gravitational radiation could then be produced to a significant level. More in general, mode coupling typically leads to an interesting phenomenology, thus it is worth investigating in the context of star perturbations. In this paper we develop the relativistic formalism to study the coupling of radial and nonradial first order perturbations of a compact spherical star. From a mathematical point of view, it is convenient to treat the two sets of perturbations as separately parametrized, using a 2-parameter perturbative expansion of the metric, the energy-momentum tensor and Einstein equations in which λ is associated with the radial modes, ɛ with the nonradial perturbations, and the λɛ terms describe the coupling. This approach provides a well-defined framework to consider the gauge dependence of perturbations, allowing us to use ɛ order gauge-invariant nonradial variables on the static background and to define new second order λɛ gauge-invariant variables representing the result of the nonlinear coupling. We present the evolution and constraint equations for our variables outlining the setup for numerical computations, and briefly discuss the surface boundary conditions in terms
Nonlinearly Coupled Superconducting Lumped Element Resonators
Collodo, Michele C.; Potočnik, Anton; Rubio Abadal, Antonio; Mondal, Mintu; Oppliger, Markus; Wallraff, Andreas
We study SQUID-mediated tunable coupling between two superconducting on-chip resonators in the microwave frequency range. In this circuit QED implementation, we employ lumped-element type resonators, which consist of Nb thin film structured into interdigitated finger shunt capacitors and meander inductors. A SQUID, functioning as flux dependent and intrinsically nonlinear inductor, is placed as a coupling element together with an interdigitated capacitor between the two resonators (cf. A. Baust et al., Phys Rev. B 91 014515 (2015)). We perform a spectroscopic measurement in a dilution refrigerator and find the linear photon hopping rate between the resonators to be widely tunable as well as suppressible for an appropriate choice of parameters, which is made possible due to the interplay of inductively and capacitively mediated coupling. Vanishing linear coupling promotes nonlinear effects ranging from onsite- to cross-Kerr interaction. A dominating cross-Kerr interaction related to this configuration is notable, as it induces a unique quantum state. In the course of analog quantum simulations, such elementary building blocks can serve as a precursor for more complex geometries and thus pave the way to a number of novel quantum phases of light
Methods for Stability and Noise Analysis of Coupled Oscillating Systems
DEFF Research Database (Denmark)
Djurhuus, Torsten
2008-01-01
and phase-noise filters; to name but a few of the possible applications areas. Taking outset in the established single-oscillator phase-macro model, a novel numerical algorithm for the automated phase-noise characterization of coupled oscillators, perturbed by noise, is developed. The algorithm, which......In this thesis a study of analytical and numerical models of coupled oscillating systems, perturbed by delta-correlated noise sources, is undertaken. These models are important for the attainment of a qualitative understanding of the complex dynamics seen in various physical, biological, electronic...
The vertical oscillations of coupled magnets
Kewei, Li; Jiahuang, Lin; Yang, Kang Zi; Liang, Samuel Yee Wei; Wong Say Juan, Jeremias
2011-07-01
The International Young Physicists' Tournament (IYPT) is a worldwide, annual competition for high school students. This paper is adapted from the winning solution to Problem 14, Magnetic Spring, as presented in the final round of the 23rd IYPT in Vienna, Austria. Two magnets were arranged on top of each other on a common axis. One was fixed, while the other could move vertically. Various parameters of interest were investigated, including the effective gravitational acceleration, the strength, size, mass and geometry of the magnets, and damping of the oscillations. Despite its simplicity, this setup yielded a number of interesting and unexpected relations. The first stage of the investigation was concerned only with the undamped oscillations of small amplitudes, and the period of small amplitude oscillations was found to be dependent only on the eighth root of important magnet properties such as its strength and mass. The second stage sought to investigate more general oscillations. A numerical model which took into account magnet size, magnet geometry and damping effects was developed to model the general oscillations. Air resistance and friction were found to be significant sources of damping, while eddy currents were negligible.
The vertical oscillations of coupled magnets
Energy Technology Data Exchange (ETDEWEB)
Li Kewei; Lin Jiahuang; Kang Zi Yang [Raffles Institution, 1 Raffles Institution Lane, Singapore 575954 (Singapore); Liang, Samuel Yee Wei [Anglo-Chinese School Independent, 121 Dover Road, Singapore 139650 (Singapore); Juan, Jeremias Wong Say, E-mail: likewei92@gmail.com [NUS High School of Mathematics and Science, 20 Clementi Avenue 1, Singapore 129957 (Singapore)
2011-07-15
The International Young Physicists' Tournament (IYPT) is a worldwide, annual competition for high school students. This paper is adapted from the winning solution to Problem 14, Magnetic Spring, as presented in the final round of the 23rd IYPT in Vienna, Austria. Two magnets were arranged on top of each other on a common axis. One was fixed, while the other could move vertically. Various parameters of interest were investigated, including the effective gravitational acceleration, the strength, size, mass and geometry of the magnets, and damping of the oscillations. Despite its simplicity, this setup yielded a number of interesting and unexpected relations. The first stage of the investigation was concerned only with the undamped oscillations of small amplitudes, and the period of small amplitude oscillations was found to be dependent only on the eighth root of important magnet properties such as its strength and mass. The second stage sought to investigate more general oscillations. A numerical model which took into account magnet size, magnet geometry and damping effects was developed to model the general oscillations. Air resistance and friction were found to be significant sources of damping, while eddy currents were negligible.
Two-oscillator model of trapped-modes interaction in a nonlinear bilayer fish-scale metamaterial
Tuz, Vladimir R; Kochetova, Lyudmila A; Mladyonov, Pavel L; Prosvirnin, Sergey L
2014-01-01
We discuss the similarity between the nature of resonant oscillations in two nonlinear systems, namely, a chain of coupled Duffing oscillators and a bilayer fish-scale metamaterial. In such systems two different resonant states arise which differ in their spectral lines. The spectral line of the first resonant state has a Lorentzian form, while the second one has a Fano form. This difference leads to a specific nonlinear response of the systems which manifests itself in appearance of closed loops in spectral lines and bending and overlapping of resonant curves. Conditions of achieving bistability and multistability are found out.
Shukla, P K; Eliasson, B
2007-08-31
We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schrödinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.
Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators
Lakshmanan, M
1997-01-01
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.
Modified Semi-Classical Methods for Nonlinear Quantum Oscillations Problems
Moncrief, Vincent; Maitra, Rachel
2012-01-01
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. Under smoothness, convexity and coercivity hypotheses on its potential energy function, we prove, using the calculus of variations together with the Banach space implicit function theorem, the existence of a global, smooth `fundamental solution'. Higher order quantum corrections, for ground and excited states, are computed through the integration of associated systems of linear transport equations, and formal expansions for the corresponding energy eigenvalues obtained by imposing smoothness on the quantum corrections to the eigenfunctions. For linear oscillators our expansions naturally truncate, reproducing the well-known solutions for the energy eigenfunctions and eigenvalues. As an application, w...
Nonlinear oscillations in a muscle pacemaker cell model
González-Miranda, J. M.
2017-02-01
This article presents a numerical simulation study of the nonlinear oscillations displayed by the Morris-Lecar model [Biophys. J. 35 (1981) 193] for the oscillations experimentally observed in the transmembrane potential of a muscle fiber subject to an external electrical stimulus. We consider the model in the case when there is no external stimulation, aiming to establish the ability of the model to display biophysically reasonable pacemaker dynamics. We obtain 2D bifurcation diagrams showing that indeed the model presents oscillatory dynamics, displaying the two main types of action potentials that are observed in muscle fibers. The results obtained are shown to be structurally stable; that is, robust against changes in the values of system parameters. Moreover, it is demonstrated how the model is appropriate to analyze the action potentials observed in terms of the transmembrane currents creating them.
Nonlinear inertial oscillations of a multilayer eddy: An analytical solution
Dotsenko, S. F.; Rubino, A.
2008-06-01
Nonlinear axisymmetric oscillations of a warm baroclinic eddy are considered within the framework of an reduced-gravity model of the dynamics of a multilayer ocean. A class of exact analytical solutions describing pure inertial oscillations of an eddy formation is found. The thicknesses of layers in the eddy vary according to a quadratic law, and the horizontal projections of the velocity in the layers depend linearly on the radial coordinate. Owing to a complicated structure of the eddy, weak limitations on the vertical distribution of density, and an explicit form of the solution, the latter can be treated as a generalization of the exact analytical solutions of this form that were previously obtained for homogeneous and baroclinic eddies in the ocean.
Directory of Open Access Journals (Sweden)
Anatoly V. Klyuchevskii
2013-11-01
Full Text Available The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation. The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures (RAS. The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes, proximal in time but distant in space, may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors. The space-time distribution of coupled MLH > 5.5 events has been stable for the period of instrumental seismicity, with the largest events occurring in pairs, one shortly after another, on two ends of the rift system and with couples of smaller events in the central part of the rift. The event couples appear as peaks of earthquake ‘migration’ rate with an approximately decadal periodicity. Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation. The new knowledge, with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis, may be of theoretical and practical value for earthquake prediction issues. Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region, i.e., there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.
Nonlinear Dynamic Reliability of Coupled Stay Cables and Bridge Tower
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Nonlinear vibration can cause serious problems in long span cable-stayed bridges. When the internal resonance threshold is reached between the excitation frequency and natural frequency,large amplitudes occur in the cable. Based on the current situation of lacking corresponding constraint criteria, a model was presented for analyzing the dynamic reliability of coupling oscillation between the cable and tower in a cable-stayed bridge. First of all, in the case of cable sag, the d'Alembert principle is applied to studying the nonlinear dynamic behavior of the structure, and resonance failure interval of parametric oscillation is calculated accordingly. Then the dynamic reliability model is set up using the JC method. An application of this model has been developed for the preliminary design of one cable-stayed bridge located on Hai River in Tianjin, and time histories analysis as well as reliability indexes have been obtained. When frequency ratio between the cable and tower is approaching 1∶2, the reliability index is 0.98, indicating high failure probability. And this is consistent with theoretical derivation and experimental results in reference. This model, which is capable of computing the reliability index of resonance failure, provides theoretical basis for the establishment of corresponding rule.
Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case
Ghorbanian, Parham; Ramakrishnan, Subramanian; Ashrafiuon, Hashem
2015-01-01
In this article, the Electroencephalography (EEG) signal of the human brain is modeled as the output of stochastic non-linear coupled oscillator networks. It is shown that EEG signals recorded under different brain states in healthy as well as Alzheimer's disease (AD) patients may be understood as distinct, statistically significant realizations of the model. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) resting conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing—van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects by selecting the model physical parameters and noise intensity. The selected signal characteristics are power spectral densities in major brain frequency bands Shannon and sample entropies. These measures allow matching of linear time varying frequency content as well as non-linear signal information content and complexity. The main finding of the work is that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. However, it is also shown that the inclusion of sample entropy in the optimization process, to match the complexity of the EEG signal, enhances the stochastic non-linear oscillator model performance. PMID:25964756
Oscillations in the spectrum of nonlinear Thomson-backscattered radiation
Directory of Open Access Journals (Sweden)
C. A. Brau
2004-02-01
Full Text Available When an electron beam collides with a high-intensity laser beam, the spectrum of the nonlinear Thomson scattering in the backward direction shows strong oscillations like those in the spectrum of an optical klystron. Laser gain on the backward Thomson scattering is estimated using the Madey theorem, and the results suggest that Thomson-backscatter free-electron lasers are possible at wavelengths extending to the far uv using a terawatt laser beam from a chirped-pulse amplifier and a high-brightness electron beam from a needle cathode.
Infinite invariant densities due to intermittency in a nonlinear oscillator
Meyer, Philipp; Kantz, Holger
2017-08-01
Dynamical intermittency is known to generate anomalous statistical behavior of dynamical systems, a prominent example being the Pomeau-Manneville map. We present a nonlinear oscillator, i.e., a physical model in continuous time, whose properties in terms of weak ergodity breaking and aging have a one-to-one correspondence to the properties of the Pomeau-Manneville map. So for both systems in a wide range of parameters no physical invariant density exists. We show how this regime can be characterized quantitatively using the techniques of infinite invariant densities and the Thaler-Dynkin limit theorem. We see how expectation values exhibit aging in terms of scaling in time.
Nonlinear dynamics of the wake of an oscillating cylinder
Olinger, D. J.; Sreenivasan, K. R.
1988-02-01
The wake of an oscillating cylinder at low Reynolds numbers is a nonlinear system in which a limit cycle due to natural vortex shedding is modulated, generating in phase space a flow on a torus. It is experimentally shown that the system displays Arnol'd tongues for rational frequency ratios, and approximates the devil's staircase along the critical line. The 'singularity spectrum' as well as spectral peaks at various Fibonacci sequences accompanying quasi-periodic transition to chaos shows that the system belongs to the same universality class as the sine circle map.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Energy Technology Data Exchange (ETDEWEB)
Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Frequency Response and Gap Tuning for Nonlinear Electrical Oscillator Networks
Bhat, Harish S.; Vaz, Garnet J.
2013-01-01
We study nonlinear electrical oscillator networks, the smallest example of which consists of a voltage-dependent capacitor, an inductor, and a resistor driven by a pure tone source. By allowing the network topology to be that of any connected graph, such circuits generalize spatially discrete nonlinear transmission lines/lattices that have proven useful in high-frequency analog devices. For such networks, we develop two algorithms to compute the steady-state response when a subset of nodes are driven at the same fixed frequency. The algorithms we devise are orders of magnitude more accurate and efficient than stepping towards the steady-state using a standard numerical integrator. We seek to enhance a given network's nonlinear behavior by altering the eigenvalues of the graph Laplacian, i.e., the resonances of the linearized system. We develop a Newton-type method that solves for the network inductances such that the graph Laplacian achieves a desired set of eigenvalues; this method enables one to move the eigenvalues while keeping the network topology fixed. Running numerical experiments using three different random graph models, we show that shrinking the gap between the graph Laplacian's first two eigenvalues dramatically improves a network's ability to (i) transfer energy to higher harmonics, and (ii) generate large-amplitude signals. Our results shed light on the relationship between a network's structure, encoded by the graph Laplacian, and its function, defined in this case by the presence of strongly nonlinear effects in the frequency response. PMID:24223751
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-01-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science and technology, is illustrated through concrete examples of coupled biological cell models.
Dynamics of order parameters for globally coupled oscillators
DEFF Research Database (Denmark)
De Monte, Silvia; D'ovidio, Francesco
2002-01-01
The equation of motion for the centroid of globally coupled oscillators with natural frequency mismatch is obtained through a series expansion in order parameters, valid for any population size. In the case of strong coupling and narrow-frequency distribution the first-order expansion (correspond...
Coupled predator-prey oscillations in a chaotic food web
Beninca, E.; Jöhnk, K.; Heerkloss, R.; Huisman, J.
2009-01-01
Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles
Coupled predator-prey oscillations in a chaotic food web
Benincà, E.; Johnk, K.D.; Heerkloss, R.; Huisman, J.
2009-01-01
Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles
Dynamics of chaotic oscillations in mutually coupled microchip lasers
Uchida, A; Kinugawa, S; Yoshimori, S
2003-01-01
We have numerically and experimentally investigated the dynamics of mutually coupled microchip lasers. Chaotic oscillations are observed in the vicinity of the boundary of the injection-locking range when the coupling strength and the difference of the optical frequencies are varied. Synchronization of chaos is always achieved under the condition to generate chaos.
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-01-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science and t...... and technology, is illustrated through concrete examples of coupled biological cell models....
Mattei, P.-O.; Ponçot, R.; Pachebat, M.; Côte, R.
2016-07-01
In order to control the sound radiation by a structure, one aims to control vibration of radiating modes of vibration using "Energy Pumping" also named "Targeted Energy Transfer". This principle is here applied to a simplified model of a double leaf panel. This model is made of two beams coupled by a spring. One of the beams is connected to a nonlinear absorber. This nonlinear absorber is made of a 3D-printed support on which is clamped a buckled thin small beam with a small mass fixed at its centre having two equilibrium positions. The experiments showed that, once attached onto a vibrating system to be controlled, under forced excitation of the primary system, the light bistable oscillator allows a reduction of structural vibration up to 10 dB for significant amplitude and frequency range around the first two vibration modes of the system.
Nonlinear longitudinal oscillations of fuel in rockets feed lines with gas-liquid damper
Avramov, K. V.; Filipkovsky, S.; Tonkonogenko, A. M.; Klimenko, D. V.
2016-03-01
The mathematical model of the fuel oscillations in the rockets feed lines with gas-liquid dampers is derived. The nonlinear model of the gas-liquid damper is suggested. The vibrations of fuel in the feed lines with the gas-liquid dampers are considered nonlinear. The weighted residual method is applied to obtain the finite degrees of freedom nonlinear model of the fuel oscillations. Shaw-Pierre nonlinear normal modes are applied to analyze free vibrations. The forced oscillations of the fuel at the principle resonances are analyzed. The stability of the forced oscillations is investigated. The results of the forced vibrations analysis are shown on the frequency responses.
An Improved Nonlinear Circuit Model for GaAs Gunn Diode in W-Band Oscillator
Zhang, Bo; Fan, Yong; Zhang, Yonghong
An improved nonlinear circuit model for a GaAs Gunn diode in an oscillator is proposed based on the physical mechanism of the diode. This model interprets the nonlinear harmonic character on the Gunn diode. Its equivalent nonlinear circuit of which can assist in the design of the Gunn oscillator and help in the analysis of the fundamental and harmonic characteristics of the GaAs Gunn diode. The simulation prediction and the experiment of the Gunn oscillator show the feasibility of the nonlinear circuit model for the GaAs Gunn oscillator.
Synchronization of indirectly coupled Lorenz oscillators: An experimental study
Indian Academy of Sciences (India)
Amit Sharma; Manish Dev Shrimali
2011-11-01
The dynamics of indirectly coupled Lorenz circuits is investigated experimentally. The in-phase and anti-phase synchronization of indirectly coupled chaotic oscillators reported in Phys. Rev. E 81, 046216 (2010) is veriﬁed by physical experiments with electronic circuits. Two chaotic systems coupled through a common dynamic environment shows the verity of synchronization behaviours such as anti-phase synchronization, in-phase synchronization, identical synchronization, anti-synchronization, etc.
Bursting Ca2+ Oscillations and Synchronization in Coupled Cells
Institute of Scientific and Technical Information of China (English)
JI Quan-Bao; LU Qi-Shao; Yang Zhuo-Qin; Duan Li-Xia
2008-01-01
A mathematical model proposed by Grubelnk et al. [Biophys. Chem. 94 (2001) 59] is employed to study the physiological role of mitochondria and the cytosolic proteins in generating complex Ca2+ oscillations. Intracellular bursting calcium oscillations of point-point, point cycle and two-folded limit cycle types are observed and explanations are given based on the fast/slow dynamical analysis, especially for point-cycle and two-folded limit cycle types, which have not been reported before. Furthermore, synchronization of coupled bursters of Ca2+oscillations via gap junctions and the effect of bursting types on synchronization of coupled cells are studied. It is argued that bursting oscillations of point-point type may be superior to achieve synchronization than that of point-cycle type.
Institute of Scientific and Technical Information of China (English)
FU Jing-Li; FU Hao
2008-01-01
We deai with the generalization of the field method to weakly non-linear mechanico-electricai coupling systems.The field co-ordinates and field momenta approaches are combined with the method of multiple time scales in order to obtain the amplitudes and phase of oscillations in the frst approximation. An example in mechanico-electrical coupling systems is given to illustrate this method.
Birth of oscillation in coupled non-oscillatory Rayleigh-Duffing oscillators
Guin, A.; Dandapathak, M.; Sarkar, S.; Sarkar, B. C.
2017-01-01
We have studied the dynamics of two bilaterally-coupled non-oscillatory Rayleigh-Duffing oscillators (RDOs). With the increase of coupling factor (CF) between RDOs, birth of periodic oscillations observed. For increased values of CF, dynamics becomes chaotic through a quasi-periodicroute but for even higher CF, synchronized stable periodic oscillations in RDOs are found. Taking direct and anti-diffusive coupling cases into consideration, we derive conditions for periodic bifurcation in parameter space analytically and verified them through numerical solution of system equations. Numerical simulation is also used to predict system states in two parameter space involving CF and linear damping parameter of RDOs. It indicates non-oscillatory, periodic, quasi-periodic and chaotic zones of system dynamics. Qualitative explanation of the simulated dynamics is given using homoclinic perturbation theory. Hardware experiment is performed on analog circuits simulating RDO model and obtained results confirm the predictions regarding birth of periodic oscillation and other features of system dynamics. Experimental results examining onset of oscillations in two under-biased bi-laterally coupled X-band Gunn oscillators (which are modelled as RDOs) is presented in support of the analysis.
Bloch oscillations of THz acoustic phonons in coupled nanocavity structures.
Lanzillotti-Kimura, N D; Fainstein, A; Perrin, B; Jusserand, B; Mauguin, O; Largeau, L; Lemaître, A
2010-05-14
Nanophononic Bloch oscillations and Wannier-Stark ladders have been recently predicted to exist in specifically tailored structures formed by coupled nanocavities. Using pump-probe coherent phonon generation techniques we demonstrate that Bloch oscillations of terahertz acoustic phonons can be directly generated and probed in these complex nanostructures. In addition, by Fourier transforming the time traces we had access to the proper eigenmodes in the frequency domain, thus evidencing the related Wannier-Stark ladder. The observed Bloch oscillation dynamics are compared with simulations based on a model description of the coherent phonon generation and photoelastic detection processes.
Wang, Zhengxin; Duan, Zhisheng; Cao, Jinde
2012-03-01
This paper aims to investigate the synchronization problem of coupled dynamical networks with nonidentical Duffing-type oscillators without or with coupling delays. Different from cluster synchronization of nonidentical dynamical networks in the previous literature, this paper focuses on the problem of complete synchronization, which is more challenging than cluster synchronization. By applying an impulsive controller, some sufficient criteria are obtained for complete synchronization of the coupled dynamical networks of nonidentical oscillators. Furthermore, numerical simulations are given to verify the theoretical results.
Indian Academy of Sciences (India)
Horacio Castellini; Efta Yudiarsah; Lilia Romanelli; Hilda A Cerdeira
2005-04-01
Animal locomotion employs different periodic patterns known as animal gaits. In 1993, Collins and Stewart recognized that gaits possessed certain symmetries and characterized the gaits of quadrupeds and bipeds using permutation symmetry groups, which impose constraints on the locomotion center called the central pattern generator (CPG) in the animal brain. They modeled the CPG by coupling four nonlinear oscillators and found that it was possible to reproduce all symmetries of the gaits by changing the coupling strength. Here we propose to extend this idea using coupled chaotic oscillators synchronized using the Pyragas method in order to characterize the CPG symmetries. We also evaluate the time series behavior when the foot is in contact with the ground: this has potential robotic applications.
A sustained oscillation in a toy-model of the coupled atmosphere-ocean system
Bothe, Oliver
2011-01-01
Interaction between atmospheric mid-latitude flow and wind-driven ocean circulation is studied coupling two idealized low-order spectral models. The barotropic Charney-DeVore model with three components simulates a bimodal mid-latitude atmospheric circulation in a channel with two stable flow patterns induced by topography. The wind-driven ocean double gyre circulation in a square basin (of half the channel length) is modeled by an equivalent barotropic formulation of the Veronis model with 21 components, which captures Rossby-wave dynamics and nonlinear decadal variability. When coupled, the atmosphere forces the ocean by wind-stress while, simultaneously, the ocean affects the atmosphere by thermal forcing in terms of a vorticity source. Coupled atmosphere-ocean simulations show two stable flow patterns associated with the topographically induced atmospheric bimodality and a sustained oscillation due to interaction between atmospheric bimodality and oceanic Rossby dynamics. The oscillation is of inter-annua...
Nonlinear dynamical analysis of carbachol induced hippocampal oscillations in mice
Institute of Scientific and Technical Information of China (English)
Metin AKAY; Kui WANG; Yasemin M AKAY; Andrei DRAGOMIR; Jie WU
2009-01-01
Aim: Hippocampal neuronal network and synaptic impairment underlie learning and memory deficit in Alzheimer's disease (AD) patients and animal models. In this paper, we analyzed the dynamics and complexity of hippocampal neuronal network synchronization induced by acute exposure to carbachol, a nicotinic and muscarinic receptor co-agonist, using the nonlinear dynamical model based on the Lempel-Ziv estimator. We compared the dynamics of hippocampal oscillations between wild-type (WT) and triple-transgenic (3xTg) mice, as an AD animal model. We also compared these dynamic alterations between different age groups (5 and 10 months). We hypothesize that there is an impairment of complexity of CCh-induced hippocampal oscillations in 3xTg AD mice compared to WT mice, and that this impairment is age-dependent. Methods: To test this hypothesis, we used electrophysiological recordings (field potential) in hippocampal slices. Results: Acute exposure to 100 nmol/L CCh induced field potential oscillations in hippocampal CA1 region, which exhibited three distinct patterns: (1) continuous neural firing, (2) repeated burst neural firing and (3) the mixed (continuous and burst) pattern in both WT and 3xTg AD mice. Based on Lempel-Ziv estimator, pattern (2) was significantly lower than patterns (1) and (3) in 3xTg AD mice compared to WT mice (P<0.001), and also in 10-month old WT mice compared to those in 5-month old WT mice (P<0.01).Conclusion: These results suggest that the burst pattern (theta oscillation) of hippocampal network is selectively impaired in 3xTg AD mouse model, which may reflect a learning and memory deficit in the AD patients.
A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network
Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien
2017-01-01
With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices’ non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing. PMID:28322262
A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network
Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien
2017-03-01
With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices’ non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing.
Emergence of a negative resistance in noisy coupled linear oscillators
Quiroz-Juárez, M. A.; Aragón, J. L.; León-Montiel, R. de J.; Vázquez-Medina, R.; Domínguez-Juárez, J. L.; Quintero-Torres, R.
2016-12-01
We report on the experimental observation of an emerging negative resistance in a system of coupled linear electronic RLC harmonic oscillators under the influence of multiplicative noise with long correlation time. When two oscillators are coupled by a noisy inductor, an analysis in the Fourier space of the electrical variables unveils the presence of an effective negative resistance, which acts as an energy transport facilitator. This might constitute a simple explanation of the now fashionable problem of energy transport assisted by noise in classical systems. The experimental setup is based on the working principle of an analog computer and by itself constitutes a versatile platform for studying energy transport in noisy systems by means of coupled electrical oscillator systems.
Intermittent Behavior and Synchronization of Two Coupled Noisy Driven Oscillators
Directory of Open Access Journals (Sweden)
Ângela Maria dos Santos
2009-01-01
Full Text Available The coupled system of two forced Liénard-type oscillators has applications in diode-based electric circuits and phenomenological models for the heartbeat. These systems typically exhibit intermittent transitions between laminar and chaotic states; what affects their performance and, since noise is always present in such systems, dynamical models should include these effects. Accordingly, we investigated numerically the effect of noise in two intermittent phenomena: the intermittent transition to synchronized behavior for identical and unidirectionally coupled oscillators, and the intermittent transition to chaos near a periodic window of bidirectionally coupled oscillators. We found that the transition from a nonsynchronized to a synchronized state exhibits a power-law scaling with exponent 3/2 characterizing on-off intermittency. The inclusion of noise adds an exponential tail to this scaling.
Sensory segmentation with coupled neural oscillators.
von der Malsburg, C; Buhmann, J
1992-01-01
We present a model of sensory segmentation that is based on the generation and processing of temporal tags in the form of oscillations, as suggested by the Dynamic Link Architecture. The model forms the basis for a natural solution to the sensory segmentation problem. It can deal with multiple segments, can integrate different cues and has the potential for processing hierarchical structures. Temporally tagged segments can easily be utilized in neural systems and form a natural basis for object recognition and learning. The model consists of a "cortical" circuit, an array of units that act as local feature detectors. Units are formulated as neural oscillators. Knowledge relevant to segmentation is encoded by connections. In accord with simple Gestalt laws, our concrete model has intracolumnar connections, between all units with overlapping receptive fields, and intercolumnar connections, between units responding to the same quality in different positions. An inhibitory connection system prevents total correlation and controls the grain of the segmentation. In simulations with synthetic input data we show the performance of the circuit, which produces signal correlation within segments and anticorrelation between segments.
Dynamics of phase oscillators with generalized frequency-weighted coupling
Xu, Can; Gao, Jian; Xiang, Hairong; Jia, Wenjing; Guan, Shuguang; Zheng, Zhigang
2016-12-01
Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during recent years. In this paper, we extend the Kuramoto model by considering a particular heterogeneous coupling scheme in an ensemble of phase oscillators, where each oscillator pair interacts with different coupling strength that is weighted by a general function of the natural frequency. The Kuramoto theory for the transition to synchronization can be explicitly generalized, such as the expression for the critical coupling strength. Also, a self-consistency approach is developed to predict the stationary states in the thermodynamic limit. Moreover, Landau damping effects are further revealed by means of linear stability analysis and resonance poles theory below the critical threshold, which turns to be far more generic. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings.
Damped driven coupled oscillators: entanglement, decoherence and the classical limit
Energy Technology Data Exchange (ETDEWEB)
Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M [Grupo de Optica e Informacion Cuantica, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia)], E-mail: rdguerrerom@unal.edu.co, E-mail: rrreyg@unal.edu.co, E-mail: kmfonsecar@unal.edu.co
2009-03-13
We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.
Complex Dynamical Behavior of a Two-Stage Colpitts Oscillator with Magnetically Coupled Inductors
Directory of Open Access Journals (Sweden)
V. Kamdoum Tamba
2014-01-01
Full Text Available A five-dimensional (5D controlled two-stage Colpitts oscillator is introduced and analyzed. This new electronic oscillator is constructed by considering the well-known two-stage Colpitts oscillator with two further elements (coupled inductors and variable resistor. In contrast to current approaches based on piecewise linear (PWL model, we propose a smooth mathematical model (with exponential nonlinearity to investigate the dynamics of the oscillator. Several issues, such as the basic dynamical behaviour, bifurcation diagrams, Lyapunov exponents, and frequency spectra of the oscillator, are investigated theoretically and numerically by varying a single control resistor. It is found that the oscillator moves from the state of fixed point motion to chaos via the usual paths of period-doubling and interior crisis routes as the single control resistor is monitored. Furthermore, an experimental study of controlled Colpitts oscillator is carried out. An appropriate electronic circuit is proposed for the investigations of the complex dynamics behaviour of the system. A very good qualitative agreement is obtained between the theoretical/numerical and experimental results.
Directory of Open Access Journals (Sweden)
Imran Talib
2015-12-01
Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-02-22
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
Goto, Hayato
2016-02-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Time Delay in the Kuramoto Model of Coupled Oscillators
Yeung, M K S; Strogatz, Steven H.
1999-01-01
We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive exact formulas for the stability boundaries of the incoherent and synchronized states, as a function of the delay, in the special case where the oscillators are identical. The experimental implications of the model are discussed for populations of chirping crickets, where the finite speed of sound causes communication delays, and for physical systems such as coupled phase-locked loops or lasers.
Coupled, Active Oscillators and Lizard Otoacoustic Emissions
Bergevin, Christopher; Velenovsky, David S.; Bonine, Kevin E.
2011-11-01
The present study empirically explores the relationship between spontaneous otoacoustic emissions (SOAEs) and stimulus-frequency emissions (SFOAEs) in lizards, an ideal group for such research given their relatively simple inner ear (e.g., lack of basilar membrane traveling waves), diverse morphology across species/families (e.g., tectorial membrane structure) and robust emissions. In a nutshell, our results indicate that SFOAEs evoked using low-level tones are intimately related to underlying SOAE activity, and appear to represent the entrained response of active oscillators closely tuned to the probe frequency. The data described here indicate several essential features that are desirable to capture in theoretical models for auditory transduction in lizards, and potentially represent generic properties at work in many different classes of "active" ears.
Energy Technology Data Exchange (ETDEWEB)
Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)
2014-11-03
We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.
Energy Technology Data Exchange (ETDEWEB)
Khorashadizadeh, S. M., E-mail: smkhorashadi@birjand.ac.ir; Taheri Boroujeni, S. [Physics Department, University of Birjand, Birjand (Iran, Islamic Republic of); Niknam, A. R. [Laser and Plasma Research Institute, Shahid Beheshti University, G.C., Tehran (Iran, Islamic Republic of)
2015-11-15
In this paper, we have investigated the nonlinear interaction between high-frequency surface plasmons and low-frequency ion oscillations in a semi-bounded collisional quantum plasma. By coupling the nonlinear Schrodinger equation and quantum hydrodynamic model, and taking into account the ponderomotive force, the dispersion equation is obtained. By solving this equation, it is shown that there is a modulational instability in the system, and collisions and quantum forces play significant roles on this instability. The quantum tunneling increases the phase and group velocities of the modulated waves and collisions increase the growth rate of the modulational instability. It is also shown that the effect of quantum forces and collisions is more significant in high modulated wavenumber regions.
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit
History of nonlinear oscillations theory in France (1880-1940)
Ginoux, Jean-Marc
2017-01-01
This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own...
Barut—Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass
Amir, Naila; Iqbal, Shahid
2016-07-01
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut—Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.
Inhomogeneous stationary and oscillatory regimes in coupled chaotic oscillators.
Liu, Weiqing; Volkov, Evgeny; Xiao, Jinghua; Zou, Wei; Zhan, Meng; Yang, Junzhong
2012-09-01
The dynamics of linearly coupled identical Lorenz and Pikovsky-Rabinovich oscillators are explored numerically and theoretically. We concentrate on the study of inhomogeneous stable steady states ("oscillation death (OD)" phenomenon) and accompanying periodic and chaotic regimes that emerge at an appropriate choice of the coupling matrix. The parameters, for which OD occurs, are determined by stability analysis of the chosen steady state. Three model-specific types of transitions to and from OD are observed: (1) a sharp transition to OD from a nonsymmetric chaotic attractor containing random intervals of synchronous chaos; (2) transition to OD from the symmetry-breaking chaotic regime created by negative coupling; (3) supercritical bifurcation of OD into inhomogeneous limit cycles and further evolution of the system to inhomogeneous chaotic regimes that coexist with complete synchronous chaos. These results may fill a gap in the understanding of the mechanism of OD in coupled chaotic systems.
Dynamical bifurcation in a system of coupled oscillators with slowly varying parameters
Directory of Open Access Journals (Sweden)
Igor Parasyuk
2016-08-01
Full Text Available This paper deals with a fast-slow system representing n nonlinearly coupled oscillators with slowly varying parameters. We find conditions which guarantee that all omega-limit sets near the slow surface of the system are equilibria and invariant tori of all dimensions not exceeding n, the tori of dimensions less then n being hyperbolic. We show that a typical trajectory demonstrates the following transient process: while its slow component is far from the stationary points of the slow vector field, the fast component exhibits damping oscillations; afterwards, the former component enters and stays in a small neighborhood of some stationary point, and the oscillation amplitude of the latter begins to increase; eventually the trajectory is attracted by an n-dimesional invariant torus and a multi-frequency oscillatory regime is established.
Anti-phase synchronization and ergodicity in arrays of oscillators coupled by an elastic force
Dilão, Rui
2014-04-01
We have proposed a mechanism of interaction between two non-linear dissipative oscillators, leading to exact and robust anti-phase and in-phase synchronization. The system we have analyzed is a model for the Huygens's two pendulum clocks system, as well as a model for synchronization mediated by an elastic media. Here, we extend these results to arrays, finite or infinite, of conservative pendula coupled by linear elastic forces. We show that, for two interacting pendula, this mechanism leads always to synchronized anti-phase small amplitude oscillations, and it is robust upon variation of the parameters. For three or more interacting pendula, this mechanism leads always to ergodic non-synchronized oscillations. In the continuum limit, the pattern of synchronization is described by a quasi-periodic longitudinal wave.
Mechanical filtering in forced-oscillation of two coupled pendulums
Foulaadvand, M Ebrahim
2010-01-01
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the amplitudes and phases of in terms of the frequency of the sinusoidal driving force. The resonance frequencies are obtained and the amplitude ratio is discussed in details. Contrary to a single oscillator, in this two-degree of freedom system four resonant frequencies, which are close to mode frequencies, appear. Within the pass-band interval the system is shown to exhibit a rich and complicated behaviour. It is shown that damping crucially affects the system properties. Under certain circumstances, the amplitude of the oscillator which is directly connected to the driving force becomes smaller than the one far from it. Particularly we show the existence of a driving frequency at which the connected oscillator's amplitude goes zero.
Nonlinear dynamics of spin transfer nano-oscillators
Indian Academy of Sciences (India)
B Subash; V K Chandrasekar; M Lakshmanan
2015-03-01
The evolution equation of a ferromagnetic spin system described by Heisenberg nearest-neighbour interaction is given by Landau–Lifshitz–Gilbert (LLG) equation, which is a fascinating nonlinear dynamical system. For a nanomagnetic trilayer structure (spin valve or pillar) an additional torque term due to spin-polarized current has been suggested by Slonczewski, which gives rise to a rich variety of dynamics in the free layer. Under appropriate conditions the spin-polarized current gives a time-varying resistance to the magnetic structure thereby inducing magnetization oscillations of frequency which lies in the microwave region. Such a device is called a spin transfer nanooscillator (STNO). However, this interesting nanoscale level source of microwaves lacks efficiency due to its low emitting power typically of the order of nWs. To over-come this difficulty, one has to consider the collective dynamics of synchronized arrays/networks of STNOs as suggested by Fert and coworkers so that the power can be enhanced 2 times that of a single STNO. We show that this goal can be achieved by applying a common microwave magnetic field to an array of STNOs. In order to make the system technically more feasible to practical level integration with CMOS circuits, we establish suitable electrical connections between the oscillators. Although the electrical connection makes the system more complex, the applied microwave magnetic field drives the system to synchronization in large regions of parameter space.
Weakly coupled oscillators in a slowly varying world.
Park, Youngmin; Ermentrout, Bard
2016-06-01
We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through cholinergic activation. Our method extends and simplifies the recent work of Kurebayashi (Physical Review Letters, 111, 214101, 2013) to include coupling. We apply the method to an all-to-all network and show that there is a waxing and waning of synchrony of modulated neurons.
Light-Matter Interactions: A Coupled Oscillator Description
Frimmer, Martin
2016-01-01
The semiclassical theory of light-matter interactions describes the interaction between a classical electromagnetic field with a quantum mechanical two-level system.We show that the quantum mechanical two-level system can be modeled by a system of two coupled classical harmonic oscillators whose eigenstates are split in frequency according to the coupling strength and play the roles of the two levels of the quantum mechanical two-level system. The effect of the light field on the mechanical system is modeled as a modulation of the spring constants of the individual oscillators. Using this fully classical model, we derive the Bloch equations for a two-level system and discuss the mechanical analogues of Rabi oscillations and coherent control experiments
Regular nonlinear response of the driven Duffing oscillator to chaotic time series
Institute of Scientific and Technical Information of China (English)
YuanYe; Li Yue; Danilo P. Mandic; Yang Bao-Jun
2009-01-01
Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated.
Collective dynamics of delay-coupled limit cycle oscillators
Indian Academy of Sciences (India)
Abhijit Sen; Ramana Dodla; George L Johnston
2005-04-01
Coupled limit cycle oscillators with instantaneous mutual coupling offer a useful but idealized mathematical paradigm for the study of collective behavior in a wide variety of biological, physical and chemical systems. In most real-life systems however the interaction is not instantaneous but is delayed due to finite propagation times of signals, reaction times of chemicals, individual neuron firing periods in neural networks etc. We present a brief overview of the effect of time-delayed coupling on the collective dynamics of such coupled systems. Simple model equations describing two oscillators with a discrete time-delayed coupling as well as those describing linear arrays of a large number of oscillators with time-delayed global or local couplings are studied. Analytic and numerical results pertaining to time delay induced changes in the onset and stability of amplitude death and phase-locked states are discussed. A number of recent experimental and theoretical studies reveal interesting new directions of research in this field and suggest exciting future areas of exploration and applications.
Searching for robust quantum memories in many coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Bosco de Magalhaes, A.R., E-mail: arthur.magalhaes@pq.cnpq.br [Departamento de Fisica e Matematica, Centro Federal de Educacao Tecnologica de Minas Gerais, 30510-000, Belo Horizonte, MG (Brazil)
2011-11-07
The relation between microscopic symmetries in the system-environment interaction and the emergence of robust states is studied for many linearly coupled harmonic oscillators. Different types of symmetry, which are introduced into the model as terms in the coupling constants between each system's oscillator and a common reservoir, lead to distinct robust modes. Since these modes are partially or completely immune to the symmetric part of the environmental noise, they are good candidates for building quantum memories. A comparison of the model investigated here, with bilinear system-reservoir coupling, and a model where such coupling presents an exponential dependence on the variables of interest is performed. -- Highlights: → Macroscopic symmetries may lead to microscopic ones in system-environment coupling. → Robust modes related to these symmetries are found for N coupled oscillators. → They can be used to enhance the lifetime of quantum memories. → They can be built in cavity modes in photonic-band-gap material or trapped ions.
String-Coupled Pendulum Oscillators: Theory and Experiment.
Moloney, Michael J.
1978-01-01
A coupled-oscillator system is given which is readily set up, using only household materials. The normal-mode analysis of this system is worked out, and an experiment or demonstration is recommended in which one verifies the theory by measuring two times and four lengths. (Author/GA)
Synchronizing large number of nonidentical oscillators with small coupling
Wu, Ye; Xiao, Jinghua; Hu, Gang; Zhan, Meng
2012-02-01
The topic of synchronization of oscillators has attracted great and persistent interest, and all previous conclusions and intuitions have convinced that large coupling is required for synchronizing a large number of coupled nonidentical oscillators. Here the influences of different spatial frequency distributions on the efficiency of frequency synchronization are investigated by studying arrays of coupled oscillators with diverse natural frequency distributions. A universal log-normal distribution of critical coupling strength Kc for synchronization irrespective of the initial natural frequency is found. In particular, a physical quantity "roughness"R of spatial frequency configuration is defined, and it is found that the efficiency of synchronization increases monotonously with R. For large R we can reach full synchronization of arrays with a large number of oscillators at finite Kc. Two typical kinds of synchronization, the "multiple-clustering" one and the "single-center-clustering" one, are identified for small and large R's, respectively. The mechanism of the latter type is the key reason for synchronizing long arrays with finite Kc.
String-Coupled Pendulum Oscillators: Theory and Experiment.
Moloney, Michael J.
1978-01-01
A coupled-oscillator system is given which is readily set up, using only household materials. The normal-mode analysis of this system is worked out, and an experiment or demonstration is recommended in which one verifies the theory by measuring two times and four lengths. (Author/GA)
Mori, Hiroki; Okuyama, Yuji; Asada, Minoru
2017-01-01
Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed. PMID:28796797
Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, Axel; Gordon, Christopher R. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2013-04-15
We analyze the spectral behaviour of a nonlinear quantum oscillator model under confinement. The underlying potential is given by a harmonic oscillator interaction plus a nonlinear term that can be weakened or strengthened through a parameter. Numerical eigenvalues of the model in one and three dimensions are presented. The asymptotic behaviour of the eigenvalues for confinement relaxation and for vanishing nonlinear term in the potential is investigated. Our findings are compared with existing results.
Teodorescu, Razvan
2009-10-01
Systems of oscillators coupled non-linearly (stochastically or not) are ubiquitous in nature and can explain many complex phenomena: coupled Josephson junction arrays, cardiac pacemaker cells, swarms or flocks of insects and birds, etc. They are know to have a non-trivial phase diagram, which includes chaotic, partially synchronized, and fully synchronized phases. A traditional model for this class of problems is the Kuramoto system of oscillators, which has been studied extensively for the last three decades. The model is a canonical example for non-equilibrium, dynamical phase transitions, so little understood in physics. From a stochastic analysis point of view, the transition is described by the large deviations principle, which offers little information on the scaling behavior near the critical point. I will discuss a special case of the model, which allows a rigorous analysis of the critical properties of the model, and reveals a new, anomalous scaling behavior in the vicinity of the critical point.
Emergent organization of oscillator clusters in coupled self-regulatory chaotic maps
Indian Academy of Sciences (India)
Hiroyasu Ando; Sudeshna Sinha; Kazuyuki Aihara
2008-06-01
Here we introduce a model of parametrically coupled chaotic maps on a one-dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a power-law distribution. Moreover, we find that the transient dynamics gives rise to a 1/ power spectrum. All these characteristics indicate self-organization and emergent scaling behavior in this system. We also interpret the power-law characteristics of the proposed system from an ecological point of view.
Chimera regimes in a ring of oscillators with local nonlinear interaction
Shepelev, Igor A.; Zakharova, Anna; Vadivasova, Tatiana E.
2017-03-01
One of important problems concerning chimera states is the conditions of their existence and stability. Until now, it was assumed that chimeras could arise only in ensembles with nonlocal character of interactions. However, this assumption is not exactly right. In some special cases chimeras can be realized for local type of coupling [1-3]. We propose a simple model of ensemble with local coupling when chimeras are realized. This model is a ring of linear oscillators with the local nonlinear unidirectional interaction. Chimera structures in the ring are found using computer simulations for wide area of values of parameters. Diagram of the regimes on plane of control parameters is plotted and scenario of chimera destruction are studied when the parameters are changed.
Qin, Jiahu; Gao, Huijun; Zheng, Wei Xing
2015-03-01
A unified approach to the analysis of synchronization for complex dynamical networks, i.e., networks of partial-state coupled linear systems and networks of full-state coupled nonlinear oscillators, is introduced. It is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks, thus making it feasible to consider the error dynamics for the whole network system. Different from the other various methods given in the existing literature, the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form, but also explicitly specifying the convergence rate.
Harmonic response of a class of finite extensibility nonlinear oscillators
Febbo, M.
2011-06-01
Finite extensibility oscillators are widely used to simulate those systems that cannot be extended to infinity. For example, they are used when modelling the bonds between molecules in a polymer or DNA molecule or when simulating filaments of non-Newtonian liquids. In this paper, the dynamic behavior of a harmonically driven finite extensibility oscillator is presented and studied. To this end, the harmonic balance method is applied to determine the amplitude-frequency and amplitude-phase equations. The distinguishable feature in this case is the bending of the amplitude-frequency curve to the frequency axis, making it asymptotically approach the limit of maximum elongation of the oscillator, which physically represents the impossibility of the system reaching this limit. Also, the stability condition that defines stable and unstable steady-state solutions is derived. The study of the effect of the system parameters on the response reveals that a decreasing value of the damping coefficient or an increasing value of the excitation amplitude leads to the appearance of a multi-valued response and to the existence of a jump phenomenon. In this sense, the critical amplitude of the excitation, which means here a certain value of external excitation that results in the occurrence of jump phenomena, is also derived. Numerical experiments to observe the effects of system parameters on the frequency-amplitude response are performed and compared with analytical calculations. At a low value of the damping coefficient or at a high value of excitation amplitude, the agreement is poor for low frequencies but good for high frequencies. It is demonstrated that the disagreement is caused by the neglect of higher-order harmonics in the analytical formulation. These higher-order harmonics, which appear as distinguishable peaks at certain values in the frequency response curves, are possible to calculate considering not the linearized frequency of the oscillator but its actual
Brandão, P. A.; Cavalcanti, S. B.
2017-10-01
Propagation of wide optical beams in transverse periodic lattices have been reported to induce power oscillations between Fourier modes related by the Bragg resonance condition, resulting from the coupling between the beam and the periodic structure. These oscillations have been referred to as Rabi optical oscillations due to the analogy with matter Rabi oscillations. In this work, we investigate the behavior of Bragg-induced Rabi-type oscillations of a multimode Gaussian beam in the presence of optical nonlinearity. We find a combination of oscillation and spectrum broadening under both self-focusing and self-defocusing nonlinearities, in the sense that the oscillations are maintained while the spectrum is broadened and therefore partially transferred to the twin frequency. For intense self-focusing nonlinearities a complete leak of the initial mode profile to other modes is rapidly attained so that no oscillation is observed. In contrast, for intense self-defocusing nonlinearities the redistribution rate is so dramatic that oscillations cease and power only fades away.
Three people can synchronize as coupled oscillators during sports activities.
Directory of Open Access Journals (Sweden)
Keiko Yokoyama
2011-10-01
Full Text Available We experimentally investigated the synchronized patterns of three people during sports activities and found that the activity corresponded to spatiotemporal patterns in rings of coupled biological oscillators derived from symmetric Hopf bifurcation theory, which is based on group theory. This theory can provide catalogs of possible generic spatiotemporal patterns irrespective of their internal models. Instead, they are simply based on the geometrical symmetries of the systems. We predicted the synchronization patterns of rings of three coupled oscillators as trajectories on the phase plane. The interactions among three people during a 3 vs. 1 ball possession task were plotted on the phase plane. We then demonstrated that two patterns conformed to two of the three patterns predicted by the theory. One of these patterns was a rotation pattern (R in which phase differences between adjacent oscillators were almost 2π/3. The other was a partial anti-phase pattern (PA in which the two oscillators were anti-phase and the third oscillator frequency was dead. These results suggested that symmetric Hopf bifurcation theory could be used to understand synchronization phenomena among three people who communicate via perceptual information, not just physically connected systems such as slime molds, chemical reactions, and animal gaits. In addition, the skill level in human synchronization may play the role of the bifurcation parameter.
Design of triply-resonant microphotonic parametric oscillators based on Kerr nonlinearity.
Zeng, Xiaoge; Popović, Miloš A
2014-06-30
We propose optimal designs for triply-resonant optical parametric oscillators (OPOs) based on degenerate four-wave mixing (FWM) in microcavities. We show that optimal designs in general call for different external coupling to pump and signal/idler resonances. We provide a number of normalized performance metrics including threshold pump power and maximum achievable conversion efficiency for OPOs with and without two-photon (TPA) and free-carrier absorption (FCA). We find that the maximum achievable conversion efficiency is bound to an upper limit by nonlinear and free-carrier losses independent of pump power, while linear losses only increase the pump power required to achieve a certain conversion efficiency. The results of this work suggest unique advantages in on-chip implementations that allow explicit engineering of resonances, mode field overlaps, dispersion, and wavelength-and mode-selective coupling. We provide universal design curves that yield optimum designs, and give example designs of microring-resonator-based OPOs in silicon at the wavelengths 1.55 μm (with TPA) and 2.3 μm (no TPA) as well as in silicon nitride (Si(3)N(4)) at 1.55 μm. For typical microcavity quality factor of 10(6), we show that the oscillation threshold in excitation bus can be well into the sub-mW regime for silicon microrings and a few mW for silicon nitride microrings. The conversion efficiency can be a few percent when pumped at 10 times of the threshold. Next, based on our results, we suggest a family of synthetic "photonic molecule"-like, coupled-cavity systems to implement optimum FWM, where structure design for control of resonant wavelengths can be separated from that of optimizing nonlinear conversion efficiency, and where furthermore pump, signal, and idler coupling to bus waveguides can be controlled independently, using interferometric cavity supermode coupling as an example. Finally, consideration of these complex geometries calls for a generalization of the nonlinear
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FUZun-Tao; LIUShi-Da; LIUShi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. Itis shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wavesolutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
Novel Localized Excitations of Nonlinear Coupled Scalar Fields
Institute of Scientific and Technical Information of China (English)
ZHU Ren-Gui; LI Jin-Hua; WANG An-Min; WU Huang-Jiao
2008-01-01
Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ4 model are presented. Simultaneously, inspired by the new solutions of the famous φ4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scalar field (NCSF) system are obtained.
Nonlinear Super Integrable Couplings of Super Classical-Boussinesq Hierarchy
Directory of Open Access Journals (Sweden)
Xiuzhi Xing
2014-01-01
Full Text Available Nonlinear integrable couplings of super classical-Boussinesq hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then, its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.
Nonlinear interaction of meta-atoms through optical coupling
Energy Technology Data Exchange (ETDEWEB)
Slobozhanyuk, A. P.; Kapitanova, P. V.; Filonov, D. S.; Belov, P. A. [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Powell, D. A. [Nonlinear Physics Centre and Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), Australian National University, Canberra, ACT 0200 (Australia); Shadrivov, I. V.; Kivshar, Yu. S. [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Nonlinear Physics Centre and Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), Australian National University, Canberra, ACT 0200 (Australia); Lapine, M., E-mail: mlapine@physics.usyd.edu.au [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, New South Wales 2006 (Australia); McPhedran, R. C. [Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, New South Wales 2006 (Australia)
2014-01-06
We propose and experimentally demonstrate a multi-frequency nonlinear coupling mechanism between split-ring resonators. We engineer the coupling between two microwave resonators through optical interaction, whilst suppressing the direct electromagnetic coupling. This allows for a power-dependent interaction between the otherwise independent resonators, opening interesting opportunities to address applications in signal processing, filtering, directional coupling, and electromagnetic compatibility.
Collective cell movement promotes synchronization of coupled genetic oscillators.
Uriu, Koichiro; Morelli, Luis G
2014-07-15
Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.
Phase Structure of the Non-Linear σ-MODEL with Oscillator Representation Method
Mishchenko, Yuriy; Ji, Chueng-R.
2004-03-01
Non-Linear σ-model plays an important role in many areas of theoretical physics. Been initially uintended as a simple model for chiral symmetry breaking, this model exhibits such nontrivial effects as spontaneous symmetry breaking, asymptotic freedom and sometimes is considered as an effective field theory for QCD. Besides, non-linear σ-model can be related to the strong-coupling limit of O(N) ϕ4-theory, continuous limit of N-dim. system of quantum spins, fermion gas and many others and takes important place in undertanding of how symmetries are realized in quantum field theories. Because of this variety of connections, theoretical study of the critical properties of σ-model is interesting and important. Oscillator representation method is a theoretical tool for studying the phase structure of simple QFT models. It is formulated in the framework of the canonical quantization and is based on the view of the unitary non-equivalent representations as possible phases of a QFT model. Successfull application of the ORM to ϕ4 and ϕ6 theories in 1+1 and 2+1 dimensions motivates its study in more complicated models such as non-linear σ-model. In our talk we introduce ORM, establish its connections with variational approach in QFT. We then present results of ORM in non-linear σ-model and try to interprete them from the variational point of view. Finally, we point out possible directions for further research in this area.
Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect
Institute of Scientific and Technical Information of China (English)
LI Xiao-Wen; ZHENG Zhi-Gang
2007-01-01
Phase synchronization of two linearly coupled Rossler oscillators with parameter misfits is explored.It is found that depending on parameter mismatches,the synchronization of phases exhibits different manners.The synchronization regime can be divided into three regimes.For small mismatches,the amplitude-insensitive regime gives the phase-dominant synchronization; When the parameter misfit increases,the amplitudes and phases of oscillators are correlated,and the amplitudes will dominate the synchronous dynamics for very large mismatches.The lag time among phases exhibits a power law when phase synchronization is achieved.
Average dynamics of a finite set of coupled phase oscillators
Energy Technology Data Exchange (ETDEWEB)
Dima, Germán C., E-mail: gdima@df.uba.ar; Mindlin, Gabriel B. [Laboratorio de Sistemas Dinámicos, IFIBA y Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, Buenos Aires (Argentina)
2014-06-15
We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.
Time Delay Effect in a Living Coupled Oscillator System with the Plasmodium of Physarum polycephalum
Takamatsu, Atsuko; Fujii, Teruo; Endo, Isao
2000-08-01
A living coupled oscillator system was constructed by a cell patterning method with a plasmodial slime mold, in which parameters such as coupling strength and distance between the oscillators can be systematically controlled. Rich oscillation phenomena between the two-coupled oscillators, namely, desynchronizing and antiphase/in-phase synchronization were observed according to these parameters. Both experimental and theoretical approaches showed that these phenomena are closely related to the time delay effect in interactions between the oscillators.
A Closed Form Solution for Nonlinear Oscillators Frequencies Using Amplitude-Frequency Formulation
Directory of Open Access Journals (Sweden)
A. Barari
2012-01-01
Full Text Available Many nonlinear systems in industry including oscillators can be simulated as a mass-spring system. In reality, all kinds of oscillators are nonlinear due to the nonlinear nature of springs. Due to this nonlinearity, most of the studies on oscillation systems are numerically carried out while an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude-Frequency Formulation (AFF approach is applied to analyze some periodic problems arising in classical dynamics. Results are compared with another approximate analytical technique called Energy Balance Method developed by the authors (EBM and also numerical solutions. Close agreement of the obtained results reveal the accuracy of the employed method for several practical problems in engineering.
Synchronization of time-delay coupled pulse oscillators
Energy Technology Data Exchange (ETDEWEB)
Klinshov, V.V., E-mail: vklin@mail.r [Institute of Applied Physics, Russian Academy of Sciences, 46 Ulyanov Str., 603950 Nizhny Novgorod (Russian Federation); Nekorkin, V.I. [Institute of Applied Physics, Russian Academy of Sciences, 46 Ulyanov Str., 603950 Nizhny Novgorod (Russian Federation)
2011-01-15
Research highlights: Oscillators can be synchronized via coupling with arbitrary large delay. Imposing of coupling delay may either result in delay-induced synchronization or delay-induced desynchronization. In-phase and antiphase synchronization zones alternate in parameter space. Two types of transitions between the in-phase and antiphase synchronization, i.e. phase-flip bifurcation and soft switching. - Abstract: We present a detailed study of the dynamics of pulse oscillators with time-delayed coupling. We get the return maps, obtain strict solutions and analyze their stability. For the case of two oscillators, a periodical structure of synchronization regions is found in parameter space, and the regions corresponding to in-phase and antiphase regimes alternate with growth of time delay. Two types of switching between in-phase and antiphase regimes are studied. We also show that for different parameters coupling delay may have synchronizing or desynchronizing effect. Another novel result is that phase locked regimes exist for arbitrary large values. The specificity of system dynamics with large delay is studied.
Coupled bloch-phonon oscillations in semiconductor superlattices
Dekorsy; Bartels; Kurz; Kohler; Hey; Ploog
2000-07-31
We investigate coherent Bloch oscillations in GaAs/AlxGa1-xAs superlattices with electronic miniband widths larger than the optical phonon energy. In these superlattices the Bloch frequency can be tuned into resonance with the optical phonon. Close to resonance a direct coupling of Bloch oscillations to LO phonons is observed which gives rise to the coherent excitation of LO phonons. The density necessary for driving coherent LO phonons via Bloch oscillations is about 2 orders of magnitude smaller than the density necessary to drive coherent LO phonons in bulk GaAs. The experimental observations are confirmed by the theoretical description of this phenomenon [A.W. Ghosh et al., Phys. Rev. Lett. 85, 1084 (2000)].
Desynchronization of systems of coupled Hindmarsh-Rose oscillators
Gjurchinovski, Aleksandar; Vasilkoski, Zlatko
2011-01-01
It is widely assumed that neural activity related to synchronous rhythms of large portions of neurons in specific locations of the brain is responsible for the pathology manifested in patients' uncontrolled tremor and other similar diseases. To model such systems Hindmarsh-Rose (HR) oscillators are considered as appropriate as they mimic the qualitative behaviour of neuronal firing. Here we consider a large number of identical HR-oscillators interacting through the mean field created by the corresponding components of all oscillators. Introducing additional coupling by feedback of Pyragas type, proportional to the difference between the current value of the mean-field and its value some time in the past, Rosenblum and Pikovsky (Phys. Rev. E 70, 041904, 2004) demonstrated that the desirable desynchronization could be achieved with appropriate set of parameters for the system. Following our experience with stabilization of unstable steady states in dynamical systems, we show that by introducing a variable delay...
Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Lennart; García-Morales, Vladimir [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany); Institute for Advanced Study, Technische Universität München, Lichtenbergstr. 2a, D-85748 Garching (Germany); Schönleber, Konrad; Krischer, Katharina, E-mail: krischer@tum.de [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany)
2014-03-15
We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.
Influence of nonlinearities on the power output of the Self-Oscillating Fluidic Heat Engine (SOFHE)
Tessier-Poirier, A.; Monin, T.; Léveillé, E.; Formosa, F.; Monfray, S.; Fréchette, L. G.
2016-11-01
In this paper, it is shown that two non-linearities drive the oscillations amplitude and the potential power density of the Self-Oscillating Fluidic Heat Engine (SOFHE). This new type of engine converts thermal energy into mechanical energy by producing self-sustained oscillations of a liquid column from a continuous heat source to power wireless sensors from waste heat. The underlying theoretical modeling shows that the pressure and the temperature nonlinearities limit the final oscillations amplitude, hence its achievable power density.
Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators
Talukdar, Abdul Hafiz
2011-05-01
Exceptional behaviours of Memristor are illustrated in Memristor based second order (Wien oscillator) and third order (phase shift oscillator) oscillator systems in this Thesis. Conventional concepts about sustained oscillation have been argued by demonstrating the possibility of sustained oscillation with oscillating resistance and dynamic poles. Mathematical models are also proposed for analysis and simulations have been presented to support the surprising characteristics of the Memristor based oscillator systems. This thesis also describes a comparative study among the Wien family oscillators with one Memristor. In case of phase shift oscillator, one Memristor and three Memristors systems are illustrated and compared to generalize the nonlinear dynamics observed for both 2nd order and 3rd order system. Detail explanations are provided with analytical models to simplify the unconventional properties of Memristor based oscillatory systems.
Coupled Optoelectronic Oscillators:. Application to Low-Jitter Pulse Generation
Yu, N.; Tu, M.; Maleki, L.
2002-04-01
Actively mode-locked Erbium-doped fiber lasers (EDFL) have been studied for generating stable ultra-fast pulses ( 5 GHz) [1,2]. These devices can be compact and environmentally stable, quite suitable for fiber-based high-data-rate communications and optical ultra-fast analog-to-digital conversions (ADC) [3]. The pulse-to-pulse jitter of an EDFL-based pulse generator will be ultimately limited by the phase noise of the mode-locking microwave source (typically electronic frequency synthesizers). On the other hand, opto-electronic oscillators (OEO) using fibers have been demonstrated to generate ultra-low phase noise microwaves at 10 GHz and higher [4]. The overall phase noise of an OEO can be much lower than commercially available synthesizers at the offset-frequency range above 100 Hz. Clearly, ultra-low jitter pulses can be generated by taking advantage of the low phase noise of OEOs. In this paper, we report the progress in developing a new low-jitter pulse generator by combing the two technologies. In our approach, the optical oscillator (mode-locked EDFL) and the microwave oscillator (OEO) are coupled through a common Mach-Zehnder (MZ) modulator, thus named coupled opto-electronic oscillator (COEO) [5]. Based on the results of previous OEO study, we can expect a 10 GHz pulse train with jitters less than 10 fs.
The numerical modelling of a driven nonlinear oscillator
Energy Technology Data Exchange (ETDEWEB)
Shew, C.
1995-11-01
The torsional oscillator in the Earth Sciences Division was developed at Lawrence Livermore National Laboratory and is the only one of its kind. It was developed to study the way rocks damp vibrations. Small rock samples are tested to determine the seismic properties of rocks, but unlike other traditional methods that propagate high frequency waves through small samples, this machine forces the sample to vibrate at low frequencies, which better models real-life properties of large masses. In this particular case, the rock sample is tested with a small crack in its middle. This forces the rock to twist against itself, causing a {open_quotes}stick-slip{close_quotes} friction, known as stiction. A numerical model that simulates the forced torsional osillations of the machine is currently being developed. The computer simulation implements the graphical language LabVIEW, and is looking at the nonlinear spring effects, the frictional forces, and the changes in amplitude and frequency of the forced vibration. Using LabVIEW allows for quick prototyping and greatly reduces the {open_quotes}time to product{close_quotes} factor. LabVIEW`s graphical environment allows scientists and engineers to use familiar terminology and icons (e.g. knobs, switches, graphs, etc.). Unlike other programming systems that use text-based languages, such as C and Basic, LabVIEW uses a graphical programming language to create programs in block diagram form.
Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses
Bressloff, P. C.
1999-08-01
We analyze the effects of synaptic depression or facilitation on the existence and stability of the splay or asynchronous state in a population of all-to-all, pulse-coupled neural oscillators. We use mean-field techniques to derive conditions for the local stability of the splay state and determine how stability depends on the degree of synaptic depression or facilitation. We also consider the effects of noise. Extensions of the mean-field results to finite networks are developed in terms of the nonlinear firing time map.
Surface second harmonic generation of chiral molecules using three-coupled-oscillator model
Institute of Scientific and Technical Information of China (English)
Wang Xiao-Ou; Li Chun-Fei; Li Jun-Qing
2006-01-01
Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic parameters on the second-order susceptibilities is simulated numerically and the difference between the efficiencies of s-polarized second-harmonic fields induced by the left- and the right-handed circularly-polarized fundamental beams is discussed. The theoretical basis for studying second-order nonlinear optical properties of the chiral molecular media with a tripod-like structure is provided in this paper.
Non-linear Oscillations of Compact Stars and Gravitational Waves
Passamonti, A
2006-01-01
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions. As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative or...
Variational collocation for systems of coupled anharmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2010-04-15
By means of a collocation approach based on little sinc functions (LSF), we obtain accurate eigenvalues and eigenfunctions of the stationary Schroedinger equation for systems of coupled oscillators. Adjustable parameters introduced by means of scaling and rotation of the coordinates improve the rate of convergence of the approach. A careful comparison with the results published earlier by other authors shows the advantages of the present approach.
Synchronization of Cross-Well Chaos in Coupled Duffing Oscillators
Vincent, U. E.; Njah, A. N.; Akinlade, O.; Solarin, A. R. T.
Numerical simulations have been used to investigate the synchronization behavior of a unidirectionally coupled pair of double-well duffing oscillators (DDOs). The DDOs were simulated in their structurally stable chaotic zone and their state variables were found to completely synchronized. The essential feature of the transition to the synchronous state is shown to correspond to a boundary crisis in which the cross-well chaotic attractor is destroyed.
Scaling Features of Multimode Motions in Coupled Chaotic Oscillators
DEFF Research Database (Denmark)
Pavlov, A.N.; Sosnovtseva, Olga; Mosekilde, Erik
2003-01-01
Two different methods (the WTMM- and DFA-approaches) are applied to investigate the scaling properties in the return-time sequences generated by a system of two coupled chaotic oscillators. Transitions from twomode asynchronous dynamics (torus or torus-Chaos) to different states of chaotic phase...... synchronization are found to significantly reduce the degree of multiscality. The influence of external noise on the possibility of distinguishing the various chaotic states is considered....
Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators
Uriu, Koichiro; Morelli, Luis G.
2014-01-01
Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somito...
Quantum coherent oscillations between two coupled bose-einstein condensates
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The theoretical investigation of quantum coherent atomic oscillations between two coupled Bose-Einstein condensates(BECs) is studied. We apply the inseparable wave function of time-space to describe two trapped BECs in a double-well magnetic trap. According to Thomas-Fermi approximation, dynamical equations of the interwell phase difference and population imbalance are obtained. Using numerical method, coherent atomic tunneling and macroscopic quantum self-trapping(MQST) effect are investigated.
Environmental coupling in ecosystems: From oscillation quenching to rhythmogenesis
Arumugam, Ramesh; Dutta, Partha Sharathi; Banerjee, Tanmoy
2016-08-01
How landscape fragmentation affects ecosystems diversity and stability is an important and complex question in ecology with no simple answer, as spatially separated habitats where species live are highly dynamic rather than just static. Taking into account the species dispersal among nearby connected habitats (or patches) through a common dynamic environment, we model the consumer-resource interactions with a ring type coupled network. By characterizing the dynamics of consumer-resource interactions in a coupled ecological system with three fundamental mechanisms such as the interaction within the patch, the interaction between the patches, and the interaction through a common dynamic environment, we report the occurrence of various collective behaviors. We show that the interplay between the dynamic environment and the dispersal among connected patches exhibits the mechanism of generation of oscillations, i.e., rhythmogenesis, as well as suppression of oscillations, i.e., amplitude death and oscillation death. Also, the transition from homogeneous steady state to inhomogeneous steady state occurs through a codimension-2 bifurcation. Emphasizing a network of a spatially extended system, the coupled model exposes the collective behavior of a synchrony-stability relationship with various synchronization occurrences such as in-phase and out-of-phase.
Cluster synchrony in systems of coupled phase oscillators with higher-order coupling.
Skardal, Per Sebastian; Ott, Edward; Restrepo, Juan G
2011-09-01
We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the dynamics in the limit of a large number of oscillators and use it to quantify the degree of cluster synchrony, cluster asymmetry, and switching. We use a variation of the recent dimensionality-reduction technique of Ott and Antonsen [Chaos 18, 037113 (2008)] and find an analytic description of the degree of cluster synchrony valid on a globally attracting manifold. Shaped by this manifold, there is an infinite family of steady-state distributions of oscillators, resulting in a high degree of multistability in the cluster asymmetry. We also show how through external forcing the degree of asymmetry can be controlled, and suggest that systems displaying cluster synchrony can be used to encode and store data.
Cluster Synchrony in Systems of Coupled Phase Oscillators with Higher-Order Coupling
Skardal, Per Sebastian; Restrepo, Juan G
2011-01-01
We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the dynamics in the limit of a large number of oscillators and use it to quantify the degree of cluster synchrony, cluster asymmetry, and switching. We use a variation of the recent dimensionality-reduction technique of Ott and Antonsen \\cite{OA1} and find an analytic description of the degree of cluster synchrony valid on a globally attracting manifold. Shaped by this manifold, there is an infinite family of steady-state distributions of oscillators, resulting in a high degree of multi-stability in the cluster asymmetry. We also show how through external forcing the degree of asymmetry can be controlled, and suggest that systems displaying cluster synchrony can be used to encode and store data.
Kim, Joo-Von; Mistral, Q.; Chappert, C.; Tiberkevich, V. S.; Slavin, A. N.
2007-01-01
The lineshape in an auto-oscillator with a large nonlinear frequency shift in the presence of thermal noise is calculated. Near the generation threshold, this lineshape becomes strongly non-Lorentzian, broadened, and asymmetric. A Lorentzian lineshape is recovered far below and far above threshold, which suggests that lineshape distortions provide a signature of the generation threshold. The theory developed adequately describes the observed behavior of a strongly nonlinear spin-torque nano-o...
Dynamic nonlinear thermal optical effects in coupled ring resonators
Directory of Open Access Journals (Sweden)
Chenguang Huang
2012-09-01
Full Text Available We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple “shark fins” and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.
Smirnov, D A; Velazquez, J L P; Wennberg, R A; Bezruchko, B P
2005-01-01
We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and non-vanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.
Oscillation of solutions to neutral nonlinear impulsive hyperbolic equations with several delays
Directory of Open Access Journals (Sweden)
Jichen Yang
2013-01-01
Full Text Available In this article, we study oscillatory properties of solutions to neutral nonlinear impulsive hyperbolic partial differential equations with several delays. We establish sufficient conditions for oscillation of all solutions.
Systematic treatment of non-linear effects in Baryon Acoustic Oscillations
Ivanov, Mikhail M
2016-01-01
In this contribution we will discuss the non-linear effects in the baryon acoustic oscillations and present a systematic and controllable way to account for them within time-sliced perturbation theory.
Nonlinear dynamics in sudden cardiac death syndrome: heartrate oscillations and bifurcations.
Goldberger, A L; Rigney, D R; Mietus, J; Antman, E M; Greenwald, S
1988-12-01
Patients at high risk of sudden cardiac death show evidence of nonlinear heartrate dynamics, including abrupt spectral changes (bifurcations) and sustained low frequency (.01-.04 Hz) oscillations in heartrate.
Oscillation Criteria for Fourth-Order Nonlinear Dynamic Equations on Time Scales
Directory of Open Access Journals (Sweden)
Xin Wu
2013-01-01
Full Text Available We establish some new oscillation criteria for nonlinear dynamic equation of the form on an arbitrary time scale with , where are positive rd-continuous functions. An example illustrating the importance of our result is included.
Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales
Institute of Scientific and Technical Information of China (English)
YANG Jia-shan
2013-01-01
The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article.By using the generalized Riccati technique,integral averaging technique and the time scales theory,some new sufficient conditions for oscillation of the equation are proposed.These results generalize and extend many known results for second order dynamic equations.Some examples are given to illustrate the main results of this article.
Directory of Open Access Journals (Sweden)
Ruilan Tian
2016-06-01
Full Text Available The coupled system of smooth and discontinuous absorber and beam bridge under moving loads is constructed in order to detect the effectiveness of smooth and discontinuous absorber. It is worth pointing out that the coupled system contains an irrational restoring force which is a barrier for conventional nonlinear techniques. Hence, the harmonic balance method and Fourier expansion are used to obtain the approximate solutions of the system. The first and the second kind of generalized complete elliptic integrals are introduced. Furthermore, using power flow approach, the performance of smooth and discontinuous absorber in vibration reduction is estimated through the input energy, the dissipated energy, and the damping efficiency. It is interesting that only depending on the value of the smoothness parameter, the efficiency parameter of vibration reduction is optimized. Therefore, smooth and discontinuous absorber can adapt itself to effectively reducing the amplitude of the vibration of the beam bridge, which provides an insight to the understanding of the applications of smooth and discontinuous oscillator in engineering and power flow characteristics in nonlinear system.
Dynamical Recurrence and the Quantum Control of Coupled Oscillators
Genoni, Marco G.; Serafini, Alessio; Kim, M. S.; Burgarth, Daniel
2012-04-01
Controllability—the possibility of performing any target dynamics by applying a set of available operations—is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, such as spin systems, precise criteria to establish controllability, such as the so-called rank criterion, are well known. However, most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems—encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nanomechanical oscillators—governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend the rank criterion to infinite-dimensional quadratic systems. Further, we present a useful application of our finding, by proving indirect controllability of a chain of harmonic oscillators.
Inertial Force Coupling to Nonlinear Aeroelasticity of Flexible Wing Aircraft
Nguyen, Nhan T.; Ting, Eric
2016-01-01
This paper investigates the inertial force effect on nonlinear aeroelasticity of flexible wing aircraft. The geometric are nonlinearity due to rotational and tension stiffening. The effect of large bending deflection will also be investigated. Flutter analysis will be conducted for a truss-braced wing aircraft concept with tension stiffening and inertial force coupling.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Synchrony and chaos in coupled oscillators and neural networks
Raghavachari, Sridhar
1999-09-01
This dissertation studies the dynamics of ensembles of coupled, dynamical elements with discrete and continuous time dynamics. Specific problems include the appearance of synchronous behavior in an ensemble of dynamical elements. We show that the dynamics of coupled map lattices with connectivity that scales with inter-site distance exhibit a transition from spatial disorder to spatially uniform temporal chaos as the scaling varies. We investigate the eigenvalue spectrum of the stochastic matrix characterizing fluctuations from the uniform state numerically and show that the spectrum is bounded, real and the largest eigenvalue (corresponding to the uniform solution) has a gap separating it from the remaining N-1 eigenvalues which correspond to non-uniform solutions. The width of this gap depends on the scaling exponent. We relate the stability of the uniform state to this gap and show that the state is globally stable even in a strongly chaotic region of the uncoupled map. Bursting is a prototypical pattern of voltage oscillations of membrane potentials of biological cells, where the membrane potential alternates between fast oscillations and a slow drift. These complex oscillations arise as a result of interactions between the kinetics of fast and slow ion channels. While bursting in isolated cells Is, well understood, the study of populations of interacting bursters is less developed. We study a one- dimensional continuum model of bursting and show that a spatial wave of bursting separating active and quiescent cells extinguishes synchronous bursting when the coupling is weak. This result places bounds on the measured values of coupling strength between secretory cells in the pancreas. The interactions of cellular and synaptic mechanisms acting on several timescales control rhythmic behavior in animals, such as locomotion, digestion and respiration. We explore a simple rhythmic circuit model with two cells reciprocally inhibiting each other with fast and slow
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Thermally induced nonlinear mode coupling in high power fiber amplifiers
DEFF Research Database (Denmark)
Johansen, Mette Marie; Hansen, Kristian Rymann; Alkeskjold, Thomas T.;
2013-01-01
Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W.......Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W....
Amplitude Expansions for Instabilities in Populations of Globally-Coupled Oscillators
Crawford, J D
1994-01-01
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to obtain the amplitude equations for steady-state and Hopf bifurcation from the equilibrium state with a uniform phase distribution. When the population is described by a native frequency distribution that is reflection-symmetric about zero, the problem has circular symmetry. In the limit of zero extrinsic noise, although the critical eigenvalues are embedded in the continuous spectrum, the nonlinear coefficients in the amplitude equation remain finite in contrast to the singular behavior found in similar instabilities described by the Vlasov-Poisson equation. For a bimodal reflection-symmetric distribution, both types of bifurcation are possible and they coincide at a codimension-two Takens Bogdanov point. The steady-state bifurcation may be supercritical or subcritical and prod...
Coupled Oscillations and Circadian Rhythms in Molecular Replication Networks.
Wagner, Nathaniel; Alasibi, Samaa; Peacock-Lopez, Enrique; Ashkenasy, Gonen
2015-01-02
Living organisms often display rhythmic and oscillatory behavior. We investigate here a challenge in contemporary Systems Chemistry, that is, to construct "bottom-up" molecular networks that display such complex behavior. We first describe oscillations during self-replication by applying kinetic parameters relevant to peptide replication in an open environment. Small networks of coupled oscillators are then constructed in silico, producing various functions such as logic gates, integrators, counters, triggers, and detectors. These networks are finally utilized to simulate the connectivity and network topology of the Kai proteins circadian clocks from the S. elongatus cyanobacteria, thus producing rhythms whose constant frequency is independent of the input intake rate and robust toward concentration fluctuations. We suggest that this study helps further reveal the underlying principles of biological clocks and may provide clues into their emergence in early molecular evolution.
Multistable states in a system of coupled phase oscillators with inertia
Yuan, Di; Lin, Fang; Wang, Limei; Liu, Danyang; Yang, Junzhong; Xiao, Yi
2017-01-01
We investigate the generalized Kuramoto model of globally coupled oscillators with inertia, in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians. We consider the correlation between the coupling strengths of oscillators and the distributions of natural frequencies. Two different types of correlations are studied. It is shown that the model supports multistable synchronized states such as different types of travelling wave states, π state and another type of nonstationary state: an oscillating π state. The phase distribution oscillates in a confined region and the phase difference between conformists and contrarians oscillates around π periodically in the oscillating π state. The different types of travelling wave state may be characterized by the speed of travelling wave and the effective frequencies of oscillators. Finally, the bifurcation diagrams of the model in the parameter space are presented. PMID:28176829
Multistable states in a system of coupled phase oscillators with inertia
Yuan, Di; Lin, Fang; Wang, Limei; Liu, Danyang; Yang, Junzhong; Xiao, Yi
2017-02-01
We investigate the generalized Kuramoto model of globally coupled oscillators with inertia, in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians. We consider the correlation between the coupling strengths of oscillators and the distributions of natural frequencies. Two different types of correlations are studied. It is shown that the model supports multistable synchronized states such as different types of travelling wave states, π state and another type of nonstationary state: an oscillating π state. The phase distribution oscillates in a confined region and the phase difference between conformists and contrarians oscillates around π periodically in the oscillating π state. The different types of travelling wave state may be characterized by the speed of travelling wave and the effective frequencies of oscillators. Finally, the bifurcation diagrams of the model in the parameter space are presented.
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators
Villanueva, L. G.; Kenig, E.; Karabalin, R. B.; Matheny, M. H.; Lifshitz, R; Cross, M. C.; Roukes, M. L.
2013-01-01
Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic, regime. Contrary ...
OSCILLATION FOR NONLINEAR SECOND-ORDER DYNAMIC EQUATIONS ON TIME SCALES
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references.
Collective dynamics of time-delay-coupled phase oscillators in a frustrated geometry
Thakur, Bhumika; Sharma, Devendra; Sen, Abhijit; Johnston, George L.
2017-01-01
We study the effect of time delay on the dynamics of a system of repulsively coupled nonlinear oscillators that are configured as a geometrically frustrated network. In the absence of time delay, frustrated systems are known to possess a high degree of multistability among a large number of coexisting collective states except for the fully synchronized state that is normally obtained for attractively coupled systems. Time delay in the coupling is found to remove this constraint and to lead to such a synchronized ground state over a range of parameter values. A quantitative study of the variation of frustration in a system with the amount of time delay has been made and a universal scaling behavior is found. The variation in frustration as a function of the product of time delay and the collective frequency of the system is seen to lie on a characteristic curve that is common for all natural frequencies of the identical oscillators and coupling strengths. Thus time delay can be used as a tuning parameter to control the amount of frustration in a system and thereby influence its collective behavior. Our results can be of potential use in a host of practical applications in physical and biological systems in which frustrated configurations and time delay are known to coexist.
Directory of Open Access Journals (Sweden)
J. Kengne
2014-01-01
Full Text Available The analog circuit implementation and the experimental bifurcation analysis of coupled anisochronous self-driven systems modelled by two mutually coupled van der Pol-Duffing oscillators are considered. The coupling between the two oscillators is set in a symmetrical way that linearly depends on the difference of their velocities (i.e., dissipative coupling. Interest in this problem does not decrease because of its significance and possible application in the analysis of different, biological, chemical, and electrical systems (e.g., coupled van der Pol-Duffing electrical system. Regions of quenching behavior as well as conditions for the appearance of Hopf bifurcations are analytically defined. The scenarios/routes to chaos are studied with particular emphasis on the effects of cubic nonlinearity (that is responsible for anisochronism of small oscillations. When monitoring the control parameter, various striking dynamic behaviors are found including period-doubling, symmetry-breaking, multistability, and chaos. An appropriate electronic circuit describing the coupled oscillator is designed and used for the investigations. Experimental results that are consistent with results from theoretical analyses are presented and convincingly show quenching phenomenon as well as bifurcation and chaos.
Directory of Open Access Journals (Sweden)
Jianping Cai
2003-01-01
Full Text Available A method of approximate potential is presented for the study of certain kinds of strongly nonlinear oscillators. This method is to express the potential for an oscillatory system by a polynomial of degree four such that the leading approximation may be derived in terms of elliptic functions. The advantage of present method is that it is valid for relatively large oscillations. As an application, the elapsed time of periodic motion of a strongly nonlinear oscillator with slowly varying parameters is studied in detail. Comparisons are made with other methods to assess the accuracy of the present method.
Directory of Open Access Journals (Sweden)
H. M. Abdelhafez
2016-03-01
Full Text Available The modified differential transform method (MDTM, Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obtained using the fourth-order Runge-Kutta numerical solution method. A comparison of the result by the numerical Runge-Kutta fourth-order accuracy method is compared with the result by the MDTM and plotted in a long time domain.
Directory of Open Access Journals (Sweden)
Šutová Zuzana
2014-12-01
Full Text Available The article deals with the active control of oscillation patterns in nonlinear dynamical systems and its possible use. The purpose of the research is to prove the possibility of oscillations frequency control based on a change of value of singular perturbation parameter placed into a mathematical model of a nonlinear dynamical system at the highest derivative. This parameter is in singular perturbation theory often called small parameter, as ε → 0+. Oscillation frequency change caused by a different value of the parameter is verified by modelling the system in MATLAB.
Coupled slow and fast surface dynamics in an electrocatalytic oscillator: Model and simulations
Energy Technology Data Exchange (ETDEWEB)
Nascimento, Melke A. [Institute of Chemistry of São Carlos, University of São Paulo, PO Box 780, 13560-970, São Carlos, SP (Brazil); Fritz Haber Institute of the Max Planck Society, Department of Physical Chemistry, Faradayweg 4-6, D-14195 Berlin (Germany); Nagao, Raphael [Institute of Chemistry of São Carlos, University of São Paulo, PO Box 780, 13560-970, São Carlos, SP (Brazil); Eiswirth, Markus [Fritz Haber Institute of the Max Planck Society, Department of Physical Chemistry, Faradayweg 4-6, D-14195 Berlin (Germany); Ertl Center for Electrochemistry and Catalysis, GIST, Cheomdan-gwagiro 261, Buk-gu, Gwangju 500-712 (Korea, Republic of); Varela, Hamilton, E-mail: varela@iqsc.usp.br [Institute of Chemistry of São Carlos, University of São Paulo, PO Box 780, 13560-970, São Carlos, SP (Brazil); Fritz Haber Institute of the Max Planck Society, Department of Physical Chemistry, Faradayweg 4-6, D-14195 Berlin (Germany); Ertl Center for Electrochemistry and Catalysis, GIST, Cheomdan-gwagiro 261, Buk-gu, Gwangju 500-712 (Korea, Republic of)
2014-12-21
The co-existence of disparate time scales is pervasive in many systems. In particular for surface reactions, it has been shown that the long-term evolution of the core oscillator is decisively influenced by slow surface changes, such as progressing deactivation. Here we present an in-depth numerical investigation of the coupled slow and fast surface dynamics in an electrocatalytic oscillator. The model consists of four nonlinear coupled ordinary differential equations, investigated over a wide parameter range. Besides the conventional bifurcation analysis, the system was studied by means of high-resolution period and Lyapunov diagrams. It was observed that the bifurcation diagram changes considerably as the irreversible surface poisoning evolves, and the oscillatory region shrinks. The qualitative dynamics changes accordingly and the chaotic oscillations are dramatically suppressed. Nevertheless, periodic cascades are preserved in a confined region of the resistance vs. voltage diagram. Numerical results are compared to experiments published earlier and the latter reinterpreted. Finally, the comprehensive description of the time-evolution in the period and Lyapunov diagrams suggests further experimental studies correlating the evolution of the system's dynamics with changes of the catalyst structure.
Lengyel, Iván M; Oates, Andrew C; Morelli, Luis G
2015-01-01
We study the effects of multiple binding sites in the promoter of a genetic oscillator. We evaluate the regulatory function of a promoter with multiple binding sites in the absence of cooperative binding, and consider different hypotheses for how the number of bound repressors affects transcription rate. Effective Hill exponents of the resulting regulatory functions reveal an increase in the nonlinearity of the feedback with the number of binding sites. We identify optimal configurations that maximize the nonlinearity of the feedback. We use a generic model of a biochemical oscillator to show that this increased nonlinearity is reflected in enhanced oscillations, with larger amplitudes over wider oscillatory ranges. Although the study is motivated by genetic oscillations in the zebrafish segmentation clock, our findings may reveal a general principle for gene regulation.
Nonlinear Resistor with Polynomial AV Characteristics and Its Application in Chaotic Oscillator
Directory of Open Access Journals (Sweden)
V. Pospisil
2004-06-01
Full Text Available This paper shows the realization of two terminal devices with anarbitrary polynomial nonlinearity up to the fifth order. The proposeddesign procedure is completely systematic using minimum of components.The very heart of our conception is four-channel four-quadrant analogmultiplier MLT04. The implementation of synthesized nonlinear resistoras a general nonlinearity in chaotic oscillator is also presented andexperimentally verified.
Passamonti, A; Gualtieri, L; Nagar, A; Sopuerta, C F
2006-01-01
We investigate the non-linear coupling between radial and non-radial oscillations of static spherically symmetric neutron stars as a possible mechanism for the generation of gravitational waves that may lead to observable signatures. In this paper we concentrate on the axial sector of the non-radial perturbations. By using a multi-parameter perturbative framework we introduce a complete description of the non-linear coupling between radial and axial non-radial oscillations; we study the gauge invariant character of the associated perturbative variables and develop a computational scheme to evolve the non-linear coupling perturbations in the time domain. We present results of simulations corresponding to different physical situations and discuss the dynamical behaviour of this non-linear coupling. Of particular interest is the occurrence of signal amplifications in the form of resonance phenomena when a frequency associated with the radial pulsations is close to a frequency associated with one of the axial w-m...
On the Approximate Analytical Solution to Non-Linear Oscillation Systems
Directory of Open Access Journals (Sweden)
Mahmoud Bayat
2013-01-01
Full Text Available This study describes an analytical method to study two well-known systems of nonlinear oscillators. One of these systems deals with the strongly nonlinear vibrations of an elastically restrained beam with a lumped mass. The other is a Duffing equation with constant coefficients. A new implementation of the Variational Approach (VA is presented to obtain highly accurate analytical solutions to free vibration of conservative oscillators with inertia and static type cubic nonlinearities. In the end, numerical comparisons are conducted between the results obtained by the Variational Approach and numerical solution using Runge-Kutta's [RK] algorithm to illustrate the effectiveness and convenience of the proposed methods.
GENERAL: Bistability in Coupled Oscillators Exhibiting Synchronized Dynamics
Olusola, O. I.; Vincent, U. E.; Njah, A. N.; Olowofela, J. A.
2010-05-01
We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators (DDOs). Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues — a signature of mode locking phenomenon are found.
Quasi-BLOCH oscillations in curved coupled optical waveguides.
Joushaghani, Arash; Iyer, Rajiv; Poon, Joyce K S; Aitchison, J Stewart; de Sterke, C Martijn; Wan, Jun; Dignam, Marc M
2009-10-01
We report the observation of quasi-Bloch oscillations, a recently proposed, new type of dynamic localization in the spatial evolution of light in a curved coupled optical waveguide array. By spatially resolving the optical intensity at various propagation distances, we show the delocalization and final relocalization of the beam in the waveguide array. Through comparisons with other structures, we show that this dynamic localization is robust beyond the nearest-neighbor tight-binding approximation and exhibits a wavelength dependence different from conventional dynamic localization.
Coupled-oscillator based active-array antennas
Pogorzelski, Ronald J
2012-01-01
Describing an innovative approach to phased-array control in antenna design This book explores in detail phased-array antennas that use coupled-oscillator arrays, an arrangement featuring a remarkably simple beam steering control system and a major reduction in complexity compared with traditional methods of phased-array control. It brings together in one convenient, self-contained volume the many salient research results obtained over the past ten to fifteen years in laboratories around the world, including the California Institute of Technology's Jet Propulsion Laboratory.
Intermittent lag synchronization in a driven system of coupled oscillators
Indian Academy of Sciences (India)
Alexander N Pisarchik; Rider Jaimes-Reátegui
2005-04-01
We study intermittent lag synchronization in a system of two identical mutually coupled Duffing oscillators with parametric modulation in one of them. This phenomenon in a periodically forced system can be seen as intermittent jump from phase to lag synchronization, during which the chaotic trajectory visits a periodic orbit closely. We demonstrate different types of intermittent lag synchronizations, that occur in the vicinity of saddle-node bifurcations where the system changes its dynamical state, and characterize the simplest case of period-one intermittent lag synchronization.
Signatures of nonlinearity in single cell noise-induced oscillations
Thomas, P.; Straube, A.V.; Timmer, J.; Fleck, C.; Grima, R.
2013-01-01
A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power
Signatures of nonlinearity in single cell noise-induced oscillations
Thomas, P.; Straube, A.V.; Timmer, J.; Fleck, C.; Grima, R.
2013-01-01
A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power spec
Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others.
Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Du Wei-Shih
2010-01-01
Full Text Available We establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions.
Remote synchronization of amplitudes across an experimental ring of non-linear oscillators
Minati, Ludovico
2015-12-01
In this paper, the emergence of remote synchronization in a ring of 32 unidirectionally coupled non-linear oscillators is reported. Each oscillator consists of 3 negative voltage gain stages connected in a loop to which two integrators are superimposed and receives input from its preceding neighbour via a "mixing" stage whose gains form the main system control parameters. Collective behaviour of the network is investigated numerically and experimentally, based on a custom-designed circuit board featuring 32 field-programmable analog arrays. A diverse set of synchronization patterns is observed depending on the control parameters. While phase synchronization ensues globally, albeit imperfectly, for certain control parameter values, amplitudes delineate subsets of non-adjacent but preferentially synchronized nodes; this cannot be trivially explained by synchronization paths along sequences of structurally connected nodes and is therefore interpreted as representing a form of remote synchronization. Complex topology of functional synchronization thus emerges from underlying elementary structural connectivity. In addition to the Kuramoto order parameter and cross-correlation coefficient, other synchronization measures are considered, and preliminary findings suggest that generalized synchronization may identify functional relationships across nodes otherwise not visible. Further work elucidating the mechanism underlying this observation of remote synchronization is necessary, to support which experimental data and board design materials have been made freely downloadable.
Das, Saptarshi
2014-01-01
In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators which are coupled by time delays and gains. In this paper, we suitably modify the three state equations corresponding to the nonlinear cross-product of states, time delay coupling of the two oscillators and low-pass filtering, using the concept of fractional derivatives. Our results show that a wide variety of ECG like waveforms can be simulated from the proposed generalized models, characterizing heart conditions under different physiological conditions. Such generalization of the modelling of ECG waveforms may be useful to understand the physiological process behind ECG signal generation in normal and abnormal heart conditions. Along with the proposed FO models, an optimization based approach is also presented to estimate the VdP oscillator parameters for representing a realistic ...
Nonlinear feedback control of spatiotemporal chaos in coupled map lattices
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
1998-01-01
Full Text Available We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos. The method is illustrated by the coupled map lattices with five different connection forms. A key issue addressed is to find nonlinear feedback functions. Two large types of nonlinear feedback functions are introduced. The efficient and robustness of the method based on the flexibility of choices of nonlinear feedback functions are discussed. Various numerical results of nonlinear control are given. We have not found any difficulty for study both of control and synchronization using nonlinear feedback functional method. The method can also be extended to time continuous dynamical systems as well as to society problems.
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Duffing oscillator . As an example of the results, the predicted period of a simple pendulum swinging between −90° and +90° is found to be only 0.4% larger...Eq. (42). 4.5 The Duffing oscillator with zero linear term For an anharmonic oscillator having restoring force f(x) = αx3, define ω0 = A √ α. Using...Double Fourier harmonic balance method for nonlinear oscillators by means of Bessel series T.C. Lipscombe∗1 and C.E. Mungan†2 1Catholic University of
Kohira, Masahiro I.; Kitahata, Hiroyuki; Magome, Nobuyuki; Yoshikawa, Kenichi
2012-02-01
An oscillatory system called a plastic bottle oscillator is studied, in which the downflow of water and upflow of air alternate periodically in an upside-down plastic bottle containing water. It is demonstrated that a coupled two-bottle system exhibits in- and antiphase synchronization according to the nature of coupling. A simple ordinary differential equation is deduced to interpret the characteristics of a single oscillator. This model is also extended to coupled oscillators, and the model reproduces the essential features of the experimental observations.
Isochronous dynamics in pulse coupled oscillator networks with delay
Li, Pan; Lin, Wei; Efstathiou, Konstantinos
2017-05-01
We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions—subsets of the phase space filled with periodic orbits having the same period. For each fixed value of the network parameters, such an isochronous region corresponds to a subset of initial states on an appropriate surface of section with non-zero dimensions such that all periodic orbits in this set have qualitatively similar dynamical behaviour. We analytically and numerically study in detail such an isochronous region, give proof of its existence, and describe its properties. We further describe other isochronous regions that appear in the system.
EDFA-based coupled opto-electronic oscillator and its phase noise
Salik, Ertan; Yu, Nan; Tu, Meirong; Maleki, Lute
2004-01-01
EDFA-based coupled opto-electronic oscillator (COEO), an integrated optical and microwave oscillator that can generate picosecond optical pulses, is presented. the phase noise measurements of COEO show better performance than synthesizer-driven mode-locked laser.
Subharmonic phase clusters in the complex Ginzburg-Landau equation with nonlinear global coupling.
García-Morales, Vladimir; Orlov, Alexander; Krischer, Katharina
2010-12-01
A wide variety of subharmonic n -phase cluster patterns was observed in experiments with spatially extended chemical and electrochemical oscillators. These patterns cannot be captured with a phase model. We demonstrate that the introduction of a nonlinear global coupling (NGC) in the complex Ginzburg-Landau equation has subharmonic cluster pattern solutions in wide parameter ranges. The NGC introduces a conservation law for the oscillatory state of the homogeneous mode, which describes the strong oscillations of the mean field in the experiments. We show that the NGC causes a pronounced 2:1 self-resonance on any spatial inhomogeneity, leading to two-phase subharmonic clustering, as well as additional higher resonances. Nonequilibrium Ising-Bloch transitions occur as the coupling strength is varied.
Spatiotemporal Symmetry in Rings of Coupled Biological Oscillators of Physarum Plasmodial Slime Mold
Energy Technology Data Exchange (ETDEWEB)
Takamatsu, Atsuko; Tanaka, Reiko; Yamada, Hiroyasu; Nakagaki, Toshiyuki; Fujii, Teruo; Endo, Isao
2001-08-13
Spatiotemporal patterns in rings of coupled biological oscillators of the plasmodial slime mold, Physarum polycephalum, were investigated by comparing with results analyzed by the symmetric Hopf bifurcation theory based on group theory. In three-, four-, and five-oscillator systems, all types of oscillation modes predicted by the theory were observed including a novel oscillation mode, a half period oscillation, which has not been reported anywhere in practical systems. Our results support the effectiveness of the symmetric Hopf bifurcation theory in practical systems.
Manimala, James M; Sun, C T
2016-06-01
The amplitude-dependent dynamic response in acoustic metamaterials having nonlinear local oscillator microstructures is studied using numerical simulations on representative discrete mass-spring models. Both cubically nonlinear hardening and softening local oscillator cases are considered. Single frequency, bi-frequency, and wave packet excitations at low and high amplitude levels were used to interrogate the models. The propagation and attenuation characteristics of harmonic waves in a tunable frequency range is found to correspond to the amplitude and nonlinearity-dependent shifts in the local resonance bandgap for such nonlinear acoustic metamaterials. A predominant shift in the propagated wave spectrum towards lower frequencies is observed. Moreover, the feasibility of amplitude and frequency-dependent selective filtering of composite signals consisting of individual frequency components which fall within propagating or attenuating regimes is demonstrated. Further enrichment of these wave manipulation mechanisms in acoustic metamaterials using different combinations of nonlinear microstructures presents device implications for acoustic filters and waveguides.
Elwakil, Ahmed S.
2009-04-28
Two novel sinusoidal oscillator structures with an explicit tanh(x) nonlinearity are proposed. The oscillators have the attractive feature: the higher the operating frequency, the lower the necessary gain required to start oscillations. A nonlinear model for the two oscillators is derived and verified numerically. Spice simulations using AMS BiCMOS 0.35 μ model parameters and experimental results are shown. Copyright © 2009 John Wiley & Sons, Ltd.
Lenci, Stefano; Rega, Giuseppe
2016-06-01
The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.
Coupled parametric processes in binary nonlinear photonic structures
Saygin, M Yu
2016-01-01
We study parametric interactions in a new type of nonlinear photonic structures, which is realized in the vicinity of a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be implemented simultaneously, owing to multiple phase-matching conditions, fulfilled separately in the constituent crystals. The coupling between the nonlinear processes by means of modes sharing similar frequency is attained by the spatially-broadband nature of the parametric fields. We investigate the spatial properties of the fields generated in the binary structure constructed from periodically poled crystals for the two examples: 1) single parametric down-conversion, and 2) coupled parametric down-conversion and up-conversion processes. The efficacy of the fields' generation in these examples is analyzed through comparison with the cases of traditional single periodically poled crystal and aperiodic photonic structure, respectively. It has been shown that the relative s...
Directory of Open Access Journals (Sweden)
Chen Bor-Sen
2012-10-01
Full Text Available Abstract Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI. We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI-based design problem
Oscillation quenching in third order phase locked loop coupled by mean field diffusive coupling
Chakraborty, S.; Dandapathak, M.; Sarkar, B. C.
2016-11-01
We explored analytically the oscillation quenching phenomena (amplitude death and parameter dependent inhomogeneous steady state) in a coupled third order phase locked loop (PLL) both in periodic and chaotic mode. The phase locked loops were coupled through mean field diffusive coupling. The lower and upper limits of the quenched state were identified in the parameter space of the coupled PLL using the Routh-Hurwitz technique. We further observed that the ability of convergence to the quenched state of coupled PLLs depends on the design parameters. For identical systems, both the systems converge to the homogeneous steady state, whereas for non-identical parameter values they converge to an inhomogeneous steady state. It was also observed that for identical systems, the quenched state is wider than the non-identical case. When the system parameters are so chosen that each isolated loop is chaotic in nature, we observe narrowing down of the quenched state. All these phenomena were also demonstrated through numerical simulations.
A Coupled Analysis of Nonlinear Sloshing and Ship Motion
Institute of Scientific and Technical Information of China (English)
Shuo Huang; Wenyang Duan; Hao Zhang
2012-01-01
Nonlinear interactions among incident wave,tank-sloshing and floating body coupling motion are investigated.The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline (NURBS) higher-order panel method in time domain based on the potential theory.A robust and stable improved iterative procedure (Yan and Ma,2007) for floating bodies is used for calculating the time derivative of velocity potential and floating body motion.An energy dissipation condition based on linear theory adopted by Huang (2011) is developed to consider flow viscosity effects of sloshing flow in nonlinear model.A two-dimensional tank model test was performed to identify its validity.The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen (2003)'s experimental results,showing fair agreement.Thus,the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.
Asymptotic analysis of a coupled nonlinear parabolic system
Institute of Scientific and Technical Information of China (English)
Lan QIAO; Sining ZHENG
2008-01-01
This paper deals with asymptotic analysis of a parabolic system with inner absorptions and coupled nonlinear boundary fluxes. Three simultaneous blow-up rates are established under different dominations of nonlinearities, and simply represented in a characteristic algebraic system introduced for the problem. In particular, it is observed that two of the multiple blow-up rates are absorption-related. This is substantially different from those for nonlinear parabolic problems with absorptions in all the previous literature, where the blow-up rates were known as absorption-independent. The results of the paper rely on the scaling method with a complete classification for the nonlinear parameters of the model. The first example of absorption-related blow-up rates was recently proposed by the authors for a coupled parabolic system with mixed type nonlinearities. The present paper shows that the newly observed phenomena of absorption-related blow-up rates should be due to the coupling mechanism, rather than the mixed type nonlinearities.
New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators
Karahan, M. M. Fatih; Pakdemirli, Mehmet
2016-06-01
Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-09-22
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities.
A stochastic model for circadian rhythms from coupled ultradian oscillators
Directory of Open Access Journals (Sweden)
Illner Reinhard
2007-01-01
Full Text Available Abstract Background Circadian rhythms with varying components exist in organisms ranging from humans to cyanobacteria. A simple evolutionarily plausible mechanism for the origin of such a variety of circadian oscillators, proposed in earlier work, involves the non-disruptive coupling of pre-existing ultradian transcriptional-translational oscillators (TTOs, producing "beats," in individual cells. However, like other TTO models of circadian rhythms, it is important to establish that the inherent stochasticity of the protein binding and unbinding does not invalidate the finding of clear oscillations with circadian period. Results The TTOs of our model are described in two versions: 1 a version in which the activation or inhibition of genes is regulated stochastically, where the 'unoccupied" (or "free" time of the site under consideration depends on the concentration of a protein complex produced by another site, and 2 a deterministic, "time-averaged" version in which the switching between the "free" and "occupied" states of the sites occurs so rapidly that the stochastic effects average out. The second case is proved to emerge from the first in a mathematically rigorous way. Numerical results for both scenarios are presented and compared. Conclusion Our model proves to be robust to the stochasticity of protein binding/unbinding at experimentally determined rates and even at rates several orders of magnitude slower. We have not only confirmed this by numerical simulation, but have shown in a mathematically rigorous way that the time-averaged deterministic system is indeed the fast-binding-rate limit of the full stochastic model.
UV Nano Lights - Nonlinear Quantum Dot-Plasmon Coupling
2016-06-20
AFRL-AFOSR-JP-TR-2016-0072 UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling Eric Waclawik QUEENSLAND UNIVERSITY OF TECHNOLOGY Final Report 06...Final 3. DATES COVERED (From - To) 03 Feb 2014 to 02 Feb 2016 4. TITLE AND SUBTITLE UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling 5a...CONTRACT NUMBER 5b. GRANT NUMBER FA2386-14-1-4056 5c. PROGRAM ELEMENT NUMBER 61102F 6. AUTHOR(S) Eric Waclawik 5d. PROJECT NUMBER 5e. TASK NUMBER 5f
Rabi oscillations of two-photon states in nonlinear optical resonators
Sherkunov, Y.; Whittaker, David M.; Fal'ko, Vladimir
2016-02-01
We demonstrate that four-wave mixing processes in high-quality nonlinear resonators can lead to Rabi-like oscillations in photon occupation numbers and second-order correlation functions, being a characteristic feature of the presence of entangled photon pairs in the optical signal. In the case of a system driven by a continuous coherent pump, the oscillations occur in the transient regime. We show that driving the system with pulsed coherent pumping would generate strongly antibunched photon states.
Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities
Beléndez,Augusto; Beléndez Vázquez, Tarsicio; Martínez Guardiola, Francisco Javier; Pascual Villalobos, Carolina; Álvarez López, Mariela Lázara; Arribas Garde, Enrique
2016-01-01
The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, unforced cubic–quintic Duffing oscillator is solved exactly, providing exact expressions for the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solution involves Jacobi elliptic functions. Some particular cases obtained varying the parameters that characterize this oscillator are presented and discussed. The behaviour of the per...
Properties of finite difference models of non-linear conservative oscillators
Mickens, R. E.
1988-01-01
Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.
Removal of Noise Oscillation Term Appearing in the Nonlinear Equation Solution
Directory of Open Access Journals (Sweden)
Yasir Khan
2012-01-01
Full Text Available This paper suggests a novel modified Laplace method for removal of noise oscillation term appearing in the nonlinear equation solutions. The modified method overcomes the noise oscillation during the iteration procedure by suitable choice of an initial solution. Several examples are tested, and the obtained results suggest that this newly developed technique could lead to a promising tool and powerful improvement for many applications in differential and integral equations.
Frequency and Phase Noise in Non-Linear Microwave Oscillator Circuits
Tannous, C.
2003-01-01
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of stochastic differential equations representing the circuit. Our theoretical evaluations can be used in order to make detailed comparisons with the experimental measurements of phase noise spectra in selected oscillating circuits.
Properties of Coupled Oscillator Model for Bidirectional Associative Memory
Kawaguchi, Satoshi
2016-08-01
In this study, we consider the stationary state and dynamical properties of a coupled oscillator model for bidirectional associative memory. For the stationary state, we apply the replica method to obtain self-consistent order parameter equations. The theoretical results for the storage capacity and overlap agree well with the numerical simulation. For the retrieval process, we apply statistical neurodynamics to include temporal noise correlations. For the successful retrieval process, the theoretical result obtained with the fourth-order approximation qualitatively agrees with the numerical simulation. However, for the unsuccessful retrieval process, higher-order noise correlations suppress severely; therefore, the maximum value of the overlap and the relaxation time are smaller than those of the numerical simulation. The reasons for the discrepancies between the theoretical result and numerical simulation, and the validity of our analysis are discussed.
Elementary modes of coupled oscillators as whispering-gallery microresonators
Banerjee, Rabin; Mukherjee, Pradip
2015-10-01
We obtain the elementary modes of a system of parity-time reversal (PT)-symmetric coupled oscillators with balanced loss and gain. These modes are used to give a physical picture of the phase transition recently reported [C. M. Bender, M. Gianfreda, B. Peng, S. K. Özdemir and L. Yang, Phys. Rev. A 88, 062111 (2013); L. Yang, S. K. Özdemir and B. Peng, 12th Int. Workshop and Conf. Pseudo-Hermitian Hamiltonians in Quantum Physics, Istanbul, Turkey, July 2013; B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender and L. Yang, Nat. Phys. 10, 394 (2014)] in experiments with whispering-gallery microresonators.
Energy Technology Data Exchange (ETDEWEB)
Zhang Wei [College of Mechanical Engineering, Beijing University of Technology, Beijing 100022 (China)] e-mail: sandyzhang0@yahoo.com
2005-11-01
This paper presents an analysis of the chaotic motion and its control for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. A new method of controlling chaotic motion for the nonlinear nonplanar oscillations of the cantilever beam, refereed as to the force control approach, is proposed for the first time. The governing nonlinear equations of nonplanar motion under combined parametric and external excitations are obtained. The Galerkin procedure is applied to the governing equation to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations for the in-plane and out-of-plane modes. The work is focused on the case of 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance-primary resonance for the out-of-plane mode. The method of multiple scales is used to transform the parametrically and externally excited system to the averaged equations which have a constant perturbation force. Based on the averaged equations obtained here, numerical simulation is utilized to discover the periodic and chaotic motions for the nonlinear nonplanar oscillations of the cantilever beam. The numerical results indicate that the transverse excitation in the z direction at the free end can control the chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam. The methodology of controlling chaotic motion by using the transverse excitation is proposed. The transverse excitation in the z direction at the free end may be thought about to be an open-loop control. For the problem investigated in this paper, this approach is an effective methodology of controlling chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam.
Wind farm non-linear control for damping electromechanical oscillations of power systems
Energy Technology Data Exchange (ETDEWEB)
Fernandez, R.D. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900 La Plata (Argentina); Laboratorio de Electronica. Facultad de Ingenieria, Universidad Nacional de la Patagonia San Juan Bosco, Ciudad Universitaria, Km. 4, 9000 Comodoro Rivadavia (Argentina); Battaiotto, P.E. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900 La Plata (Argentina); Mantz, R.J. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, CICpba, Universidad Nacional de La Plata, CC 91, 1900 La Plata (Argentina)
2008-10-15
This paper deals with the non-linear control of wind farms equipped with doubly fed induction generators (DFIGs). Both active and reactive wind farm powers are employed in two non-linear control laws in order to increase the damping of the oscillation modes of a power system. The proposed strategy is derived from the Lyapunov Theory and is independent of the network topology. In this way, the strategy can be added to the central controller as another added control function. Finally, some simulations, showing the oscillation modes of a power system, are presented in order to support the theoretical considerations demonstrating the potential contributions of both control laws. (author)
Low-frequency band gaps in chains with attached non-linear oscillators
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Jensen, Jakob Søndergaard
2007-01-01
in structures with periodic or random inclusions are located mainly in the high frequency range, as the wavelength has to be comparable with the distance between the alternating parts. Band gaps may also exist in structures with locally attached oscillators. In the linear case the gap is located around......The aim of this article is to investigate the wave propagation in one-dimensional chains with attached non-linear local oscillators by using analytical and numerical models. The focus is on the influence of non-linearities on the filtering properties of the chain in the low frequency range...
Coherent states for nonlinear harmonic oscillator and some of its properties
Energy Technology Data Exchange (ETDEWEB)
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk [School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Oscillation criteria for third order nonlinear delay differential equations with damping
Directory of Open Access Journals (Sweden)
Said R. Grace
2015-01-01
Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.
Oscillations of the soliton parameters in nonlinear interference phenomena
Energy Technology Data Exchange (ETDEWEB)
Tsoy, Eduard N. [Centre of Excellence for Ultrahigh-bandwidth Devices for Optical Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia)], E-mail: etsoy@physic.uzsci.net; Sterke, C. Martijn de [Centre of Excellence for Ultrahigh-bandwidth Devices for Optical Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia)
2008-03-10
Applying the inverse scattering transform method, we show that a soliton modified by an amplitude or phase filter can evolve into several solitons. The oscillation period upon subsequent propagation follows from the wavenumbers of the emerging solitons and the radiation. Our results clarify spectral variations observed in recent supercontinuum experiments.
Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Díaz-Bautista, Erik
2016-01-01
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.
Low Voltage Low Power Quadrature LC Oscillator Based on Back-gate Superharmonic Capacitive Coupling
Ma, Minglin; Li, Zhijun
2013-09-01
This work introduces a new low voltage low power superharmonic capacitive coupling quadrature LC oscillator (QLCO) made by coupling two identical cross-connected LC oscillators without tail transistor. In each of the core oscillators, the back-gate nodes of the cross-coupled NMOS pair and PMOS pair, acting as common mode nodes, have been connected directly. Then the core oscillators are coupled together via capacitive coupling of the PMOS common mode node in one of the core oscillators to the NMOS common mode node in the other core oscillator, and vice versa. Only capacitors are used for coupling of the two core oscillators and therefore no extra noise sources are imposed on the circuit. Operation of the proposed QLCO was investigated with simulation using a commercial 0.18 µm RF CMOS technology: it shows a power dissipation of 5.2 mW from a 0.6 V supply voltage. Since the proposed core oscillator has Complementary NMOS and PMOS cross coupled pairs, and capacitive coupling method will not introduce extra phase noise, so this circuit can operate with a low phase noise as low as -126.8 dBc/Hz at 1 MHz offset from center oscillation frequency of 2.4 GHz, as confirmed with simulation.
A coupled oscillator model of shelf and ocean tides
Arbic, Brian K.; Garrett, Chris
2010-04-01
The resonances of tides in the coupled open ocean and shelf are modeled by a mechanical analogue consisting of a damped driven larger mass and spring (the open-ocean) connected to a damped smaller mass and spring (the shelf). When both masses are near resonance, the addition of even a very small mass can significantly affect the oscillations of the larger mass. The influence of the shelf is largest if the shelf is resonant with weak friction. In particular, an increase of friction on a near-resonant shelf can, perhaps surprisingly, lead to an increase in ocean tides. On the other hand, a shelf with large friction has little effect on ocean tides. Comparison of the model predictions with results from numerical models of tides during the ice ages, when lower sea levels led to a much reduced areal extent of shelves, suggests that the predicted larger tidal dissipation then is related to the ocean basins being close to resonance. New numerical simulations with a forward global tide model are used to test expectations from the mechanical analogue. Setting friction to unrealistically large values in Hudson Strait yields larger North Atlantic M2 amplitudes, very similar to those seen in a simulation with the Hudson Strait blocked off. Thus, as anticipated, a shelf with very large friction is nearly equivalent in its effect on the open ocean to the removal of the shelf altogether. Setting friction in shallow waters throughout the globe to unrealistically large values yields even larger open ocean tidal amplitudes, similar to those found in simulations of ice-age tides. It thus appears that larger modeled tides during the ice ages can be a consequence of enhanced friction in shallower water on the shelf in glacial times as well as a reduced shelf area then. Single oscillator and coupled oscillator models for global tides show that the maximum extractable power for human use is a fraction of the present dissipation rate, which is itself a fraction of global human power
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France); University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Markou, Chrysoula [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France)
2015-12-15
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R - λ){sup 2} = 0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories. (orig.)
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios, E-mail: antoniad@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France); Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlestrasse 5, 3012, Bern (Switzerland); Markou, Chrysoula, E-mail: chrysoula@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France)
2015-12-09
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R-λ){sup 2}=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.
Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy
Directory of Open Access Journals (Sweden)
Zhengduo Shan
2014-01-01
Full Text Available With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.
Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy
Zhengduo Shan; Hongwei Yang; Baoshu Yin
2014-01-01
With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI) hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.
BAND GAP EFFECTS IN PERIODIC CHAIN WITH LOCAL LINEAR OR NON-LINEAR OSCILLATORS
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Jensen, Jakob Søndergaard
2007-01-01
attached linear oscillators. The stop band is located around the resonant frequency of the local oscillators, and thus a stop band can be created in the lower frequency range. In this paper, wave propagation in one-dimensional infinite periodic chains with attached linear and non-linear local oscillators...... within bands of frequencies called stop bands. Stop bands in structures with periodic or random inclusions are located mainly in the high frequency range, as the wave length has to be comparable with the distance between the alternating parts. Wave attenuation is also possible in structures with locally...
Equivalent Mathematical Representation of Second-Order Damped, Driven Nonlinear Oscillators
Alex Elías-Zúñiga; Oscar Martínez-Romero
2013-01-01
The aim of this paper focuses on applying a nonlinearization method to transform forced, damped nonlinear equations of motion of oscillatory systems into the well-known forced, damped Duffing equation. The accuracy obtained from the derived equivalent equations of motion is evaluated by studying the amplitude-time, the phase portraits, and the continuous wavelet transform diagrams of the cubic-quintic Duffing equation, the generalized pendulum equation, the power-form elastic term oscillator,...
Higher dimensional models of cross-coupled oscillators and application to design
Elwakil, Ahmed S.
2010-06-01
We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.
Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators
Papariello, Luca; Zilberberg, Oded; Eichler, Alexander; Chitra, R.
2016-08-01
We propose a method for linear detection of weak forces using parametrically driven nonlinear resonators. The method is based on a peculiar feature in the response of the resonator to a near resonant periodic external force. This feature stems from a complex interplay among the parametric drive, external force, and nonlinearities. For weak parametric drive, the response exhibits the standard Duffing-like single jump hysteresis. For stronger drive amplitudes, we find a qualitatively new double jump hysteresis which arises from stable solutions generated by the cubic Duffing nonlinearity. The additional jump exists only if the external force is present and the frequency at which it occurs depends linearly on the amplitude of the external force, permitting a straightforward ultrasensitive detection of weak forces. With state-of-the-art nanomechanical resonators, our scheme should permit force detection in the attonewton range.
Dilaton black holes coupled to nonlinear electrodynamic field
Sheykhi, A
2015-01-01
The theory of nonlinear electrodynamics has got a lot of attentions in recent years. It was shown that Born-Infeld nonlinear electrodynamics is not the only modification of the linear Maxwell's field which keeps the electric field of a charged point particle finite at the origin, and other type of nonlinear Lagrangian such as exponential and logarithmic nonlinear electrodynamics can play the same role. In this paper, we generalize the study on the exponential nonlinear electrodynamics by adding a scalar dilaton field to the action. By suitably choosing the coupling of the matter field to the dilaton field, we vary the action and obtain the corresponding field equations. Then, by making a proper ansatz, we construct a new class of charged dilaton black hole solutions coupled to the exponential nonlinear electrodynamics field in the presence of two Liouville-type potentials for the dilaton field. Due to the presence of the dilaton field, the asymptotic behavior of these solutions are neither flat nor (A)dS. In ...
Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
Directory of Open Access Journals (Sweden)
A. Fereidoon
2012-01-01
Full Text Available In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF.The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.
Iacocca, Ezio
2012-01-01
Modulation of Spin Torque Oscillators (STOs) is investigated by analytically solving the time-dependent coupled equations of an auto-oscillator. A Fourier series solution is proposed, leading to the coefficients being determined with a linear set of equations, from which a Nonlinear Amplitude and Frequency Modulation (NFAM) scheme is obtained. In this framework, the NFAM features are related to the intrinsic STO parameters, revealing a frequency-dependence of the harmonic-dependent modulation index that allows a modulation bandwidth to be defined for these devices. The presented results expose a rich parameter space, where the modulation and the STO's operation conditions define the observed modulation features. The Fourier-series representation of the time signal is suitable for studying periodic perturbations on the auto-oscillator equation.
Synchronization of phase oscillators with coupling mediated by a diffusing substance
Batista, C. A. S.; Szezech, J. D.; Batista, A. M.; Macau, E. E. N.; Viana, R. L.
2017-03-01
We investigate the transition to phase and frequency synchronization in a one-dimensional chain of phase oscillator "cells" where the coupling is mediated by the local concentration of a chemical which can diffuse in the inter-oscillator medium and it is both secreted and absorbed by the oscillator "cells", influencing their dynamical behavior. This coupling has the advantage of having a tunable parameter which makes it possible to pass continuously from a global (all-to-all) to a local (nearest-neighbor) coupling form. We have verified that synchronous behavior depends on the coupling strength and coupling length.
The coupled nonlinear dynamics of a lift system
Crespo, Rafael Sánchez; Kaczmarczyk, Stefan; Picton, Phil; Su, Huijuan
2014-12-01
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
The coupled nonlinear dynamics of a lift system
Energy Technology Data Exchange (ETDEWEB)
Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)
2014-12-10
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Exact periodic solution in coupled nonlinear Schrodinger equations
Institute of Scientific and Technical Information of China (English)
Li Qi-Liang; Chen Jun-Lang; Sun Li-Li; Yu Shu-Yi; Qian Sheng
2007-01-01
The coupled nonlinear Schrodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.
On the recovering of a coupled nonlinear Schroedinger potential
Energy Technology Data Exchange (ETDEWEB)
Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana, Atzcapotzalco, DF (Mexico)]. E-mail: ccg@hp9000a1.uam.mx
2000-04-28
We establish a priori conditions for a Gel'fand-Levitan (GL) integral using some results of the Fredholm theory. As consequence, we obtain a recovering formula for the potential of the coupled nonlinear Schroedinger equations. The remarkable fact is that the recovering formula is given in terms of the solutions of a classical GL-integral equation. (author)
Chou, C H; Yu, T; Chou, Chung-Hsien; Yu, Ting
2007-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment made up of many harmonic oscillators at arbitrary temperature for a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is known [Hu, Paz and Zhang, Phys. Rev. D \\textbf{45}, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolution operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We ...
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragón, J. L.
2012-08-08
We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems. © 2012 American Physical Society.
Nonlinear Observers for Gyro Calibration Coupled with a Nonlinear Control Algorithm
Thienel, Julie; Sanner, Robert M.
2003-01-01
Nonlinear observers for gyro calibration are presented. The first observer estimates a constant gyro bias. The second observer estimates scale factor errors. The third observer estimates the gyro alignment for three orthogonal gyros. The observers are then combined. The convergence properties of all three observers, and the combined observers, are discussed. Additionally, all three observers are coupled with a nonlinear control algorithm. The stability of each of the resulting closed loop systems is analyzed. Simulated test results are presented for each system.
Chaos in a double driven dissipative nonlinear oscillator.
Adamyan, H H; Manvelyan, S B; Kryuchkyan, G Y
2001-10-01
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the framework of the statistical ensemble of quantum trajectories in a quantum state diffusion approach. The quantum dynamical manifestations of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement, are studied by numerical simulation of the ensemble averaged Wigner function and von Neumann entropy.
Di Egidio, Angelo; Contento, Alessandro; Vestroni, Fabrizio
2015-12-01
An open-cross section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear open-cross section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.
Electromagnetic radiation from linearly and nonlinearly oscillating charge drops
Grigor'ev, A. I.; Shiryaeva, S. O.
2016-12-01
It has been shown that analytic calculations of the intensity of electromagnetic radiation from an oscillating charged drop in the approximation linear in the oscillation amplitude (small parameter is on the order of 0.1) give only the quadrupole component of the total radiation. The dipole component can only be obtained in calculations using higher-order approximations. Nevertheless, the intensity of the dipole radiation turns out to be substantially higher (by 14-15 orders of magnitude). This is because the decomposition of radiation from a system of charges into multipole components (differing even in the rates of decrease in the potential with the distance) is carried out using the expansion in a substantially smaller parameter, viz., the ratio of the size of the emitting system (in our case, a drop of radius 10 μm) to the distance to the point of observation in the wave zone of the emission of radiation (emitted wavelength) of 100-1000 m. As a result, this second small parameter is on the order of 10-7 to 10-8. On the other hand, in accordance with the field theory, the ratio of intensities of quadrupole and dipole radiations is proportional to the squared ratio of the hydrodynamic velocity of the oscillating surface of a charged drop to the velocity of propagation of an electromagnetic signal in vacuum (velocity of light), which yields a ratio of 10-14 to 10-15.
Coriolis effects on nonlinear oscillations of rotating cylinders and rings
Padovan, J.
1976-01-01
The effects which moderately large deflections have on the frequency spectrum of rotating rings and cylinders are considered. To develop the requisite solution, a variationally constrained version of the Lindstedt-Poincare procedure is employed. Based on the solution developed, in addition to considering the effects of displacement induced nonlinearity, the role of Coriolis forces is also given special consideration.
Clustering and Synchronization in an Array of Repulsively Coupled Phase Oscillators
Institute of Scientific and Technical Information of China (English)
LI Juan; WU Liang; ZHU Shi-Qun
2007-01-01
Clustering and synchronization in an array of repulsively coupled phase oscillators are numerically investigated. It is found that oscillators are divided into several clusters according to the symmetry in the structure.Synchronization occurs between oscillators in each cluster, while those oscillators belonging to different clusters remain asynchronous. Such synchronization may collapse for all clusters when the dynamics of only one oscillator is altered properly. The synchronous state may return back after a short period of transient process. This is determined by the strength of the oscillator altered. Its application in the communication of one-to-several is suggested.
Negative Resistance Circuit for Damping an Array of Coupled FitzHugh-Nagumo Oscillators
DEFF Research Database (Denmark)
Tamaševičius, Arūnas; Adomaitienė, Elena; Bumelienė, Skaidra;
2015-01-01
An analog circuit, based on a negative impedance converter and a capacitor, for damping oscillations in an array of mean-field coupled neuronal FitzHugh–Nagumo (FHN) type oscillators is described. The circuit is essentially a two-terminal feedback controller. When coupled to an array of the FHN o...... oscillators, it stabilizes their unstable steady states. Both, numerical simulations and hardware experiments with the analog electronic circuits have been performed. The results for an array, composed of three mean-field coupled FHN oscillators, are presented....
Enhancing the injection locking range of spin torque oscillators through mutual coupling
Romera, M.; Talatchian, P.; Lebrun, R.; Merazzo, K. J.; Bortolotti, P.; Vila, L.; Costa, J. D.; Ferreira, R.; Freitas, P. P.; Cyrille, M.-C.; Ebels, U.; Cros, V.; Grollier, J.
2016-12-01
We investigate how the ability of the vortex oscillation mode of a spin-torque nano-oscillator to lock to an external microwave signal is modified when it is coupled to another oscillator. We show experimentally that the mutual electrical coupling can lead to locking range enhancements of a factor 1.64. Furthermore, we analyze the evolution of the locking range as a function of the coupling strength through experiments and numerical simulations. By uncovering the mechanisms at stake in the locking range enhancement, our results will be useful for designing spin-torque nano-oscillator arrays with high sensitivities to external microwave stimuli.
Spontaneous mode switching in coupled oscillators competing for constant amounts of resources.
Hirata, Yoshito; Aono, Masashi; Hara, Masahiko; Aihara, Kazuyuki
2010-03-01
We propose a widely applicable scheme of coupling that models competitions among dynamical systems for fixed amounts of resources. Two oscillators coupled in this way synchronize in antiphase. Three oscillators coupled circularly show a number of oscillation modes such as rotation and partially in-phase synchronization. Intriguingly, simple oscillators in the model also produce complex behavior such as spontaneous switching among different modes. The dynamics reproduces well the spatiotemporal oscillatory behavior of a true slime mold Physarum, which is capable of computational optimization.
Negative Resistance Circuit for Damping an Array of Coupled FitzHugh-Nagumo Oscillators
DEFF Research Database (Denmark)
Tamaševičius, Arūnas; Adomaitienė, Elena; Bumelienė, Skaidra
2015-01-01
An analog circuit, based on a negative impedance converter and a capacitor, for damping oscillations in an array of mean-field coupled neuronal FitzHugh–Nagumo (FHN) type oscillators is described. The circuit is essentially a two-terminal feedback controller. When coupled to an array of the FHN...... oscillators, it stabilizes their unstable steady states. Both, numerical simulations and hardware experiments with the analog electronic circuits have been performed. The results for an array, composed of three mean-field coupled FHN oscillators, are presented....
Energy Technology Data Exchange (ETDEWEB)
Romera, M.; Monteblanco, E.; Garcia-Sanchez, F.; Buda-Prejbeanu, L. D.; Ebels, U. [Univ. Grenoble Alpes, F-38000 Grenoble (France); CEA, INAC-SPINTEC, F-38000 Grenoble (France); CNRS, SPINTEC, F-38000 Grenoble (France); Delaët, B. [CEA-LETI, MINATEC, DRT/LETI/DIHS, 38054 Grenoble (France)
2015-05-11
The influence of dynamic coupling in between magnetic layers of a standard spin torque nano-oscillator composed of a synthetic antiferromagnet (SyF) as a polarizer and an in-plane magnetized free layer has been investigated. Experiments on spin valve nanopillars reveal non-continuous features such as kinks in the frequency field dependence that cannot be explained without such interactions. Comparison of experiments to numerical macrospin simulations shows that this is due to non-linear interaction between the spin torque (STT) driven mode and a damped mode that is mediated via the third harmonics of the STT mode. It only occurs at large applied currents and thus at large excitation amplitudes of the STT mode. Under these conditions, a hybridized mode characterized by a strong reduction of the linewidth appears. The reduced linewidth can be explained by a reduction of the non-linear contribution to the linewidth via an enhanced effective damping. Interestingly, the effect depends also on the exchange interaction within the SyF. An enhancement of the current range of reduced linewidth by a factor of two and a reduction of the minimum linewidth by a factor of two are predicted from simulation when the exchange interaction strength is reduced by 30%. These results open directions to optimize the design and microwave performances of spin torque nano-oscillators taking advantage of the coupling mechanisms.
Boundary control of nonlinear coupled heat systems using backstepping
Bendevis, Paul
2016-10-20
A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.
The Madden-Julian Oscillation in NCEP Coupled Model Simulation
Directory of Open Access Journals (Sweden)
Wanqiu Wang Kyong-Hwan Seo
2009-01-01
Full Text Available This study documents a detailed analysis on the Madden-Julian Oscillation (MJO simulated by the National Centers for Environmental Prediction (NCEP using the Global Forecast System (GFS model version 2003 coupled with the Climate Forecast System model (CFS consisting of the 2003 version of GFS and the Geophysical Fluid Dynamics Laboratory (GFDL Modular Ocean Model V.3 (MOM3. The analyses are based upon a 21-year simulation of AMIP-type with GFS and CMIP-type with CFS. It is found that air-sea coupling in CFS is shown to improve the coherence between convection and large-scale circulation associated with the MJO. The too fast propagation of convection from the Indian Ocean to the maritime continents and the western Pacific in GFS is improved (slowed down in CFS. Both GFS and CFS produce too strong intraseasonal convective heating and circulation anomalies in the central-eastern Pacific; further, the air-sea coupling in CFS enhances this unrealistic feature. The simulated mean slow phase speed of east ward propagating low-wavenumber components shown in the wavenumber-frequency spectra is due to the slow propagation in the central-eastern Pacific in both GFS and CFS. Errors in model climatology may have some effect upon the simulated MJO and two possible influences are: (i CFS fails to simulate the westerlies over maritime continents and western Pacific areas, resulting in an unrealistic representation of surface latent heat flux associated with the MJO; and (ii vertical easterly wind shear from the Indian Ocean to the western Pacific in CFS is much weaker than that in the observation and in GFS, which may adversely affect the eastward propagation of the simulated MJO.
Negative Resistance Circuit for Damping an Array of Coupled FitzHugh-Nagumo Oscillators
DEFF Research Database (Denmark)
Tamaševičius, Arūnas; Adomaitienė, Elena; Bumelienė, Skaidra;
2015-01-01
An analog circuit, based on a negative impedance converter and a capacitor, for damping oscillations in an array of mean-field coupled neuronal FitzHugh–Nagumo (FHN) type oscillators is described. The circuit is essentially a two-terminal feedback controller. When coupled to an array of the FHN...
Suppression of limit cycle oscillations using the nonlinear tuned vibration absorber
Habib, G.; Kerschen, G.
2015-01-01
The objective of this study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is not imposed a priori, as it is the case for most existing nonlinear absorbers. The NLTVA parameters are determined analytically using stability and bifurcation analyses, and the resulting design is validated using numerical continuation. The proposed developments are illustrated using a Van der Pol–Duffing primary system. PMID:27547085
Rational extension and Jacobi-type X{sub m} solutions of a quantum nonlinear oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, Axel [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Roy, Barnana [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2013-12-15
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type X{sub m} exceptional orthogonal polynomials.
RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS
Institute of Scientific and Technical Information of China (English)
刘俊
2002-01-01
The periodic motion and stability for a class of two-degree-of freedom nonlinear oscillating systems are studied by using the method of Liapunov function.The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.
Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.
Chaotic Solutions of a Typical Nonlinear Oscillator in a Double Potential Trap
Institute of Scientific and Technical Information of China (English)
FANG Jian-Shu
2003-01-01
We have obtained a general unstable chaotic solution of a typical nonlinear oscillator in a double potential trap with weak periodic perturbations by using the direct perturbation method. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding chaotic region and orbits in parameter space are described by numerical simulations.
NEW OSCILLATION CRITERIA RELATED TO EULER S INTEGRAL FOR CERTAIN NONLINEAR DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Using the integral average technique and a new function,some new oscillation criteria related to Euler integral are obtained for second order nonlinear differential equations with damping and forcing. Our results are of a higher degree of generality than some previous results. Information about the distribution of the zeros of solutions to the system is also obtained.
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
Nonlinear simulations of the convection-pulsation coupling
Gastine, T
2011-01-01
In cold Cepheids close to the red edge of the classical instability strip, a strong coupling between the stellar pulsations and the surface convective motions occurs. This coupling is by now poorly described by 1-D models of convection, the so-called "time-dependent convection models" (TDC). The intrinsic weakness of such models comes from the large number of unconstrained free parameters entering in the description of turbulent convection. A way to overcome these limits is to compute two-dimensional direct simulations (DNS), in which all the nonlinearities are correctly solved. Two-dimensional DNS of the convection-pulsation coupling are presented here. In an appropriate parameter regime, convective motions can actually quench the radial pulsations of the star, as suspected in Cepheids close to the red edge of the instability strip. These nonlinear simulations can also be used to determine the limits and the relevance of the TDC models.
The effects of dual-channel coupling on the transition from amplitude death to oscillation death
Chen, Jiangnan; Liu, Weiqing; Zhu, Yun; Xiao, Jinghua
2016-07-01
Oscillation quenching including amplitude death (AD) and oscillation death (OD) in addition to the transition processes between them have been hot topics in aspect of chaos control, physical and biological applications. The effects of dual-channel coupling on the AD and OD dynamics regimes, and their transition processes in coupled nonidentical oscillators are explored numerically and theoretically. Our results indicate that an additional repulsive coupling tends to shrink the AD domain while it enlarges the OD domain, however, an additional attractive coupling acts inversely. As a result, the transitions from AD to OD are replaced by transitions from oscillation state (OS) to AD or from OS to OD in the dual-channel coupled oscillators with different frequency mismatches. Our results are helpful to better understand the control of AD and OD and their transition processes.
Analytical approximate technique for strongly nonlinear oscillators problem arising in engineering
Directory of Open Access Journals (Sweden)
Y. Khan
2012-12-01
Full Text Available In this paper, a novel method called generalized of the variational iteration method is presented to obtain an approximate analytical solution for strong nonlinear oscillators problem associated in engineering phenomena. This approach resulted in the frequency of the motion as a function of the amplitude of oscillation. It is determined that the method works very well for the whole range of parameters and an excellent agreement is demonstrated and discussed between the approximate frequencies and the exact one. The most significant features of this method are its simplicity and excellent accuracy for the whole range of oscillation amplitude values. Also, the results reveal that this technique is very effective and convenient for solving conservative oscillatory systems with complex nonlinearities. Results obtained by the proposed method are compared with Energy Balance Method (EBM and exact solution showed that, contrary to EBM, simply one or two iterations are enough for obtaining highly accurate results.
Escape time from potential wells of strongly nonlinear oscillators with slowly varying parameters
Directory of Open Access Journals (Sweden)
Cai Jianping
2005-01-01
Full Text Available The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well of quadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear oscillators with slowly varying parameters, and secondly the character of modulus of Jacobian elliptic function is applied to derive the equations governing the escape time. The approximate potential method, instead of Taylor series expansion, is used to approximate the potential of an oscillation system such that the asymptotic solution can be expressed in terms of Jacobian elliptic function. Numerical examples verify the efficiency of the present method.
RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION
Institute of Scientific and Technical Information of China (English)
戎海武; 王向东; 孟光; 徐伟; 方同
2003-01-01
The principal resonance of Duffing oscillator to narrow-band random parametricexcitation was investigated. The method of multiple scales was used to determine theequations of modulation of amplitude and phase. The behavior, stability and bifurcation ofsteady state response were studied by means of qualitative analyses. The effects of damping,detuning, bandwidth and magnitudes of deterministic and random excitations wereanalyzed. The theoretical analyses were verified by numerical results. Theoretical analysesand numerical simulations show that when the intensity of the random excitation increases,the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle.Under some conditions the system may have two ,steady state solutions.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
Fan, Wei; Liu, Jin-Yang
2013-10-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
Lavrov, Roman; Peil, Michael; Jacquot, Maxime; Larger, Laurent; Udaltsov, Vladimir; Dudley, John
2009-08-01
We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.
Influence of hydrodynamic thrust bearings on the nonlinear oscillations of high-speed rotors
Chatzisavvas, Ioannis; Boyaci, Aydin; Koutsovasilis, Panagiotis; Schweizer, Bernhard
2016-10-01
This paper investigates the effect of hydrodynamic thrust bearings on the nonlinear vibrations and the bifurcations occurring in rotor/bearing systems. In order to examine the influence of thrust bearings, run-up simulations may be carried out. To be able to perform such run-up calculations, a computationally efficient thrust bearing model is mandatory. Direct discretization of the Reynolds equation for thrust bearings by means of a Finite Element or Finite Difference approach entails rather large simulation times, since in every time-integration step a discretized model of the Reynolds equation has to be solved simultaneously with the rotor model. Implementation of such a coupled rotor/bearing model may be accomplished by a co-simulation approach. Such an approach prevents, however, a thorough analysis of the rotor/bearing system based on extensive parameter studies. A major point of this work is the derivation of a very time-efficient but rather precise model for transient simulations of rotors with hydrodynamic thrust bearings. The presented model makes use of a global Galerkin approach, where the pressure field is approximated by global trial functions. For the considered problem, an analytical evaluation of the relevant integrals is possible. As a consequence, the system of equations of the discretized bearing model is obtained symbolically. In combination with a proper decomposition of the governing system matrix, a numerically efficient implementation can be achieved. Using run-up simulations with the proposed model, the effect of thrust bearings on the bifurcations points as well as on the amplitudes and frequencies of the subsynchronous rotor oscillations is investigated. Especially, the influence of the magnitude of the axial force, the geometry of the thrust bearing and the oil parameters is examined. It is shown that the thrust bearing exerts a large influence on the nonlinear rotor oscillations, especially to those related with the conical mode of the
Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators
Karahan, M. M. Fatih; Pakdemirli, Mehmet
2017-01-01
Strongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.
A quantum quasi-harmonic nonlinear oscillator with an isotonic term
Energy Technology Data Exchange (ETDEWEB)
Rañada, Manuel F., E-mail: mfran@unizar.es [Dep. de Física Teórica and IUMA, Universidad de Zaragoza, 50009 Zaragoza (Spain)
2014-08-01
The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.
Model Order and Identifiability of Non-Linear Biological Systems in Stable Oscillation.
Wigren, Torbjörn
2015-01-01
The paper presents a theoretical result that clarifies when it is at all possible to determine the nonlinear dynamic equations of a biological system in stable oscillation, from measured data. As it turns out the minimal order needed for this is dependent on the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a simulated fourth order Hodgkin-Huxley spiking neuron model, which is identified using a non-linear second order differential equation model. The simulated result illustrates that the underlying higher order model of the spiking neuron cannot be uniquely determined given only the periodic measured data. The result of the paper is of general validity when the dynamics of biological systems in stable oscillation is identified, and illustrates the need to carefully address non-linear identifiability aspects when validating models based on periodic data.
Energy Technology Data Exchange (ETDEWEB)
Fotsin, Hilaire [Laboratoire d' Electronique, Departement de Physique, Faculte des Sciences, Universite de Dschang, B.P. 67 Dschang (Cameroon); INPL-CRAN, UMR CNRS-INPL-UHP 7039 ENSEM-2, Avenue de la Foret de Haye-54516, Vandoeuvre-les-Nancy Cedex (France); E-mail: hbfotsin@yahoo.fr; Bowong, Samuel [Laboratoire de Mathematiques Appliquees, Departement de Mathematiques et Informatique, Faculte des sciences, Universite de Douala, B.P. 24157 Douala (Cameroon)] e-mail: sbowong@uycdc.uninet.cm
2006-02-01
This paper deals with the problem of control and synchronization of coupled second-order oscillators showing a chaotic behavior. A classical feedback controller is first used to stabilize the system at its equilibrium. An adaptive observer is then designed to synchronize the states of the master and slave oscillators using a single scalar signal corresponding to an observable state variable of the driving oscillator. An interesting feature of the proposed approach is that it can be used for chaos control as well as synchronization purposes. Numerical simulations results confirming the analytical predictions are shown and pspice simulations are also performed to confirm the efficiency of the proposed control scheme.
Resonant coupling of a Bose-Einstein condensate to a micromechanical oscillator
Hunger, D; Haensch, T W; Koenig, D; Kotthaus, J P; Reichel, J; Treutlein, P
2010-01-01
We report experiments in which the vibrations of a micromechanical oscillator are coupled to the motion of Bose-condensed atoms in a trap. The interaction relies on surface forces experienced by the atoms at about one micrometer distance from the mechanical structure. We observe resonant coupling to several well-resolved mechanical modes of the condensate. Coupling via surface forces does not require magnets, electrodes, or mirrors on the oscillator and could thus be employed to couple atoms to molecular-scale oscillators such as carbon nanotubes.
Collective motions of globally coupled oscillators and some probability distributions on circle
Energy Technology Data Exchange (ETDEWEB)
Jaćimović, Vladimir [Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put, bb., 81000 Podgorica (Montenegro); Crnkić, Aladin, E-mail: aladin.crnkic@hotmail.com [Faculty of Technical Engineering, University of Bihać, Ljubijankićeva, bb., 77000 Bihać, Bosnia and Herzegovina (Bosnia and Herzegovina)
2017-06-28
In 2010 Kato and Jones described a new family of probability distributions on circle, obtained as Möbius transformation of von Mises distribution. We present the model demonstrating that these distributions appear naturally in study of populations of coupled oscillators. We use this opportunity to point out certain relations between Directional Statistics and collective motion of coupled oscillators. - Highlights: • We specify probability distributions on circle that arise in Kuramoto model. • We study how the mean-field coupling affects the shape of distribution of phases. • We discuss potential applications in some experiments on cell cycle. • We apply Directional Statistics to study collective dynamics of coupled oscillators.
Enhanced interaction between a mechanical oscillator and two coupled resonant electrical circuits
Dmitriev, A V
2014-01-01
This paper reports result of calculation and experimental realization of an electromechanical system that consists of a high-Q mechanical oscillator parametrically coupled in the manner of a capacitive transducer with a RF circuit, which is in turn inductively coupled with another RF circuit. The system operates in the resolved sideband regime when the mechanical oscillator's frequency is larger than the electrical circuits' bandwidths. Using two coupled RF circuits allowed one to enhance the interaction between them and the mechanical oscillator which is one of flexural vibrational modes of a free-edge circular silicon wafer. Such a coupled electromechanical system can be used as a high-sensitive capacitive vibration sensor.
Nonlinear coupled dynamics analysis of a truss spar platform
Li, Cheng-xi; Zhang, Jun
2016-12-01
Accurate prediction of the offshore structure motion response and associate mooring line tension is important in both technical applications and scientific research. In our study, a truss spar platform, operated in Gulf of Mexico, is numerically simulated and analyzed by an in-house numerical code `COUPLE'. Both the platform motion responses and associated mooring line tension are calculated and investigated through a time domain nonlinear coupled dynamic analysis. Satisfactory agreement between the simulation and corresponding field measurements is in general reached, indicating that the numerical code can be used to conduct the time-domain analysis of a truss spar interacting with its mooring and riser system. Based on the comparison between linear and nonlinear results, the relative importance of nonlinearity in predicting the platform motion response and mooring line tensions is assessed and presented. Through the coupled and quasi-static analysis, the importance of the dynamic coupling effect between the platform hull and the mooring/riser system in predicting the mooring line tension and platform motions is quantified. These results may provide essential information pertaining to facilitate the numerical simulation and design of the large scale offshore structures.
Chaos Suppression in a Sine Square Map through Nonlinear Coupling
Institute of Scientific and Technical Information of China (English)
Eduardo L. Brugnago; Paulo C. Rech
2011-01-01
We study a pair of nonlinearly coupled identical chaotic sine square maps.More specifically,we investigate the chaos suppression associated with the variation of two parameters.Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited.Additionally,the dynamics of the coupled system is numerically characterized as the parameters are changed.In recent years,many efforts have been devoted to chaos suppression in a nonlinear dynamics field.Iglesias et al.[1] reported a chaos suppression method through numerical truncation and rounding errors,with applications in discrete-time systems.Hénon map[2] and the Burgers map[3] were used to illustrate the method.A method of feedback impulsive chaos suppression was introduced by Osipov et al.[4]It is an algorithm of suppressing chaos in continuoustime dissipative systems with an external impulsive force,whose necessary condition is a reduction of the continuous flow to a discrete-time one-dimensional map.%We study a pair of nonlinearly coupled identical chaotic sine square maps. More specifically, we investigate the chaos suppression associated with the variation of two parameters. Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited. Additionally, the dynamics of the coupled system is numerically characterized as the parameters are changed.
An efficient method for simulation of noisy coupled multi-dimensional oscillators
Stinchcombe, Adam R.; Forger, Daniel B.
2016-09-01
We present an efficient computational method for the study of populations of noisy coupled oscillators. By taking a population density approach in which the probability density of observing an oscillator at a point of state space is the primary variable instead of the states of all of the oscillators, we are able to seamlessly account for intrinsic noise within the oscillators and global coupling within the population. The population is assumed to consist of a large number of oscillators so that the noise process is well sampled over the population. Our numerical method is able to solve the governing equation even in the challenging case of limit cycle oscillators with a large number of state variables. Instead of simulating a prohibitive number of oscillators, our particle method simulates relatively few particles allowing for the efficient solution of the governing equation.
Sustained small oscillations in nonlinear control systems. [launch vehicle dynamics
George, J. H.; Gunderson, R. W.; Hahn, H.
1975-01-01
Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.
Integrable nonlinear parity-time symmetric optical oscillator
Hassan, Absar U; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N
2016-01-01
The nonlinear dynamics of a balanced parity-time symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain-thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time symmetric systems. Unlike other saturable parity time symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.
Friction self-oscillation decrease in nonlinear system of locomotive traction drive
Antipin, D. Ya; Vorobiyov, V. I.; Izmerov, O. V.; Shorokhov, S. G.; Bondarenko, D. A.
2017-02-01
The problems of the friction self-oscillation decrease in a nonlinear system of a locomotive traction drive are considered. It is determined that the self-oscillation amplitude decrease in a locomotive wheel pair during boxing in traction drives with an elastic linkage between an armature of a traction electric motor and gearing can be achieved due to drive damping capacity during impact vibro-damping in an axle reduction gear with a hard driven gear. The self-oscillation amplitude reduction in a wheel pair in the designs of locomotive traction drives with the location of elastic elements between a wheel pair and gearing can be obtained owing to the application of drive inertial masses as an anti-vibrator. On the basis of the carried out investigations, a design variant of a self-oscillation shock absorber of a traction electric motor framework on a reduction gear suspension with an absorber located beyond a wheel-motor unit was offered.
Collective oscillations and coupled modes in confined microfluidic droplet arrays
Schiller, Ulf D.; Fleury, Jean-Baptiste; Seemann, Ralf; Gompper, Gerhard
Microfluidic droplets have a wide range of applications ranging from analytic assays in cellular biology to controlled mixing in chemical engineering. Ensembles of microfluidic droplets are interesting model systems for non-equilibrium many-body phenomena. When flowing in a microchannel, trains of droplets can form microfluidic crystals whose dynamics are governed by long-range hydrodynamic interactions and boundary effects. In this contribution, excitation mechanisms for collective waves in dense and confined microfluidic droplet arrays are investigated by experiments and computer simulations. We demonstrate that distinct modes can be excited by creating specific `defect' patterns in flowing droplet trains. While longitudinal modes exhibit a short-lived cascade of pairs of laterally displacing droplets, transversely excited modes form propagating waves that behave like microfluidic phonons. We show that the confinement induces a coupling between longitudinal and transverse modes. We also investigate the life time of the collective oscillations and discuss possible mechanisms for the onset of instabilities. Our results demonstrate that microfluidic phonons can exhibit effects beyond the linear theory, which can be studied particularly well in dense and confined systems. This work was supported by Deutsche Forschungsgemeinschaft under Grant No. SE 1118/4.
Jia, Ji; Shangguan, Zhichun; Li, Haihong; Wu, Ye; Liu, Weiqing; Xiao, Jinghua; Kurths, Jürgen
2016-11-01
Upside-down bottles containing water which are common in our daily life exhibit rich vibration dynamics. Rich dynamic regimes are observed in bottle oscillators by directly measuring the pressure difference between inside and outside of a bottle with the aid of pressure sensors. We observe experimentally that an asymmetrical oscillation process between the outflow of water and the inflow of air is formed in a single bottle oscillator and, in addition, a kind of 2:1 frequency synchronization occurs in a coupled system of two non-identical bottle oscillators. The peak values of the oscillation of pressure differences between inside and outside of the bottle decease as the height of the liquid surface steps down, while the oscillation period increases gradually. The theoretical model of the oscillator is amended to understand the regimes in the experiment by introducing time-dependent parameters related to the asymmetrical oscillation processes. Our numerical results based on the model fit well with the experimental ones.
Mathematical Modeling and Control of Nonlinear Oscillators with Shape Memory Alloys
Bendame, Mohamed
Shape memory alloys (SMAs) belong to an interesting type of materials that have attracted the attention of scientists and engineers over the last few decades. They have some interesting properties that made them the subject of extensive research to find the best ways to utilize them in different engineering, biomedical, and scientific applications. In this thesis, we develop a mathematical model and analyze the behavior of SMAs by considering a one degree of freedom nonlinear oscillator consisting of a mass connected to a fixed frame through a viscous damping and a shape memory alloy device. Due to the nonlinear and dissipative nature of shape memory alloys, optimal control and Lyapunov stability theories are used to design a controller to stabilize the response of the one degree of freedom nonlinear oscillator. Since SMAs exist in two phases, martensite and austenite, and their phase transformations are dependent on stress and temperature, this work is presented in two parts. The first part deals with the nonlinear oscillator system in its two separate phases by considering a temperature where the SMA exists in only one of the phases. A model for each phase is developed based on Landau-Ginzburg-Devonshire theory that defines the free energy in a polynomial form enabling us to describe the SMAs shape memory effect and pseudoelasticity. However, due to the phenomenon of hysteresis in SMAs, the response of the nonlinear oscillator with a SMA element, in either phase, is chaotic and unstable. In order to stabilize the chaotic behavior, an optimal linear quadratic regulator controller is designed around a stable equilibrium for the martensitic and the austenitic phases. The closed-loop response for each phase is then simulated and computational results are presented. The second part of the thesis deals with the entire system in its dynamics by combining the two phases and taking into account the effect of temperature on the response of the system. Governing equations
Hosen, Md. Alal; Chowdhury, M. S. H.; Ali, Mohammad Yeakub; Ismail, Ahmad Faris
In the present paper, a novel analytical approximation technique has been proposed based on the energy balance method (EBM) to obtain approximate periodic solutions for the focus generalized highly nonlinear oscillators. The expressions of the natural frequency-amplitude relationship are obtained using a novel analytical way. The accuracy of the proposed method is investigated on three benchmark oscillatory problems, namely, the simple relativistic oscillator, the stretched elastic wire oscillator (with a mass attached to its midpoint) and the Duffing-relativistic oscillator. For an initial oscillation amplitude A0 = 100, the maximal relative errors of natural frequency found in three oscillators are 2.1637%, 0.0001% and 1.201%, respectively, which are much lower than the errors found using the existing methods. It is highly remarkable that an excellent accuracy of the approximate natural frequency has been found which is valid for the whole range of large values of oscillation amplitude as compared with the exact ones. Very simple solution procedure and high accuracy that is found in three benchmark problems reveal the novelty, reliability and wider applicability of the proposed analytical approximation technique.
Implication of Two-Coupled Differential Van der Pol Duffing Oscillator in Weak Signal Detection
Peng, Hang-hang; Xu, Xue-mei; Yang, Bing-chu; Yin, Lin-zi
2016-04-01
The principle of the Van der Pol Duffing oscillator for state transition and for determining critical value is described, which has been studied to indicate that the application of the Van der Pol Duffing oscillator in weak signal detection is feasible. On the basis of this principle, an improved two-coupled differential Van der Pol Duffing oscillator is proposed which can identify signals under any frequency and ameliorate signal-to-noise ratio (SNR). The analytical methods of the proposed model and the construction of the proposed oscillator are introduced in detail. Numerical experiments on the properties of the proposed oscillator compared with those of the Van der Pol Duffing oscillator are carried out. Our numerical simulations have confirmed the analytical treatment. The results demonstrate that this novel oscillator has better detection performance than the Van der Pol Duffing oscillator.
Energy Technology Data Exchange (ETDEWEB)
Wang, Hailing [Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong); Chung, Kwok-wai, E-mail: makchung@cityu.edu.hk [Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)
2012-02-27
The analytical solutions of nonlinear oscillators obtained from most perturbation or approximate methods usually have poor accuracy near homoclinic/heteroclinic (HH) orbits. In this Letter, we propose a nonlinear time transformation method to overcome such difficulty. In particular, we apply such method with Padé approximation to find analytical solutions of a generalized Duffing-harmonic oscillator having a rational form for the potential energy. For some parametric ranges, HH orbits exist in such an oscillator. For analytical approximation of periodic solution obtained from the present method, it is shown that the relative error of period with respect to the exact period tends to zero when the amplitude of periodic solution tends to either zero or infinity. The relative error is still very small even near to HH orbits. Furthermore, analytical approximate of HH orbits can also be obtained. From the illustrative examples, the phase portraits are in excellent agreement with the exact HH orbits. The results from the present method are compared with the exact solutions and that from the cubication method. -- Highlights: ► A nonlinear transformation is proposed for a generalized Duffing-harmonic oscillator. ► The relative error of period with respect to the exact one is always very small. ► Approximate solution of homoclinic/heteroclinic orbits can be obtained. ► Phase portraits are in excellent agreement even at homoclinic/heteroclinic orbits.
Quantum annealing with all-to-all connected nonlinear oscillators
DEFF Research Database (Denmark)
Puri, Shruti; Andersen, Christian Kraglund; Grimsmo, Arne L.
2017-01-01
Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr......-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic...... annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising...
Sensitivity and chaos control for the forced nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina [Department of Mathematics, Ural State University, 620083 Ekaterinburg (Russian Federation); Ryashko, Lev [Department of Mathematics, Ural State University, 620083 Ekaterinburg (Russian Federation)] e-mail: lev.ryashko@usu.ru
2005-12-01
This paper is devoted to study the problem of controlling chaos for forced nonlinear dynamic systems. We suggest a new control technique based on sensitivity analysis. With the help of approximation of nonequilibrium quasipotential, stochastic sensitivity function (SSF) is constructed. This function is used as basic tool of a quantitative description for a system response on the random external disturbances. The possibilities of SSF to predict chaotic dynamics for the periodic and stochastic forced Brusselator are shown. The problem of chaos control based on SSF is considered. A design of attractors with the desired features by feedback regulator is discussed. Analysis of controllability and effective technique for regulator synthesis is presented. An example of suppressing chaos for Brusselator is considered.
Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks
Directory of Open Access Journals (Sweden)
Chengrong Xie
2013-01-01
Full Text Available We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.
Global solution for coupled nonlinear Klein-Gordon system
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2007-01-01
The global solution for a coupled nonlinear Klein-Gordon system in twodimensional space was studied.First,a sharp threshold of blowup and global existenoe for the system was obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow.Then the result of how small the initial data for which the solution exists globally was proved by using the scaling argument.
Magneto-elastic oscillator: Modeling and analysis with nonlinear magnetic interaction
Kumar, K. Aravind; Ali, Shaikh Faruque; Arockiarajan, A.
2017-04-01
The magneto-elastically buckled beam is a classic example of a nonlinear oscillator that exhibits chaotic motions. This system serves as a model to analyze the motion of elastic structures in magnetic fields. The system follows a sixth order magneto-elastic potential and may have up to five static equilibrium positions. However, often the non-dimensional Duffing equation is used to approximate the system, with the coefficients being derived from experiments. In few other instances, numerical methods are used to evaluate the magnetic field values. These field values are then used to approximate the nonlinear magnetic restoring force. In this manuscript, we derive analytical closed form expressions for the magneto-elastic potential and the nonlinear restoring forces in the system. Such an analytical formulation would facilitate tracing the effect of change in a parameter, such as the magnet dimension, on the dynamics of the system. The model is derived assuming a single mode approximation, taking into account the effect of linear elastic and nonlinear magnetic forces. The developed model is then numerically simulated to show that it is accurate in capturing the system dynamics and bifurcation of equilibrium positions. The model is validated through experiments based on forced vibrations of the magneto-elastic oscillator. To gather further insights about the magneto-elastic oscillator, a parametric study has been conducted based on the field strength of the magnets and the distance between the magnets and the results are reported.
Directory of Open Access Journals (Sweden)
Saul Hazledine
Full Text Available Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia, with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.
Synchronization and quorum sensing in an ensemble of indirectly coupled chaotic oscillators
Li, Bing-Wei; Fu, Chenbo; Zhang, Hong; Wang, Xingang
2012-10-01
The fact that the elements in some realistic systems are influenced by each other indirectly through a common environment has stimulated a new surge of studies on the collective behavior of coupled oscillators. Most of the previous studies, however, consider only the case of coupled periodic oscillators, and it remains unknown whether and to what extent the findings can be applied to the case of coupled chaotic oscillators. Here, using the population density and coupling strength as the tuning parameters, we explore the synchronization and quorum sensing behaviors in an ensemble of chaotic oscillators coupled through a common medium, in which some interesting phenomena are observed, including the appearance of the phase synchronization in the process of progressive synchronization, the various periodic oscillations close to the quorum sensing transition, and the crossover of the critical population density at the transition. These phenomena, which have not been reported for indirectly coupled periodic oscillators, reveal a corner of the rich dynamics inherent in indirectly coupled chaotic oscillators, and are believed to have important implications to the performance and functionality of some realistic systems.
Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Berkemer, Rainer; Gorria, C.;
2011-01-01
The dynamics of asymmetrically coupled nonlinear elements is considered. It is shown that there are two distinctive regimes of oscillatory behavior of one-way nonlinearly coupled elements depending on the relaxation time and the strength of the coupling. In the subcritical regime when...... nonlinear model....
A nonlinear discrete integrable coupling system and its infinite conservation laws
Institute of Scientific and Technical Information of China (English)
Yu Fa-Jun
2012-01-01
We construct a nonlinear integrable coupling of discrete soliton hierarchy,and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy.As an explicit application of the method proposed in the paper,the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.
Fitting and forecasting non-linear coupled dark energy
Casas, Santiago; Baldi, Marco; Pettorino, Valeria; Vollmer, Adrian
2015-01-01
We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range $z=0-1.6$ and wave modes below $k=10 \\text{h/Mpc}$. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and w...
Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions
Indian Academy of Sciences (India)
Ajey K Tiwari; A Durga Devi; R Gladwin Pradeep; V K Chandrasekar
2015-11-01
In this paper, we briefly present an overview of the recent developments made in identifying/generating systems of Liénard-type nonlinear oscillators exhibiting isochronous properties, including linear, quadratic and mixed cases and their higher-order generalizations. There exists several procedures/methods in the literature to identify/generate isochronous systems. The application of local as well as nonlocal transformations and -modified Hamiltonian method in identifying and generating systems exhibiting isochronous properties of arbitrary dimensions is also discussed in detail. The identified oscillators include singular and nonsingular Hamiltonian systems and PT-symmetric systems.
DEFF Research Database (Denmark)
Blekhman, I. I.; Sorokin, V. S.
2016-01-01
A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics...... equations). The approach is named as the oscillatory strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that capture the averaged effect of oscillations. The method of direct separation of motions appears to be an efficient...
Amir, Naila; Iqbal, Shahid
2017-08-01
We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau-Klauder formalism and discuss some of their properties. In order to investigate the temporal evolution we first explore the statistical properties by means of weighting distribution and the Mandel parameter. It is found that the temporal evolution of the coherent states may exhibit the phenomena of quantum revivals and fractional revivals for a particular choice of position-dependent mass oscillator.