Nonlinear analysis of ring oscillator circuits

KAUST Repository

Ge, Xiaoqing; Arcak, Murat; Salama, Khaled N.

2010-01-01

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.

On the nonlinear modeling of ring oscillators

KAUST Repository

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.

On the nonlinear modeling of ring oscillators

KAUST Repository

Elwakil, Ahmed S.; Salama, Khaled N.

2009-01-01

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.

Oscillations in nonlinear systems

CERN Document Server

Hale, Jack K

2015-01-01

By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

Aeroelastic Limit-Cycle Oscillations resulting from Aerodynamic Non-Linearities

NARCIS (Netherlands)

van Rooij, A.C.L.M.

2017-01-01

Aerodynamic non-linearities, such as shock waves, boundary layer separation or boundary layer transition, may cause an amplitude limitation of the oscillations induced by the fluid flow around a structure. These aeroelastic limit-cycle oscillations (LCOs) resulting from aerodynamic non-linearities

Chaotic synchronization of two complex nonlinear oscillators

International Nuclear Information System (INIS)

Mahmoud, Gamal M.; Mahmoud, Emad E.; Farghaly, Ahmed A.; Aly, Shaban A.

2009-01-01

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.

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...... alternatives to overcome the difficulty of capturing the periodic behavior of the solution, as the most evident characteristic of oscillators. It can be clearly observed that approximate frequencies and periodic solutions are in excellent agreement with the exact ones. First approximation leads to high...

Analytical solution of strongly nonlinear Duffing oscillators

OpenAIRE

El-Naggar, A.M.; Ismail, G.M.

2016-01-01

In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε)α=α(ε) is defined such that the value of α is always small regardless of the magnitude of the original parameter εε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to αα. Approximate solution obtained by the present method is compared with the solution of energy balance m...

Stabilization of a Network of the FitzHugh–Nagumo Oscillators by Means of a Single Capacitor Based RC Filter Feedback Technique

Directory of Open Access Journals (Sweden)

Elena Adomaitienė

2017-01-01

Full Text Available We suggest employing the first-order stable RC filters, based on a single capacitor, for control of unstable fixed points in an array of oscillators. A single capacitor is sufficient to stabilize an entire array, if the oscillators are coupled strongly enough. An array, composed of 24 to 30 mean-field coupled FitzHugh–Nagumo (FHN type asymmetric oscillators, is considered as a case study. The investigation has been performed using analytical, numerical, and experimental methods. The analytical study is based on the mean-field approach, characteristic equation for finding the eigenvalue spectrum, and the Routh–Hurwitz stability criteria using low-rank Hurwitz matrix to calculate the threshold value of the coupling coefficient. Experiments have been performed with a hardware electronic analog, imitating dynamical behavior of an array of the FHN oscillators.

Nonlinear resonance in Duffing oscillator with fixed and integrative ...

Indian Academy of Sciences (India)

We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter and the strength of the ...

Nonlinear resonance in Duffing oscillator with fixed and integrative ...

Indian Academy of Sciences (India)

2012-03-02

Mar 2, 2012 ... Abstract. We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter α and the ...

Oscillators from nonlinear realizations

Science.gov (United States)

Kozyrev, N.; Krivonos, S.

2018-02-01

We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of nonlinear realizations. We prove that it is always possible to choose time and the fields within this formalism in such a way that the equations of motion become linear and, therefore, reduce to ones of ordinary harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce these equations, can also be provided. As particular examples of this construction, we discuss the so(2, 3) and G 2(2) algebras.

Experimental analysis of nonlinear oscillations in the undergraduate physics laboratory

International Nuclear Information System (INIS)

Moreno, R; Page, A; Riera, J; Hueso, J L

2014-01-01

In this paper, we present a simple experiment to introduce the nonlinear behaviour of oscillating systems in the undergraduate physics laboratory. The transverse oscillations of a spring allow reproduction of three totally different scenarios: linear oscillations, nonlinear oscillations reducible to linear for small displacements, and intrinsically nonlinear oscillations. The chosen approach consists of measuring the displacements using video photogrammetry and computing the velocities and the accelerations by means of a numerical differentiation algorithm. In this way, one can directly check the differential equation of the motion without having to integrate it, or perform an experimental study of the potential energy in each of the analysed scenarios. This experiment allows first year students to reflect on the consequences and the limits of the linearity assumption for small displacements that is so often made in technical studies. (paper)

Classical Yang-Mills mechanics. Nonlinear colour oscillations

International Nuclear Information System (INIS)

Matinyan, S.G.; Savvidi, G.K.; Ter-Arutyunyan-Savvidi, N.G.

1981-01-01

A novel class of solutions of the classical Yang-Mills equations in the Minkowsky space which leads to nonlinear colour oscillations is studied. The system discribing these oscillations is apparently stochastic. Periodic trajectories corresponding to the solutions are found and studied and it is demonstrated that they constitute at least an enumerable set [ru

PT -symmetric dimer of coupled nonlinear oscillators

Indian Academy of Sciences (India)

We provide a systematic analysis of a prototypical nonlinear oscillator ... recently, a number of nonlinear variants have been explored, like split-ring resonator chain .... Note that these solutions are valid for any value of ǫ (and hence δ) including ǫ ..... [16] M Abramowitz and I A Stegun, Handbook of mathematical functions ...

Oscillating solitons in nonlinear optics

Indian Academy of Sciences (India)

The study of solitons in those physical systems reveals some exciting .... With the following power series expansions for g(z,t) and f(z,t): g(z,t) = εg1(z,t) + ... If nonlinearity γ (z) is also taken as a function in figure 1b, the periodic and oscillation.

Nonlinear oscillation regime of electromagnetic disturbances in the equatorial F region

International Nuclear Information System (INIS)

Sazonov, S.V.

1990-01-01

Nonlinear oscillation regime of electromagnetic dicturbances within equatorial ionosphere F-region resulted from Rayleigh-Taylor instability, gradient-drift instability and recombination processes is investigated on the basis of two-liquid quasihydrodynamics equations. It is shown, that at positive linear increment the oscillations are developing in regime with aggregation and are terminated by increment the effect of threshold destabilization, when under certain initial conditions underlgoes oscillation nonlinear swinging, resulting, as well, in bubble formation in contrast to small damping oscillations, is detected

Non-linear neutron star oscillations viewed as deviations from an equilibrium state

International Nuclear Information System (INIS)

Sperhake, U

2002-01-01

A numerical technique is presented which facilitates the evolution of non-linear neutron star oscillations with a high accuracy essentially independent of the oscillation amplitude. We apply this technique to radial neutron star oscillations in a Lagrangian formulation and demonstrate the superior performance of the new scheme compared with 'conventional' techniques. The key feature of our approach is to describe the evolution in terms of deviations from an equilibrium configuration. In contrast to standard perturbation analysis we keep all higher order terms in the evolution equations and thus obtain a fully non-linear description. The advantage of our scheme lies in the elimination of background terms from the equations and the associated numerical errors. The improvements thus achieved will be particularly significant in the study of mildly non-linear effects where the amplitude of the dynamic signal is small compared with the equilibrium values but large enough to warrant non-linear effects. We apply the new technique to the study of non-linear coupling of Eigenmodes and non-linear effects in the oscillations of marginally stable neutron stars. We find non-linear effects in low amplitude oscillations to be particularly pronounced in the range of modes with vanishing frequency which typically mark the onset of instability. (author)

Chimera states in bipartite networks of FitzHugh-Nagumo oscillators

Science.gov (United States)

Wu, Zhi-Min; Cheng, Hong-Yan; Feng, Yuee; Li, Hai-Hong; Dai, Qiong-Lin; Yang, Jun-Zhong

2018-04-01

Chimera states consisting of spatially coherent and incoherent domains have been observed in different topologies such as rings, spheres, and complex networks. In this paper, we investigate bipartite networks of nonlocally coupled FitzHugh-Nagumo (FHN) oscillators in which the units are allocated evenly to two layers, and FHN units interact with each other only when they are in different layers. We report the existence of chimera states in bipartite networks. Owing to the interplay between chimera states in the two layers, many types of chimera states such as in-phase chimera states, antiphase chimera states, and out-of-phase chimera states are classified. Stability diagrams of several typical chimera states in the coupling strength-coupling radius plane, which show strong multistability of chimera states, are explored.

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.

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...

An exactly solvable three-dimensional nonlinear quantum oscillator

International Nuclear Information System (INIS)

Schulze-Halberg, A.; Morris, J. R.

2013-01-01

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

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.

Nonlinearly driven oscillations in the gyrotron traveling-wave amplifier

International Nuclear Information System (INIS)

Chiu, C. C.; Pao, K. F.; Yan, Y. C.; Chu, K. R.; Barnett, L. R.; Luhmann, N. C. Jr.

2008-01-01

By delivering unprecedented power and gain, the gyrotron traveling-wave amplifier (gyro-TWT) offers great promise for advanced millimeter wave radars. However, the underlying physics of this complex nonlinear system is yet to be fully elucidated. Here, we report a new phenomenon in the form of nonlinearly driven oscillations. A zero-drive stable gyro-TWT is shown to be susceptible to a considerably reduced dynamic range at the band edge, followed by a sudden transition into driven oscillations and then a hysteresis effect. An analysis of this unexpected behavior and its physical interpretation are presented.

SIMULATION OF SYNCHRONIZATION OF NONLINEAR OSCILLATORS BY THE EXTERNAL FIELD

Directory of Open Access Journals (Sweden)

V. M. Kuklin

2017-05-01

Full Text Available In this paper, the self-consistent model was considered, consisting of a system of oscillators, the coupling between them was assumed to be integral (due to the fields formed as a result of their co-radiation. With the help of this model, the features of synchronization by waves of finite amplitude of a system of oscillators were refined, the initial phase values of which are random. The effect of nonlinearity, in particular, due to the change in the mass of the oscillator due to relativistic effects, was taken into account. It was shown that the nonlinearity does not violate the nature of the energy exchange between the wave and the oscillator system, leading only to a slight decrease in the efficiency of such an exchange.

SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÖDINGER

Directory of Open Access Journals (Sweden)

T B Prayitno

2012-02-01

Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master Schrödinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution can’t be normalized.   Keywords : harmonic oscillator, nonlinear Schrödinger.

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.

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.

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.

Multisynchronization of chaotic oscillators via nonlinear observer approach.

Science.gov (United States)

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L

2014-01-01

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.

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.

Detecting Nonlinear Oscillations in Broadband Signals

Czech Academy of Sciences Publication Activity Database

Vejmelka, Martin; Paluš, Milan

2009-01-01

Roč. 19, - (2009), 1015114-1-1015114-7 ISSN 1054-1500 R&D Projects: GA MŠk 7E08027 EU Projects: European Commission(XE) 200728 - BRAINSYNC Institutional research plan: CEZ:AV0Z10300504 Keywords : nonlinear dynamical systems * oscillations * random processes * time series analysis * EEG Subject RIV: FH - Neurology Impact factor: 1.795, year: 2009

Forced oscillation of hyperbolic equations with mixed nonlinearities

Directory of Open Access Journals (Sweden)

Yutaka Shoukaku

2012-04-01

Full Text Available In this paper, we consider the mixed nonlinear hyperbolic equations with forcing term via Riccati inequality. Some sufficient conditions for the oscillation are derived by using Young inequality and integral averaging method.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

Science.gov (United States)

Olejnik, Paweł; Awrejcewicz, Jan

2018-01-01

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions

International Nuclear Information System (INIS)

Schulze-Halberg, Axel; Gordon, Christopher R.

2013-01-01

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.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

Science.gov (United States)

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.

Science.gov (United States)

Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang

2017-06-12

Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.

Nonlinear coherent beam-beam oscillations in the rigid bunch model

International Nuclear Information System (INIS)

Dikansky, N.; Pestrikov, D.

1990-01-01

Within the framework of the rigid bunch model coherent oscillations of strong-strong colliding bunches are described by equations which are specific for the weak-strong beam case. In this paper some predictions of the model for properties of nonlinear coherent oscillations as well as for associated limitations of the luminosity are discussed. 14 refs.; 6 figs

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

Science.gov (United States)

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.

Nonlinear dynamics in micromechanical and nanomechanical resonators and oscillators

Science.gov (United States)

Dunn, Tyler

dynamics in passive resonators, self-sustained MEMS are becoming increasingly prevalent in both research and technology for crucial objectives, such as measurement of time. Despite some effort, much work remains in order to understand phase noise and stability for an oscillator based upon a nonlinear resonator. With the eventual goal of making comprehensive measurements of such a nonlinear oscillator with controlled amplitude and phase, this work describes the realization of a micromechanical phase feedback oscillator.

Oscillating particle-like solutions of nonlinear Klein-Gordon equation

International Nuclear Information System (INIS)

Bogolubsky, I.L.

1976-01-01

A denumerable set of oscillating spherically-symmetric particle-like solutions of the Klein-Gordon equation with cubic nonlinearity is found. Extended particles modelled by them turn out to be slightly radiating and long-lived

Non-linear phenomena in electronic systems consisting of coupled single-electron oscillators

International Nuclear Information System (INIS)

Kikombo, Andrew Kilinga; Hirose, Tetsuya; Asai, Tetsuya; Amemiya, Yoshihito

2008-01-01

This paper describes non-linear dynamics of electronic systems consisting of single-electron oscillators. A single-electron oscillator is a circuit made up of a tunneling junction and a resistor, and produces simple relaxation oscillation. Coupled with another, single electron oscillators exhibit complex behavior described by a combination of continuous differential equations and discrete difference equations. Computer simulation shows that a double-oscillator system consisting of two coupled oscillators produces multi-periodic oscillation with a single attractor, and that a quadruple-oscillator system consisting of four oscillators also produces multi-periodic oscillation but has a number of possible attractors and takes one of them determined by initial conditions

Sinusoidal oscillators with lower gain requirements at higher frequencies based on an explicit tanh(x) nonlinearity

KAUST Repository

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.

Oscillation criteria for fourth-order nonlinear delay dynamic equations

Directory of Open Access Journals (Sweden)

Yunsong Qi

2013-03-01

Full Text Available We obtain criteria for the oscillation of all solutions to a fourth-order nonlinear delay dynamic equation on a time scale that is unbounded from above. The results obtained are illustrated with examples

Nonlinear optics in germanium mid-infrared fiber material: Detuning oscillations in femtosecond mid-infrared spectroscopy

Directory of Open Access Journals (Sweden)

M. Ordu

2017-09-01

Full Text Available Germanium optical fibers hold great promise in extending semiconductor photonics into the fundamentally important mid-infrared region of the electromagnetic spectrum. The demonstration of nonlinear response in fabricated Ge fiber samples is a key step in the development of mid-infrared fiber materials. Here we report the observation of detuning oscillations in a germanium fiber in the mid-infrared region using femtosecond dispersed pump-probe spectroscopy. Detuning oscillations are observed in the frequency-resolved response when mid-infrared pump and probe pulses are overlapped in a fiber segment. The oscillations arise from the nonlinear frequency resolved nonlinear (χ(3 response in the germanium semiconductor. Our work represents the first observation of coherent oscillations in the emerging field of germanium mid-infrared fiber optics.

Oscillation criteria for third order delay nonlinear differential equations

Directory of Open Access Journals (Sweden)

E. M. Elabbasy

2012-01-01

via comparison with some first differential equations whose oscillatory characters are known. Our results generalize and improve some known results for oscillation of third order nonlinear differential equations. Some examples are given to illustrate the main results.

Complex behavior in chains of nonlinear oscillators.

Science.gov (United States)

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.

Sensitivity and Nonlinearity of Thermoacoustic Oscillations

Science.gov (United States)

Juniper, Matthew P.; Sujith, R. I.

2018-01-01

Nine decades of rocket engine and gas turbine development have shown that thermoacoustic oscillations are difficult to predict but can usually be eliminated with relatively small ad hoc design changes. These changes can, however, be ruinously expensive to devise. This review explains why linear and nonlinear thermoacoustic behavior is so sensitive to parameters such as operating point, fuel composition, and injector geometry. It shows how nonperiodic behavior arises in experiments and simulations and discusses how fluctuations in thermoacoustic systems with turbulent reacting flow, which are usually filtered or averaged out as noise, can reveal useful information. Finally, it proposes tools to exploit this sensitivity in the future: adjoint-based sensitivity analysis to optimize passive control designs and complex systems theory to warn of impending thermoacoustic oscillations and to identify the most sensitive elements of a thermoacoustic system.

Flutter and limit cycle oscillation suppression using linear and nonlinear tuned vibration absorbers

OpenAIRE

Verstraelen, Edouard; Kerschen, Gaëtan; Dimitriadis, Grigorios

2017-01-01

Aircraft are more than ever pushed to their limits for performance reasons. Consequently, they become increasingly nonlinear and they are more prone to undergo aeroelastic limit cycle oscillations. Structural nonlinearities affect aircraft such as the F-16, which can undergo store-induced limit cycle oscillations (LCOs). Furthermore, transonic buzz can lead to LCOs because of moving shock waves in transonic flight conditions on many aircraft. This study presents a numerical investigation o...

Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities

Science.gov (United States)

Yang, Tao; Cao, Qingjie

2018-03-01

This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.

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 nonlinearity...

Application of He's homotopy perturbation method to conservative truly nonlinear oscillators

International Nuclear Information System (INIS)

Belendez, A.; Belendez, T.; Marquez, A.; Neipp, C.

2008-01-01

We apply He's homotopy perturbation method to find improved approximate solutions to conservative truly nonlinear oscillators. This approach gives us not only a truly periodic solution but also the period 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 in the case of the cubic oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second order approximation we have shown that the relative error in the analytical approximate frequency is approximately 0.03% for any parameter values involved. We also compared the analytical approximate solutions and the Fourier series expansion of the exact solution. This has allowed us to compare the coefficients for the different harmonic terms in these solutions. 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

Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems

DEFF Research Database (Denmark)

Bayat, M.; Shahidi, M.; Barari, Amin

2011-01-01

approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......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...

Nonlinear transient waves in coupled phase oscillators with inertia.

Science.gov (United States)

Jörg, David J

2015-05-01

Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.

Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions

Indian Academy of Sciences (India)

2015-10-13

Oct 13, 2015 ... Isochronous system; Liénard-type system; singular and nonsingular Hamiltonian. ... Liénard-type nonlinear oscillators exhibiting isochronous properties, including linear, quadratic and ... Pramana – Journal of Physics | News.

Chaotic Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...

African Journals Online (AJOL)

With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...

Discrete oscillator design linear, nonlinear, transient, and noise domains

CERN Document Server

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

Nonreciprocity in the dynamics of coupled oscillators with nonlinearity, asymmetry, and scale hierarchy

Science.gov (United States)

Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.

2018-01-01

In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators

KAUST Repository

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.

Bifurcation and synchronization of synaptically coupled FHN models with time delay

International Nuclear Information System (INIS)

Wang Qingyun; Lu Qishao; Chen Guanrong; Feng Zhaosheng; Duan Lixia

2009-01-01

This paper presents an investigation of dynamics of the coupled nonidentical FHN models with synaptic connection, which can exhibit rich bifurcation behavior with variation of the coupling strength. With the time delay being introduced, the coupled neurons may display a transition from the original chaotic motions to periodic ones, which is accompanied by complex bifurcation scenario. At the same time, synchronization of the coupled neurons is studied in terms of their mean frequencies. We also find that the small time delay can induce new period windows with the coupling strength increasing. Moreover, it is found that synchronization of the coupled neurons can be achieved in some parameter ranges and related to their bifurcation transition. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behavior are clarified.

Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

International Nuclear Information System (INIS)

Belendez, A.; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A.

2008-01-01

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

Nonlinear dynamics of a magnetically driven Duffing-type spring–magnet oscillator in the static magnetic field of a coil

International Nuclear Information System (INIS)

Donoso, Guillermo; Ladera, Celso L

2012-01-01

We study the nonlinear oscillations of a forced and weakly dissipative spring–magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet–spring system. The second coil, located below the first, excited with an ac current, provides the oscillating magnetic driving force on the system. From the magnet–coil interactions, we obtain, analytically, the nonlinear motion equation of the system, found to be a forced and damped cubic Duffing oscillator moving in a quartic potential. The relative strengths of the coefficients of the motion equation can be easily set by varying the coils’ dc and ac currents. We demonstrate, theoretically and experimentally, the nonlinear behaviour of this oscillator, including its oscillation modes and nonlinear resonances, the fold-over effect, the hysteresis and amplitude jumps, and its chaotic behaviour. It is an oscillating system suitable for teaching an advanced experiment in nonlinear dynamics both at senior undergraduate and graduate levels. (paper)

Self-synchronization in an ensemble of nonlinear oscillators

Energy Technology Data Exchange (ETDEWEB)

Ostrovsky, L. A., E-mail: lev.ostrovsky@gmail.com [Physical Science Division, NOAA Earth Science Research Laboratory, and University of Colorado, Boulder, Colorado 80305 (United States); Galperin, Y. V.; Skirta, E. A. [Department of Mathematics, East Stroudsburg University, East Stroudsburg, Pennsylvania 18301 (United States)

2016-06-15

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.

Shocks, singularities and oscillations in nonlinear optics and fluid mechanics

CERN Document Server

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. .

Suppressing nonlinear resonances in an impact oscillator using SMAs

International Nuclear Information System (INIS)

Sitnikova, Elena; Pavlovskaia, Ekaterina; Ing, James; Wiercigroch, Marian

2012-01-01

In this paper, we study the resonant responses of an impact oscillator with a one sided SMA motion constraint operating in the pseudoelastic regime. The effectiveness of the SMA restraint in suppressing nonlinear resonances of the impact oscillator is assessed by comparing the dynamic responses of the impact oscillator with SMA and elastic restraints. It is shown that the hysteretic behaviour of the SMA restraint provides an overall vibration reduction in the resonant frequency ranges. Due to the softening behaviour of the SMA element, the resonant frequencies for the SMA oscillator were found to be lower than for the oscillator with an elastic restraint. At each resonance, a single periodic response for the oscillator with the elastic restraint corresponds to two co-existing periodic responses of the SMA oscillator. While at the first resonance peak the emergence of one of the co-existing responses is associated with the hardening effect of the SMA restraint when the pseudoelastic force varies over a complete transformation cycle, at higher frequency resonances incomplete phase transformations in the SMA were detected for both responses. The experimental study undertaken verified the response-modification effects predicted by the numerical analysis conducted under the isothermal approximation. The experimental results showed a good quantitative correspondence with the mathematical modelling. (paper)

Analysis of highly nonlinear oscillation systems using He's max–min ...

Indian Academy of Sciences (India)

Min–max method; nonlinear oscillation; duffing equation; homo- .... where c and ε are the linear and cubic stiffness which do not need to be small in the ..... an easy and direct procedure for determining approximations to the periodic solutions.

Self-oscillations of aircraft landing gear shock-strut at considerable non-linear friction

Directory of Open Access Journals (Sweden)

Б.М. Шифрин

2004-01-01

Full Text Available  The report considers self-oscillations at ε >1. The previous works were dedicated to the elastic frictional L.G. shock strut oscillations, the mathematical model of which is a non-linear differential equation with low ε parameter of its right-hand part.

Oscillation criteria for first-order forced nonlinear difference equations

OpenAIRE

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.

Direct observation of coherent energy transfer in nonlinear micromechanical oscillators.

Science.gov (United States)

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.

Self-excited nonlinear plasma series resonance oscillations in geometrically symmetric capacitively coupled radio frequency discharges

International Nuclear Information System (INIS)

Donko, Z.; Schulze, J.; Czarnetzki, U.; Luggenhoelscher, D.

2009-01-01

At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies

Two-oscillator model of trapped-modes interaction in a nonlinear bilayer fish-scale metamaterial

OpenAIRE

Tuz, Vladimir R.; Kochetov, Bogdan A.; 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 l...

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.

Closed-loop suppression of chaos in nonlinear driven oscillators

Science.gov (United States)

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.

RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios

Directory of Open Access Journals (Sweden)

Zhi-Ling Tang

2016-06-01

Full Text Available 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.

Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity

Science.gov (United States)

Paul Asir, M.; Jeevarekha, A.; Philominathan, P.

This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.

Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator

International Nuclear Information System (INIS)

Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

2009-01-01

In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+αxx+βx 3 +γx=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+αx q x+βx 2q+1 =0, where α, β, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.

Non-linear frequency and amplitude modulation of a nano-contact spin torque oscillator

OpenAIRE

Muduli, P. K.; Pogoryelov, Ye.; Bonetti, S.; Consolo, G.; Mancoff, Fred; Åkerman, Johan

2009-01-01

We study the current controlled modulation of a nano-contact spin torque oscillator. Three principally different cases of frequency non-linearity ($d^{2}f/dI^{2}_{dc}$ being zero, positive, and negative) are investigated. Standard non-linear frequency modulation theory is able to accurately describe the frequency shifts during modulation. However, the power of the modulated sidebands only agrees with calculations based on a recent theory of combined non-linear frequency and amplitude modulation.

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.

Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane

Science.gov (United States)

Zhang, Zhen; Manevitch, Leonid I.; Smirnov, Valeri; Bergman, Lawrence A.; Vakakis, Alexander F.

2018-01-01

We study the in-plane damped oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Strong nonlinearity in this system is generated by geometric effects due to the in-plane stretching of the coupling spring elements. The lattice has a finite number of nonlinear transverse standing waves (termed nonlinear normal modes - NNMs), and an equal number of axial linear modes which are nonlinearly coupled to the transverse ones. Nonlinear interactions between the transverse and axial modes under harmonic excitation give rise to unexpected and extreme nonlinear energy exchanges in the lattice. In particular, we directly excite a transverse NNM by harmonic forcing (causing simulataneous indirect excitation of a corresponding axial linear mode due to nonlinear coupling), and identify three energy transfer mechanisms in the lattice. First, we detect the stable response of the directly excited transverse NNM (despite its instability in the absence of forcing), with simultaneous stability of the indirectly excited axial linear mode. Second, by changing the system and forcing parameters we report extreme nonlinear "energy explosions," whereby, after an initial regime of stability, the directly excited transverse NNM loses stability, leading to abrupt excitation of all transverse and axial modes of the lattice, at all possible wave numbers. This strong instability is triggered by the parametric instability of an indirectly excited axial mode which builds energy until the explosion. This is proved through theoretical analysis. Finally, in other parameter ranges we report intermittent, intense energy transfers from the directly excited transverse NNM to a small set of transverse NNMs with smaller wavelengths, and from the indirectly excited axial mode to a small set of axial modes, but with larger wavelengths. These intermittent energy transfers resemble energy cascades occurring in turbulent flows. Our results show that

Reactor noise analysis based on nonlinear dynamic theory - application to power oscillation

International Nuclear Information System (INIS)

Suzudo, Tomoaki

1993-01-01

The information dimension is one of the simplest quantities that can be used to determine the asymptotic motion of the time evolution of a nonlinear system. The application of this quantity to reactor noise analysis is proposed, and the possibility of its application to power oscillation analysis is examined. The information dimension of this regime is equal to the number of independent oscillating modes, which is an intuitive physical variable. Time series data from computer experiments and experiments with an actual physical system are used for the analysis. The results indicate that the method is useful for a detailed analysis of reactor power oscillation

Coordination of the Walking Stick Insect Using a System of Nonlinear Coupled Oscillators

National Research Council Canada - National Science Library

Marvin, Daryl J

1992-01-01

The area of walking machines is investigated. A design for a central pattern generator composed of nonlinear coupled oscillators which generates the characteristic gaits of the walking stick insect is presented...

Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

International Nuclear Information System (INIS)

Chae, Jongchul; Litvinenko, Yuri E.

2017-01-01

The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D 2 and H α lines.

Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

Energy Technology Data Exchange (ETDEWEB)

Chae, Jongchul [Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826 (Korea, Republic of); Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)

2017-08-01

The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.

On the quantization of a nonlinear oscillator with quasi-harmonic behaviour

International Nuclear Information System (INIS)

Ranada, M.F.; Carinena, J.F.; Satander, M.

2006-01-01

Full text: (author)The quantum version of a non-linear oscillator, depending of a parameter λ, is studied. This λ-dependent system can be considered deformation of the harmonic oscillator in the sense that for λ→0 all the characteristics of the linear oscillator are recovered. This is a problem of quantization of a system with position-dependent mass and with a λ-dependent nonpolynominal rational potential. The quantization problem is solved using existence of a Killing vector, the λ-dependent Schroedinger equation is exactly solved and λ-dependent eigenenergies and eigenfunctions are obtained. The λ-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as deformations of the standard Hermite polynomials. In the second part, it is proved the superintegrability of the two-dimensional system

Rational extension and Jacobi-type Xm solutions of a quantum nonlinear oscillator

International Nuclear Information System (INIS)

Schulze-Halberg, Axel; Roy, Barnana

2013-01-01

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 m exceptional orthogonal polynomials

Effects produced by oscillations applied to nonlinear dynamic systems: a general approach and examples

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.......g., the requirement for the involved nonlinearities to be weak. The approach is illustrated by several relevant examples from various fields of science, e.g., mechanics, physics, chemistry and biophysics....... 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...

Large time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics

OpenAIRE

Jochmann, Frank

2005-01-01

The anharmonic oscillator model describing the propagation of electromagnetic waves in an exterior domain containing a nonlinear dielectric medium is investigated. The system under consideration consists of a generally nonlinear second order differential equation for the dielectrical polarization coupled with Maxwell's equations for the electromagnetic field. Local decay of the electromagnetic field for t to infinity in the charge free case is shown for a large class of potentials. (This pape...

An Apparatus to Demonstrate Linear and Nonlinear Oscillations of a Pendulum

Science.gov (United States)

Mayer, V. V.; Varaksina, E. I.

2016-01-01

A physical pendulum with a magnetic load is proposed for comparison of linear and nonlinear oscillations. The magnetic load is repelled by permanent magnets which are disposed symmetrically relative to the load. It is established that positions of the pendulum and the magnets determine the dependence of restoring force on displacement of the load.…

Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

International Nuclear Information System (INIS)

Lai, S K; Chow, K W

2012-01-01

Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)

Periodic oscillations in linear continuous media coupled with nonlinear discrete systems

International Nuclear Information System (INIS)

Lupini, R.

1998-01-01

A general derivation of partial differential equations with boundary conditions in the form of ordinary differential equations is obtained using the principle of stationary action for a Lagrangian function composed of continuous plus discrete parts in interaction across the boundaries of a 1-dimensional medium. This approach leads directly to the theorem of energy conservation. For linear continuous medium, homogeneous Dirichlet condition at one boundary, and nonlinear oscillator at the other boundary, the entire differential problem reduces to a nonlinear differential-difference equation of neutral type and of the second order. The lag parameter is τ = l/c, where c is the phase speed, l the length of the continuum. The Author investigate the problem of the occurrence of periodic solutions of period integer multiple of the lag (super harmonic solutions) in the case of zero inertia of the boundary system. The problem for such oscillations is shown to reduce to systems of ordinary differential equations with matching conditions in a phase space of lower dimensionality: Phase-plane techniques are used to determine solutions of period 4τ, 8τ and 6τ

Nonreciprocal acoustics and dynamics in the in-plane oscillations of a geometrically nonlinear lattice.

Science.gov (United States)

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 "NL 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

On the non-linear dynamics of potential relaxation oscillations in bounded plasmas

International Nuclear Information System (INIS)

Krssak, M.; Skalny, J.D.; Gyergyek, T.; Cercek, M.

2007-01-01

Plasma in a 1-dimensional diode is studied theoretically and the computer simulations are used for verification of the theoretical model. When collector in the diode is biased positively, a double-layer is created in the system and consequently, we are able to observe oscillations of the potential, density and other plasma parameters. When external periodic forcing is applied, spectra of these oscillations are changed and effects of synchronisation and periodic pulling can be observed. Both of these effects are of non-linear nature and a good explanation is found using the analogy with Van der Pol oscillators. Following [1] and [2] approximate analytical solutions are found and then compared with computer simulations obtained using a 1-dimensional particle-in-cell code XPDP1. (author)

Self-synchronization of populations of nonlinear oscillators in the thermodynamic limit

International Nuclear Information System (INIS)

Bonilla, L.L.; Casado, J.M.; Morillo, M.

1987-01-01

A population of identical nonlinear oscillators, subject to random forces and coupled via a mean-field interaction, is studied in the thermodynamic limit. The model presents a nonequilibrium phase transition from a stationary to a time-periodic probability density. Below the transition line, the population of oscillators is in a quiescent state with order parameter equal to zero. Above the transition line, there is a state of collective rhythmicity characterized by a time-periodic behavior of the order parameter and all moments of the probability distribution. The information entropy of the ensemble is a constant both below and above the critical line. Analytical and numerical analyses of the model are provided

Nonlinear theory for axisymmetric self-similar two-dimensional oscillations of electrons in cold plasma with constant proton background

Science.gov (United States)

Osherovich, V. A.; Fainberg, J.

2018-01-01

We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.

Signatures of nonlinearity in single cell noise-induced oscillations.

Science.gov (United States)

Thomas, Philipp; Straube, Arthur V; Timmer, Jens; Fleck, Christian; Grima, Ramon

2013-10-21

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 spectrum which measures the dependence of the oscillatory signal's power with frequency. In this paper we derive an approximate closed-form expression for the power spectrum of any monostable biochemical system close to a Hopf bifurcation, where noise-induced oscillations are most pronounced. Unlike the commonly used linear noise approximation which is valid in the macroscopic limit of large volumes, our theory is valid over a wide range of volumes and hence affords a more suitable description of single cell noise-induced oscillations. Our theory predicts that the spectra have three universal features: (i) a dominant peak at some frequency, (ii) a smaller peak at twice the frequency of the dominant peak and (iii) a peak at zero frequency. Of these, the linear noise approximation predicts only the first feature while the remaining two stem from the combination of intrinsic noise and nonlinearity in the law of mass action. The theoretical expressions are shown to accurately match the power spectra determined from stochastic simulations of mitotic and circadian oscillators. Furthermore it is shown how recently acquired single cell rhythmic fibroblast data displays all the features predicted by our theory and that the experimental spectrum is well described by our theory but not by the conventional linear noise approximation. © 2013 Elsevier Ltd. All rights reserved.

Higher-Order Approximations of Motion of a Nonlinear Oscillator Using the Parameter Expansion Technique

Science.gov (United States)

Ganji, S. S.; Domairry, G.; Davodi, A. G.; Babazadeh, H.; Seyedalizadeh Ganji, S. H.

The main objective of this paper is to apply the parameter expansion technique (a modified Lindstedt-Poincaré method) to calculate the first, second, and third-order approximations of motion of a nonlinear oscillator arising in rigid rod rocking back. The dynamics and frequency of motion of this nonlinear mechanical system are analyzed. A meticulous attention is carried out to the study of the introduced nonlinearity effects on the amplitudes of the oscillatory states and on the bifurcation structures. We examine the synchronization and the frequency of systems using both the strong and special method. Numerical simulations and computer's answers confirm and complement the results obtained by the analytical approach. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. The solutions of this method are compared with the exact ones in order to validate the approach, and assess the accuracy of the solutions. In particular, APL-PM works well for the whole range of oscillation amplitudes and excellent agreement of the approximate frequency with the exact one has been demonstrated. The approximate period derived here is accurate and close to the exact solution. This method has a distinguished feature which makes it simple to use, and also it agrees with the exact solutions for various parameters.

Quantum dynamics and breakdown of classical realism in nonlinear oscillators

International Nuclear Information System (INIS)

Gat, Omri

2007-01-01

The leading nonclassical term in the quantum dynamics of nonlinear oscillators is calculated in the Moyal quasi-trajectory representation. The irreducibility of the quantum dynamics to phase-space trajectories is quantified by the discrepancy of the canonical quasi-flow and the quasi-flow of a general observable. This discrepancy is shown to imply the breakdown of classical realism that can give rise to a dynamical violation of Bell's inequalities. (fast track communication)

Special function solutions of a spectral problem for a nonlinear quantum oscillator

International Nuclear Information System (INIS)

Schulze-Halberg, A; Morris, J R

2012-01-01

We construct exact solutions of a spectral problem involving the Schrödinger equation for a nonlinear, one-parameter oscillator potential. In contrast to a previous analysis of the problem (Carinena et al 2007 Ann. Phys. 322 434–59), where solutions were given through a Rodrigues-type formula, our approach leads to closed-form representations of the solutions in terms of special functions, not containing any derivative operators. We show normalizability and orthogonality of our solutions, as well as correct reduction of the problem to the harmonic oscillator model, if the parameter in the potential gets close to zero. (paper)

Parametric excitation of nonlinear longitudinal oscillations in a magnetoactive plasma

International Nuclear Information System (INIS)

Demchenko, V.V.

1977-01-01

Parametric excitation by HF field of nonlinear longitudinal electron oscillations in the region of hybrid resonances of a cold nonrelativistic plasma has been investigated. It is shown that the inhomogeneity of a pumping field and that of the equilibrium plasma density result in the parametric instability. Expressions are derived for the increments of instable oscillations and the widths of the instability regions are determined. The increments of instable oscillations in the order of magnitude due to the inhomogeneities of the pumping field (γsub(E)) or of the plasma density (γsub(N)) are egual to γsub(E) approximately k(zetasub(0)) ωsub(pe), γsub(N) approximately (zetasub(0))/Lωsub(pe), where (zetasub(0))=(e)Esub(0)/msub(e)ωsub(0)sup(2) is the amplitude of displacement of an electron from the equilibrium state, k, ω 0 , E 0 are the wave number, frequency and amplitude of the pumping field, L is the characteristic size of the inhomogeneity of the plasma density, ωsub(pe) is the electron plasma frequency

Robust nonlinear model predictive control for nuclear power plants in load following operations with bounded xenon oscillations

International Nuclear Information System (INIS)

Eliasi, H.; Menhaj, M.B.; Davilu, H.

2011-01-01

Research highlights: → In this work, a robust nonlinear model predictive control algorithm is developed. → This algorithm is applied to control the power level for load following. → The state constraints are imposed on the predicted trajectory during optimization. → The xenon oscillations are the main constraint for the load following problem. → In this algorithm, xenon oscillations are bounded within acceptable limits. - Abstract: One of the important operations in nuclear power plants is load-following in which imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation considered to be a constraint for the load-following operation. In this paper, a robust nonlinear model predictive control for the load-following operation problem is proposed that ensures xenon oscillations are kept bounded within acceptable limits. The proposed controller uses constant axial offset (AO) strategy to maintain xenon oscillations to be bounded. The constant AO is a robust state constraint for load-following problem. The controller imposes restricted state constraints on the predicted trajectory during optimization which guarantees robust satisfaction of state constraints without restoring to a min-max optimization problem. Simulation results show that the proposed controller for the load-following operation is so effective so that the xenon oscillations kept bounded in the given region.

Phase mixing of transverse oscillations in the linear and nonlinear regimes for IFR relativistic electron beam propagation

International Nuclear Information System (INIS)

Shokair, I.R.

1991-01-01

Phase mixing of transverse oscillations changes the nature of the ion hose instability from an absolute to a convective instability. The stronger the phase mixing, the faster an electron beam reaches equilibrium with the guiding ion channel. This is important for long distance propagation of relativistic electron beams where it is desired that transverse oscillations phase mix within a few betatron wavelengths of injection and subsequently an equilibrium is reached with no further beam emittance growth. In the linear regime phase mixing is well understood and results in asymptotic decay of transverse oscillations as 1/Z 2 for a Gaussian beam and channel system, Z being the axial distance measured in betatron wavelengths. In the nonlinear regime (which is likely mode of propagation for long pulse beams) results of the spread mass model indicate that phase mixing is considerably weaker than in the regime. In this paper we consider this problem of phase mixing in the nonlinear regime. Results of the spread mass model will be shown along with a simple analysis of phase mixing for multiple oscillator models. Particle simulations also indicate that phase mixing is weaker in nonlinear regime than in the linear regime. These results will also be shown. 3 refs., 4 figs

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.

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$.

Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems

Directory of Open Access Journals (Sweden)

Qi Wang

2012-01-01

Full Text Available This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t=β0ωμp(t−τ/(ωμ+pμ(t−τ−γp(t and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.

Dynamics of a nonlinear oscillator and a low-amplitude frequency-modulated wave

International Nuclear Information System (INIS)

White, R.C.; McNamara, B.

1987-01-01

When the frequency of a small amplitude plane wave is varied slowly over a large enough bandwidth and this wave is incident upon a nonlinear oscillator, the resulting perturbed motion can exhibit stochastic behavior. Applications for the study of this system are wide and varied. We apply Lie-transform perturbation theory and mapping techniques in the analysis of the stochastic transition and the consequent induced diffusion in the oscillator phase space. A constant of the motion to the first order in a peturbation parameter is calculated, a mapping approximation is derived, and diffusion calculations from the mapping are given. Copyright 1987 Academic Press, Inc

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

Science.gov (United States)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

Oscillation of Nonlinear Delay Differential Equation with Non-Monotone Arguments

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Özkan Öcalan

2017-07-01

Full Text Available Consider the first-order nonlinear retarded differential equation $$ x^{\\prime }(t+p(tf\\left( x\\left( \\tau (t\\right \\right =0, t\\geq t_{0} $$ where $p(t$ and $\\tau (t$ are function of positive real numbers such that $%\\tau (t\\leq t$ for$\\ t\\geq t_{0},\\ $and$\\ \\lim_{t\\rightarrow \\infty }\\tau(t=\\infty $. Under the assumption that the retarded argument is non-monotone, new oscillation results are given. An example illustrating the result is also given.

Nonlinear Oscillations in Biology and Chemistry

CERN Document Server

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...

Cardiovascular oscillations: in search of a nonlinear parametric model

Science.gov (United States)

Bandrivskyy, Andriy; Luchinsky, Dmitry; McClintock, Peter V.; Smelyanskiy, Vadim; Stefanovska, Aneta; Timucin, Dogan

2003-05-01

We suggest a fresh approach to the modeling of the human cardiovascular system. Taking advantage of a new Bayesian inference technique, able to deal with stochastic nonlinear systems, we show that one can estimate parameters for models of the cardiovascular system directly from measured time series. We present preliminary results of inference of parameters of a model of coupled oscillators from measured cardiovascular data addressing cardiorespiratory interaction. We argue that the inference technique offers a very promising tool for the modeling, able to contribute significantly towards the solution of a long standing challenge -- development of new diagnostic techniques based on noninvasive measurements.

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.

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.

Flavor Oscillations in the Supernova Hot Bubble Region: Nonlinear Effects of Neutrino Background

Science.gov (United States)

Pastor, Sergio; Raffelt, Georg

2002-10-01

The neutrino flux close to a supernova core contributes substantially to neutrino refraction so that flavor oscillations become a nonlinear phenomenon. One unexpected consequence is efficient flavor transformation for antineutrinos in a region where only neutrinos encounter a Mikheyev-Smirnov-Wolfenstein resonance or vice versa. Contrary to previous studies we find that in the neutrino-driven wind the electron fraction Ye always stays below 0.5, corresponding to a neutron-rich environment as required by r-process nucleosynthesis. The relevant range of masses and mixing angles includes the region indicated by LSND, but not the atmospheric or solar oscillation parameters.

Comparison among nonlinear excitation control strategies used for damping power system oscillations

International Nuclear Information System (INIS)

Leon, A.E.; Solsona, J.A.; Valla, M.I.

2012-01-01

Highlights: ► A description and comparison of nonlinear control strategies for synchronous generators are presented. ► Advantages of using nonlinear controllers are emphasized against the use of classical PSSs. ► We find that a particular selection of IDA gains achieve the same performance that FL controllers. - Abstract: This work is focused on the problem of power system stability. A thorough description of nonlinear control strategies for synchronous generator excitation, which are designed for damping oscillations and improving transient stability on power systems, is presented along with a detailed comparison among these modern strategies and current solutions based on power system stabilizers. The performance related to damping injection in each controller, critical time enhancement, robustness against parametric uncertainties, and control signal energy consumption is analyzed. Several tests are presented to validate discussions on various advantages and disadvantages of each control strategy.

Effect of state-dependent delay on a weakly damped nonlinear oscillator.

Science.gov (United States)

Mitchell, Jonathan L; Carr, Thomas W

2011-04-01

We consider a weakly damped nonlinear oscillator with state-dependent delay, which has applications in models for lasers, epidemics, and microparasites. More generally, the delay-differential equations considered are a predator-prey system where the delayed term is linear and represents the proliferation of the predator. We determine the critical value of the delay that causes the steady state to become unstable to periodic oscillations via a Hopf bifurcation. Using asymptotic averaging, we determine how the system's behavior is influenced by the functional form of the state-dependent delay. Specifically, we determine whether the branch of periodic solutions will be either sub- or supercritical as well as an accurate estimation of the amplitude. Finally, we choose a few examples of state-dependent delay to test our analytical results by comparing them to numerical continuation.

Nonlinearity in oscillating bridges

Directory of Open Access Journals (Sweden)

Filippo Gazzola

2013-09-01

Full Text Available We first recall several historical oscillating bridges that, in some cases, led to collapses. Some of them are quite recent and show that, nowadays, oscillations in suspension bridges are not yet well understood. Next, we survey some attempts to model bridges with differential equations. Although these equations arise from quite different scientific communities, they display some common features. One of them, which we believe to be incorrect, is the acceptance of the linear Hooke law in elasticity. This law should be used only in presence of small deviations from equilibrium, a situation which does not occur in widely oscillating bridges. Then we discuss a couple of recent models whose solutions exhibit self-excited oscillations, the phenomenon visible in real bridges. This suggests a different point of view in modeling equations and gives a strong hint how to modify the existing models in order to obtain a reliable theory. The purpose of this paper is precisely to highlight the necessity of revisiting the classical models, to introduce reliable models, and to indicate the steps we believe necessary to reach this target.

Hamiltonian formulation and statistics of an attracting system of nonlinear oscillators

International Nuclear Information System (INIS)

Tasso, H.

1987-10-01

An attracting system of r nonlinear oscillators of an extended van der Pol type was investigated with respect to Hamiltonian formulation. The case of r=2 is rather simple, though nontrivial. For r>2 the tests with Jacobi's identity and Frechet derivatives are negative if Hamiltonians in the natural variables are looked for. Independently, a Liouville theorem is proved and equilibrium statistics is made possible, which leads to a Gaussian distribution in the natural variables. (orig.)

A memristor-based third-order oscillator: beyond oscillation

KAUST Repository

Talukdar, Abdul Hafiz Ibne

2012-10-06

This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.

A memristor-based third-order oscillator: beyond oscillation

KAUST Repository

Talukdar, Abdul Hafiz Ibne; Radwan, Ahmed G.; Salama, Khaled N.

2012-01-01

This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.

Nature's Autonomous Oscillators

Science.gov (United States)

Mayr, H. G.; Yee, J.-H.; Mayr, M.; Schnetzler, R.

2012-01-01

Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

Science.gov (United States)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring

International Nuclear Information System (INIS)

Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.

2009-01-01

The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed

Quantum perturbation solution of sextic nonlinear oscillator and its classical limit

International Nuclear Information System (INIS)

Jafarpour, M.; Ashrafpour, M.

2000-01-01

We consider the time evolution of the perturbed coherent states to solve the quantum sex tic nonlinear oscillator, in the framework of time dependent perturbation theory. An appropriate limit, h-bar → 0, (absolute value of α)→ ∞,(absolute value of α )√h-bar fixed, is then taken and the classical Poincare'-Landsat series is retrieved. We observe that a proper renormalization of the amplitude and the frequency is needed, if a meaningful comparison between the quantum and the classical results are to be made

Computing with networks of nonlinear mechanical oscillators.

Directory of Open Access Journals (Sweden)

Jean C Coulombe

Full Text Available As it is getting increasingly difficult to achieve gains in the density and power efficiency of microelectronic computing devices because of lithographic techniques reaching fundamental physical limits, new approaches are required to maximize the benefits of distributed sensors, micro-robots or smart materials. Biologically-inspired devices, such as artificial neural networks, can process information with a high level of parallelism to efficiently solve difficult problems, even when implemented using conventional microelectronic technologies. We describe a mechanical device, which operates in a manner similar to artificial neural networks, to solve efficiently two difficult benchmark problems (computing the parity of a bit stream, and classifying spoken words. The device consists in a network of masses coupled by linear springs and attached to a substrate by non-linear springs, thus forming a network of anharmonic oscillators. As the masses can directly couple to forces applied on the device, this approach combines sensing and computing functions in a single power-efficient device with compact dimensions.

Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators.

Science.gov (United States)

Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao

2014-10-06

Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.

Synchronization of delay-coupled nonlinear oscillators : an approach based on the stability analysis of synchronized equilibria

NARCIS (Netherlands)

Michiels, W.; Nijmeijer, H.

2009-01-01

We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the

Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling.

Science.gov (United States)

Ryu, Jung-Wan; Kim, Jong-Ho; Son, Woo-Sik; Hwang, Dong-Uk

2017-08-01

We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.

Oscillators and Eigenvalues

DEFF Research Database (Denmark)

Lindberg, Erik

1997-01-01

In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear wit...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos....

Nonlinear state-space modelling of the kinematics of an oscillating circular cylinder in a fluid flow

Science.gov (United States)

Decuyper, J.; De Troyer, T.; Runacres, M. C.; Tiels, K.; Schoukens, J.

2018-01-01

The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing.

Science.gov (United States)

Chen, Bor-Sen; Hsu, Chih-Yuan

2012-10-26

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. 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, which could be solved with the help of LMI

Quantifying non-linear dynamics of mass-springs in series oscillators via asymptotic approach

Science.gov (United States)

Starosta, Roman; Sypniewska-Kamińska, Grażyna; Awrejcewicz, Jan

2017-05-01

Dynamical regular response of an oscillator with two serially connected springs with nonlinear characteristics of cubic type and governed by a set of differential-algebraic equations (DAEs) is studied. The classical approach of the multiple scales method (MSM) in time domain has been employed and appropriately modified to solve the governing DAEs of two systems, i.e. with one- and two degrees-of-freedom. The approximate analytical solutions have been verified by numerical simulations.

Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators

International Nuclear Information System (INIS)

El Kinani, A.H; Daoud, M.

2001-10-01

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states a la Gazeau-Klauder and those a la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways. (author)

Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators

Energy Technology Data Exchange (ETDEWEB)

Emenheiser, Jeffrey [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Chapman, Airlie; Mesbahi, Mehran [William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States); Pósfai, Márton [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Crutchfield, James P. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); D' Souza, Raissa M. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States)

2016-09-15

Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.

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.

Frequency comb generation by a continuous-wave-pumped optical parametric oscillator based on cascading quadratic nonlinearities.

Science.gov (United States)

Ulvila, Ville; Phillips, C R; Halonen, Lauri; Vainio, Markku

2013-11-01

We report optical frequency comb generation by a continuous-wave pumped optical parametric oscillator (OPO) without any active modulation. The OPO is configured as singly resonant with an additional nonlinear crystal (periodically poled MgO:LiNbO3) placed inside the OPO for phase mismatched second harmonic generation (SHG) of the resonating signal beam. The phase mismatched SHG causes cascading χ(2) nonlinearities, which can substantially increase the effective χ(3) nonlinearity in MgO:LiNbO3, leading to spectral broadening of the OPO signal beam via self-phase modulation. The OPO generates a stable 4 THz wide (-30 dB) frequency comb centered at 1.56 μm.

Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

Directory of Open Access Journals (Sweden)

Paulius Palevicius

2014-01-01

Full Text Available Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.

Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

Science.gov (United States)

Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

2014-01-01

Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467

Applicability of time-averaged holography for micro-electro-mechanical system performing non-linear oscillations.

Science.gov (United States)

Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

2014-01-21

Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.

A new analytical approach for limit cycles and quasi-periodic solutions of nonlinear oscillators: the example of the forced Van der Pol Duffing oscillator

International Nuclear Information System (INIS)

Shukla, Anant Kant; Ramamohan, T R; Srinivas, S

2014-01-01

In this paper we propose a technique to obtain limit cycles and quasi-periodic solutions of forced nonlinear oscillators. We apply this technique to the forced Van der Pol oscillator and the forced Van der Pol Duffing oscillator and obtain for the first time their limit cycles (periodic) and quasi-periodic solutions analytically. We introduce a modification of the homotopy analysis method to obtain these solutions. We minimize the square residual error to obtain accurate approximations to these solutions. The obtained analytical solutions are convergent and agree well with numerical solutions even at large times. Time trajectories of the solution, its first derivative and phase plots are presented to confirm the validity of the proposed approach. We also provide rough criteria for the determination of parameter regimes which lead to limit cycle or quasi-periodic behaviour. (papers)

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

Science.gov (United States)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

FREQUENCY CATASTROPHE AND CO-EXISTING ATTRACTORS IN A CELL Ca2+ NONLINEAR OSCILLATION MODEL WITH TIME DELAY*

Institute of Scientific and Technical Information of China (English)

应阳君; 黄祖洽

2001-01-01

Frequency catastrophe is found in a cell Ca2+ nonlinear oscillation model with time delay. The relation of the frequency transition to the time delay is studied by numerical simulations and theoretical analysis. There is a range of parameters in which two kinds of attractors with great frequency differences co-exist in the system. Along with parameter changes, a critical phenomenon occurs and the oscillation frequency changes greatly. This mechanism helps us to deepen the understanding of the complex dynamics of delay systems, and might be of some meaning in cell signalling.

Oscillating patterns in image processing and nonlinear evolution equations the fifteenth Dean Jacqueline B. Lewis memorial lectures

CERN Document Server

Meyer, Yves

2001-01-01

Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of "oscillating patterns", which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals. The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and their use in the detection of gravitational waves are covered in the final chapter. In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics invo...

Existence of periodic orbits in nonlinear oscillators of Emden–Fowler form

Energy Technology Data Exchange (ETDEWEB)

Mancas, Stefan C., E-mail: mancass@erau.edu [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, SLP (Mexico)

2016-01-28

The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden–Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also allows us to construct periodic solutions to them. Two other nonlinear equations, a zero-frequency Ermakov equation and a positive power Emden–Fowler equation, are discussed in the same context. - Highlights: • An invariant transformation is used to find periodic solution of EF equations. • Phase plane study of the EF autonomous two-dimensional ODE system is performed. • Three examples are presented from the standpoint of the phase plane analysis.

A nonlinear oscillator with parametric coloured noise: some analytical results

International Nuclear Information System (INIS)

Mallick, Kirone; Marcq, Philippe

2005-01-01

The asymptotic behaviour of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as compared to the energy. Thus, an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out. However, the standard elimination procedure, performed earlier for a Gaussian white noise, fails when the noise is coloured because of correlations between the noise and the fast angular variable. We develop here a specific averaging scheme that retains these correlations. This allows us to calculate the probability distribution function (PDF) of the system and to derive the behaviour of physical observables in the long time limit

Quantum Nonlinear Optics

CERN Document Server

Hanamura, Eiichi; Yamanaka, Akio

2007-01-01

This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.

Pure odd-order oscillators with constant excitation

Science.gov (United States)

Cveticanin, L.

2011-02-01

In this paper the excited vibrations of a truly nonlinear oscillator are analyzed. The excitation is assumed to be constant and the nonlinearity is pure (without a linear term). The mathematical model is a second-order nonhomogeneous differential equation with strong nonlinear term. Using the first integral, the exact value of period of vibration i.e., angular frequency of oscillator described with a pure nonlinear differential equation with constant excitation is analytically obtained. The closed form solution has the form of gamma function. The period of vibration depends on the value of excitation and of the order and coefficient of the nonlinear term. For the case of pure odd-order-oscillators the approximate solution of differential equation is obtained in the form of trigonometric function. The solution is based on the exact value of period of vibration. For the case when additional small perturbation of the pure oscillator acts, the so called 'Cveticanin's averaging method' for a truly nonlinear oscillator is applied. Two special cases are considered: one, when the additional term is a function of distance, and the second, when damping acts. To prove the correctness of the method the obtained results are compared with those for the linear oscillator. Example of pure cubic oscillator with constant excitation and linear damping is widely discussed. Comparing the analytically obtained results with exact numerical ones it is concluded that they are in a good agreement. The investigations reported in the paper are of special interest for those who are dealing with the problem of vibration reduction in the oscillator with constant excitation and pure nonlinear restoring force the examples of which can be found in various scientific and engineering systems. For example, such mechanical systems are seats in vehicles, supports for machines, cutting machines with periodical motion of the cutting tools, presses, etc. The examples can be find in electronics

Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators

Energy Technology Data Exchange (ETDEWEB)

Senthilkumar, D. V., E-mail: skumarusnld@gmail.com [School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016 (India); Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Suresh, K. [Department of Physics, Anjalai Ammal-Engineering College, Kovilvenni 614 403, Tamilnadu (India); Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Chandrasekar, V. K. [Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Zou, Wei [School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 (China); Centre for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074 (China); Dana, Syamal K. [CSIR-Indian Institute of Chemical Biology, Kolkata 700032 (India); Kathamuthu, Thamilmaran [Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, Telegrafenberg, Potsdam D-14415 (Germany); Institute of Physics, Humboldt University Berlin, Berlin D-12489 (Germany); Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX (United Kingdom); Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod (Russian Federation)

2016-04-15

We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.

The colpitts oscillator family

DEFF Research Database (Denmark)

Lindberg, Erik; Murali, K.; Tamasevicius, A.

A tutorial study of the Colpitts oscillator family defined as all oscillators based on a nonlinear amplifier and a three- terminal linear resonance circuit with one coil and two capacitors. The original patents are investigated. The eigenvalues of the linearized Jacobian for oscillators based...

Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.

Energy Technology Data Exchange (ETDEWEB)

Robinson, Brandon [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Rocha da Costa, Leandro Jose [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Poirel, Dominique [Royal Military College of Canada, Kingston (Canada). Dept. of Mechanical and Aerospace Engineering; Pettit, Chris [US Naval Academy, Annapolis, MD (United States). Dept. of Mechanical and Aerospace Engineering; Khalil, Mohammad [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sarkar, Abhijit [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering

2017-09-01

Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.

Small systems of Duffing oscillators and the Fermi-Pasta-Ulam-Tsingou system An examination of the possible reasons for the unusual stability of localized nonlinear excitations in these systems

Science.gov (United States)

Kashyap, Rahul; Westley, Alexandra; Sen, Surajit

The Duffing oscillator, a nonlinear oscillator with a potential energy with both quadratic and cubic terms, is known to show highly chaotic solutions in certain regions of its parameter space. Here, we examine the behaviors of small chains of harmonically and anharmonically coupled Duffing oscillators and show that these chains exhibit localized nonlinear excitations (LNEs) similar to the ones seen in the Fermi-Pasta-Ulam-Tsingou (FPUT) system. These LNEs demonstrate properties such as long-time energy localization, high periodicity, and slow energy leaking which rapidly accelerates upon frequency matching with the adjacent particles all of which have been observed in the FPUT system. Furthermore, by examining bifurcation diagrams, we will show that many qualitative properties of this system during the transition from weakly to strongly nonlinear behavior depend directly upon the frequencies associated with the individual Duffing oscillators.

Power-level regulation and simulation of nonlinear pressurized water reactor core with xenon oscillation using H-infinity loop shaping control

Directory of Open Access Journals (Sweden)

Li Gang

2016-01-01

Full Text Available This investigation is to solve the power-level control issue of a nonlinear pressurized water reactor core with xenon oscillations. A nonlinear pressurized water reactor core is modeled using the lumped parameter method, and a linear model of the core is then obtained through the small perturbation linearization way. The H∞loop shapingcontrolis utilized to design a robust controller of the linearized core model.The calculated H∞loop shaping controller is applied to the nonlinear core model. The nonlinear core model and the H∞ loop shaping controller build the nonlinear core power-level H∞loop shaping control system.Finally, the nonlinear core power-level H∞loop shaping control system is simulatedconsidering two typical load processes that are a step load maneuver and a ramp load maneuver, and simulation results show that the nonlinear control system is effective.

Noise-induced chaos in a quadratically nonlinear oscillator

International Nuclear Information System (INIS)

Gan Chunbiao

2006-01-01

The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system

State space modeling of Memristor-based Wien oscillator

KAUST Repository

Talukdar, Abdul Hafiz Ibne; Radwan, Ahmed G.; Salama, Khaled N.

2011-01-01

State space modeling of Memristor based Wien 'A' oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.

State space modeling of Memristor-based Wien oscillator

KAUST Repository

Talukdar, Abdul Hafiz Ibne

2011-12-01

State space modeling of Memristor based Wien \\'A\\' oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.

Support-Vector-Machine-Based Reduced-Order Model for Limit Cycle Oscillation Prediction of Nonlinear Aeroelastic System

Directory of Open Access Journals (Sweden)

Gang Chen

2012-01-01

Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.

History of nonlinear oscillations theory in France (1880-1940)

CERN Document Server

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...

The role of nonlinear torsional contributions on the stability of flexural-torsional oscillations of open-cross section beams

Science.gov (United States)

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.

Rayleigh-type parametric chemical oscillation

Energy Technology Data Exchange (ETDEWEB)

Ghosh, Shyamolina; Ray, Deb Shankar, E-mail: pcdsr@iacs.res.in [Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032 (India)

2015-09-28

We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.

Rayleigh-type parametric chemical oscillation.

Science.gov (United States)

Ghosh, Shyamolina; Ray, Deb Shankar

2015-09-28

We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.

Chimera regimes in a ring of oscillators with local nonlinear interaction

Science.gov (United States)

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.

Coupled oscillators with parity-time symmetry

Energy Technology Data Exchange (ETDEWEB)

Tsoy, Eduard N., E-mail: etsoy@uzsci.net

2017-02-05

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. - Highlights: • A generalization of a Hamiltonian system of linear coupled oscillators with the parity-time (PT) symmetry is suggested. • It is found that an increase of the gain-loss parameter can stabilize the system. • A family of Hamiltonian functions for two coupled nonlinear oscillators with PT-symmetry is obtained.

Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method

International Nuclear Information System (INIS)

Belendez, A.; Belendez, T.; Neipp, C.; Hernandez, A.; Alvarez, M.L.

2009-01-01

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ≤ λ ≤ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.

Effect of boundary on controlled memristor-based oscillator

KAUST Repository

Fouda, Mohamed E.

2012-10-01

Recently, the applications of memristors have spread into many fields and especially in the circuit theory. Many models have been proposed for the HP-memristor based on the window functions. In this paper, we introduce a complete mathematical analysis of the controlled reactance-less oscillator for two different window functions of Joglekar\\'s model (linear and nonlinear dopant drift) to discuss the effect of changing the window function on the oscillator\\'s behavior. The generalized necessary and sufficient conditions based on the circuit elements and control voltages for both the linear and nonlinear models are introduced. Moreover, closed form expressions for the oscillation frequency and duty cycle are derived for these models and verified using PSPICE simulations showing an excellent matching. Finally a comparison between the linear and nonlinear models which shows their effect on the oscillation frequency and conditions of oscillation is introduced. © 2012 IEEE.

Linear and nonlinear piezoelectric shunting strategies for vibration mitigation

Directory of Open Access Journals (Sweden)

Soltani P.

2014-01-01

Full Text Available This paper studies linear and nonlinear piezoelectric vibration absorbers that are designed based on the equal-peak method. A comparison between the performance of linear mechanical and electrical tuned vibration absorbers coupled to a linear oscillator is first performed. Nonlinearity is then introduced in the primary oscillator to which a new nonlinear electrical tuned vibration absorber is attached. Despite the frequency-energy dependence of nonlinear oscillations, we show that the nonlinear absorber is capable of effectively mitigating the vibrations of the nonlinear primary system in a large range of forcing amplitudes.

Phase Properties of Photon-Added Coherent States for Nonharmonic Oscillators in a Nonlinear Kerr Medium

Science.gov (United States)

Jahanbakhsh, F.; Honarasa, G.

2018-04-01

The potential of nonharmonic systems has several applications in the field of quantum physics. The photon-added coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function, Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.

Validity of the cumulant method for a pulse nonlinear Kerr oscillator

International Nuclear Information System (INIS)

Grygiel, K.; Leonski, W.; Szlachetka, P.

1998-01-01

We study the dynamics of an anharmonic oscillator driven by a train of pulses. The cumulant expansion and quantum evolution operator approaches are presented and compared. The modifications introduced by quantum mechanics into the dynamics of classical systems which manifest chaos are a problem of great importance. It is known that quantization modifies the dynamics of classical system is usually studied by means of the equation for the Wigner function derived from the quantum Liouville equation. In Wigner's formulation of quantum mechanics we treat a quantum system in a 'classical way' including all their quantum features. And what is more, we can contrast the quantum and classical dynamics within the framework of one formalism. The problem is, that the equations for the Wigner functions are mathematically cumbersome and their analytic solutions for most nonlinear systems are unknown. However, instead of the equation for the Wigner function we can use the set of equations for statistical moments generated by our equation for the Wigner function. It is obvious that in this approach a quantum system is governed by an infinite set of equations. Therefore, for numerical reasons the set of equations for statistical moments has to be truncated at a finite number, which means approximating it. It is known that first cumulant approximation represents the classical dynamics. The second cumulant approximation adds the first quantum corrections to the classical dynamics. In this paper we compare some aspects of the cumulant method and the method used by Leonski and Tanas to study an anharmonic oscillator driven by a train of pulses. The Kerr oscillator model is the same ad that is discussed in an earlier paper albeit without the damping mechanism

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator.

Science.gov (United States)

Botari, Tiago; Leonel, Edson D

2013-01-01

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization.

Non-linear oscillations of fluid in a container

NARCIS (Netherlands)

Verhagen, J.H.G.; van Wijngaarden, L.

1965-01-01

This paper is concerned with forced oscillations of fluid in a rectangular container. From the linearized approximation of the equations governing these oscillations, resonance frequencies are obtained for which the amplitude of the oscillations becomes infinite. Observation shows that under these

Modified Legendre Wavelets Technique for Fractional Oscillation Equations

Directory of Open Access Journals (Sweden)

Syed Tauseef Mohyud-Din

2015-10-01

Full Text Available Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinear fractional order oscillation equation into a fractional order recurrence relation and then Legendre wavelets method is applied on the converted problem. In order to check the efficiency and accuracy of the suggested modification, we have considered three problems namely: fractional order force-free Duffing–van der Pol oscillator, forced Duffing–van der Pol oscillator and higher order fractional Duffing equations. The obtained results are compared with the results obtained via other techniques.

Rotation and oscillation of nonlinear dipole vortex in the drift-unstable plasma

International Nuclear Information System (INIS)

Orito, Kohtaro; Hatori, Tadatsugu.

1997-10-01

The behaviors of the nonlinear dipole vortex in the drift unstable plasma are studied by numerical approaches. Model equations used in numerical simulation are derived from two-fluid model and are composed of two equations with respect to the electrostatic potential and the density perturbation. When the initial dipole vortex is inclined at some angle with respect to the direction of the drift velocity, the dipole vortex oscillates or rotates in the first stage. These phenomenon also happen in the stable system. In the second stage, one part of the dipole vortex grows and another decays because of the destabilization. The shrunk vortex rotates around the enlarged vortex. Consequently, a monopole vortex appears out of the dipole vortex. (author)

Nonlinear Waves in Complex Systems

DEFF Research Database (Denmark)

2007-01-01

The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...

Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

International Nuclear Information System (INIS)

Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge; D'Incerti, Ludovico

2015-01-01

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D 2 ), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes

Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

Energy Technology Data Exchange (ETDEWEB)

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it [Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy); Center for Mind/Brain Sciences, University of Trento, Trento (Italy); Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge [Center for Mind/Brain Sciences, University of Trento, Trento (Italy); D' Incerti, Ludovico [Neuroradiology Unit, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)

2015-03-15

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D{sub 2}), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.

OnWien Bridge Oscillators as Modified Multi-vibrators

DEFF Research Database (Denmark)

Lindberg, Erik

2014-01-01

A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals......A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals...

Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator

International Nuclear Information System (INIS)

Jeffries, C.; Perez, J.

1982-01-01

For a driven nonlinear semiconductor oscillator which shows a period-doubling pitchfork bifurcation route to chaos, we report an additional route to chaos: the Pomeau-Manneville intermittency route, characterized by a periodic (laminar) phase interrupted by bursts of aperiodic behavior. This occurs near a tangent bifurcation as the system driving parameter is reduced by epsilon from the threshold value for a periodic window. Data are presented for the dependence of the average laminar length on epsilon, and also on additive random noise voltage. The results are in reasonable agreement with the intermittency theory of Hirsch, Huberman, and Scalapino. The distribution P(l) is also reported

Nu shifts in betatron oscillations from uniform perturbations in the presence of non-linear magnetic guide fields

International Nuclear Information System (INIS)

Crebbin, K.C.

1985-05-01

Uniform magnetic field perturbations cause a closed orbit distortion in a circular accelerator. If the magnetic guide field is non-linear these perturbations can also cause a Nu shift in the betatron oscillations. Such a shift in radial Nu values has been observed in the Bevalac while studying the low energy resonant extraction system. In the Bevalac, the radial perturbation comes from the quadrants being magnetically about 0.8% longer than 90 0 . The normal effect of this type of perturbation is a radial closed orbit shift and orbit distortion. The Nu shift, associated with this type of perturbation in the presence of a non-linear guide field, is discussed in this paper. A method of handling the non-linear n values is discussed as well as the mechanism for the associated Nu shift. Computer calculations are compared to measurements. 2 refs., 4 figs

Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

Science.gov (United States)

Hoefer, Mark A.

This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued

Nonlinearity, Viscosity and Air-Compressibility Effects on the Helmholtz Resonant Wave Motion Generated by an Oscillating Twin Body in a Free Surface

Science.gov (United States)

Ananthakrishnan, Palaniswamy

2012-11-01

The problem is of practical relevance in determining the motion response of multi-hull and air-cushion vehicles in high seas and in littoral waters. The linear inviscid problem without surface pressure has been well studied in the past. In the present work, the nonlinear wave-body interaction problem is solved using finite-difference methods based on boundary-fitted coordinates. The inviscid nonlinear problem is tackled using the mixed Eulerian-Lagrangian formulation and the solution of the incompressible Navier-Stokes equations governing the viscous problem using a fractional-step method. The pressure variation in the air cushion is modeled using the isentropic gas equation pVγ = Constant. Results show that viscosity and free-surface nonlinearity significantly affect the hydrodynamic force and the wave motion at the resonant Helmholtz frequency (at which the primary wave motion is the vertical oscillation of the mean surface in between the bodies). Air compressibility suppresses the Helmholtz oscillation and enhances the wave radiation. Work supported by the ONR under the grant N00014-98-1-0151.

Higher accuracy analytical approximations to a nonlinear oscillator with discontinuity by He's homotopy perturbation method

International Nuclear Information System (INIS)

Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.

2008-01-01

He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient

Nonlinear oscillations of inviscid free drops

Science.gov (United States)

Patzek, T. W.; Benner, R. E., Jr.; Basaran, O. A.; Scriven, L. E.

1991-01-01

The present analysis of free liquid drops' inviscid oscillations proceeds through solution of Bernoulli's equation to obtain the free surface shape and of Laplace's equation for the velocity potential field. Results thus obtained encompass drop-shape sequences, pressure distributions, particle paths, and the temporal evolution of kinetic and surface energies; accuracy is verified by the near-constant drop volume and total energy, as well as the diminutiveness of mass and momentum fluxes across drop surfaces. Further insight into the nature of oscillations is provided by Fourier power spectrum analyses of mode interactions and frequency shifts.

Remote synchronization of amplitudes across an experimental ring of non-linear oscillators

Energy Technology Data Exchange (ETDEWEB)

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it [Center for Mind/Brain Science, University of Trento, 38123 Mattarello TN, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)

2015-12-15

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.

Robust Synchronization of Delayed Chaotic FitzHugh-Nagumo Neurons under External Electrical Stimulation

Directory of Open Access Journals (Sweden)

Muhammad Rehan

2012-01-01

Full Text Available Synchronization of chaotic neurons under external electrical stimulation (EES is studied in order to understand information processing in the brain and to improve the methodologies employed in the treatment of cognitive diseases. This paper investigates the dynamics of uncertain coupled chaotic delayed FitzHugh-Nagumo (FHN neurons under EES for incorporated parametric variations. A global nonlinear control law for synchronization of delayed neurons with known parameters is developed. Based on local and global Lipschitz conditions, knowledge of the bounds on the neuronal states, the Lyapunov-Krasovskii functional, and the L2 gain reduction, a less conservative local robust nonlinear control law is formulated to address the problem of robust asymptotic synchronization of delayed FHN neurons under parametric uncertainties. The proposed local control law guarantees both robust stability and robust performance and provides the L2 bound for uncertainty rejection in the synchronization error dynamics. Separate conditions for single-input and multiple-input control schemes for synchronization of a wide class of FHN systems are provided. The results of the proposed techniques are verified through numerical simulations.

An application of nonlinear supratransmission to the propagation of binary signals in weakly damped, mechanical systems of coupled oscillators

International Nuclear Information System (INIS)

Macias-Diaz, J.E.; Puri, A.

2007-01-01

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

Nonlinear Dynamics of a Magnetically Driven Duffing-Type Spring-Magnet Oscillator in the Static Magnetic Field of a Coil

Science.gov (United States)

Donoso, Guillermo; Ladera, Celso L.

2012-01-01

We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…

Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

Science.gov (United States)

Gao, Peng

2018-04-01

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

Science.gov (United States)

Gao, Peng

2018-06-01

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

Science.gov (United States)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

Directory of Open Access Journals (Sweden)

Zhonghai Guo

2012-01-01

Full Text Available We study the following second order mixed nonlinear impulsive differential equations with delay (r(tΦα(x′(t′+p0(tΦα(x(t+∑i=1npi(tΦβi(x(t-σ=e(t, t≥t0, t≠τk,x(τk+=akx(τk, x'(τk+=bkx'(τk, k=1,2,…, where Φ*(u=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.

Controlling nonlinear longitudinal space charge oscillations for high peak current bunch train generation

Directory of Open Access Journals (Sweden)

P. Musumeci

2013-10-01

Full Text Available The evolution of picosecond modulations of the longitudinal profile of an electron beam generated in an rf photoinjector is analyzed and optimized with the goal of obtaining high peak current electron bunch trains at very high frequencies (≥THz. Taking advantage of nonlinear longitudinal space charge forces, it is found that more than 500 A peak current 1 THz bunch trains can be generated using a standard 1.6 cell SLAC/UCLA/BNL rf gun. Postacceleration is used to freeze the longitudinal phase space dynamics after one half plasma oscillation. Applications range from tunable narrow bandwidth THz radiation generation to drivers for high frequency high gradient accelerators.

Suppression of chaos by weak resonant excitations in a non-linear oscillator with a non-symmetric potential

International Nuclear Information System (INIS)

Litak, Grzegorz; Syta, Arkadiusz; Borowiec, Marek

2007-01-01

We examine the Melnikov criterion for transition to chaos in case of one degree of freedom non-linear oscillator with non-symmetric potential. This system, when subjected to an external periodic force, shows homoclinic transition from regular vibrations to chaos just before escape from a potential well. We focus especially on the effect of a second resonant excitation with a different phase on the system transition to chaos. We propose a way of its control

Nonlinear asteroseismology: insight from amplitude and frequency modulations of oscillation modes in compact pulsators from Kepler photometry

Directory of Open Access Journals (Sweden)

Zong Weikai

2017-01-01

Full Text Available Nonlinear mode interactions are difficult to observe from ground-based telescopes as the typical periods of the modulations induced by those nonlinear phenomena are on timescales of weeks, months, even years. The launch of space telescopes, e.g., Kepler, has tremendously changed the situation and shredded new light on this research field. We present results from Kepler photometry showing evidence that nonlinear interactions between modes occur in the two compact pulsators KIC 8626021, a DB white dwarf, and KIC 10139564, a short period hot B subdwarf. KIC 8626021 and KIC 10139564 had been monitored by Kepler in short-cadence for nearly two years and more than three years without interruption, respectively. By analyzing these high-quality photometric data, we found that the modes within the triplets induced by rotation clearly reveal different behaviors: their frequencies and amplitudes may exhibit either periodic or irregular modulations, or remain constant. These various behaviors of the amplitude and of the frequency modulations of the oscillation modes observed in these two stars are in good agreement with those predicted within the amplitude equation formalism in the case of the nonlinear resonant mode coupling mechanism.

Neuromorphic computing with nanoscale spintronic oscillators.

Science.gov (United States)

Torrejon, Jacob; Riou, Mathieu; Araujo, Flavio Abreu; Tsunegi, Sumito; Khalsa, Guru; Querlioz, Damien; Bortolotti, Paolo; Cros, Vincent; Yakushiji, Kay; Fukushima, Akio; Kubota, Hitoshi; Yuasa, Shinji; Stiles, Mark D; Grollier, Julie

2017-07-26

Neurons in the brain behave as nonlinear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behaviour to realize high-density, low-power neuromorphic computing will require very large numbers of nanoscale nonlinear oscillators. A simple estimation indicates that to fit 10 8 oscillators organized in a two-dimensional array inside a chip the size of a thumb, the lateral dimension of each oscillator must be smaller than one micrometre. However, nanoscale devices tend to be noisy and to lack the stability that is required to process data in a reliable way. For this reason, despite multiple theoretical proposals and several candidates, including memristive and superconducting oscillators, a proof of concept of neuromorphic computing using nanoscale oscillators has yet to be demonstrated. Here we show experimentally that a nanoscale spintronic oscillator (a magnetic tunnel junction) can be used to achieve spoken-digit recognition with an accuracy similar to that of state-of-the-art neural networks. We also determine the regime of magnetization dynamics that leads to the greatest performance. These results, combined with the ability of the spintronic oscillators to interact with each other, and their long lifetime and low energy consumption, open up a path to fast, parallel, on-chip computation based on networks of oscillators.

Nonlinear dynamics of a nonsmooth shape memory alloy oscillator

International Nuclear Information System (INIS)

Cardozo dos Santos, Bruno; Amorim Savi, Marcelo

2009-01-01

In the last years, there is an increasing interest in nonsmooth system dynamics motivated by different applications including rotor dynamics, oil drilling and machining. Besides, shape memory alloys (SMAs) have been used in various applications exploring their high dissipation capacity related to their hysteretic behavior. This contribution investigates the nonlinear dynamics of shape memory alloy nonsmooth systems considering a linear oscillator with a discontinuous support built with an SMA element. A constitutive model developed by Paiva et al. [Paiva A, Savi MA, Braga AMB, Pacheco PMCL. A constitutive model for shape memory alloys considering tensile-compressive asymmetry and plasticity. Int J Solids Struct 2005;42(11-12):3439-57] is employed to describe the thermomechanical behavior of the SMA element. Numerical investigations show results where the SMA discontinuous support can dramatically change the system dynamics when compared to those associated with a linear elastic support system. A parametric study is of concern showing the system behavior for different system characteristics, forcing excitation and also gaps. These results show that smart materials can be employed in different kinds of mechanical systems exploring some of the remarkable properties of these alloys.

Oscillators - an approach for a better understanding

DEFF Research Database (Denmark)

Lindberg, Erik

2003-01-01

The aim of this tutorial is to provide an electronic engineer knowledge and insight for a better understanding of the mechanisms behind the behaviour of electronic oscillators. A linear oscillator is a mathematical fiction which can only be used as a starting point for the design of a real...... oscillator based on the Barkhausen criteria. Statements in textbooks and papers saying that the nonlinearities are bringing back the poles to the imaginary axis are wrong. The concept of "frozen eigenvalues" is introduced by means of piece-wise-linear modelling of the nonlinear components which are necessary...

The Study of a Nonlinear Duffing – Type Oscillator Driven by Two Voltage Sources

Directory of Open Access Journals (Sweden)

J. O. Maaita

2013-10-01

Full Text Available In the present work, a detailed study of a nonlinear electrical oscillator with damping and external excitation is presented. The system under study consists of a Duffing-type circuit driven by two sinusoidal voltage sources having different frequencies. The dynamical behavior of the proposed system is investigated numerically, by solving the system of state equations and simulating its behavior as a circuit using MultiSim. The tools of the theoretical approach are the bifurcation diagrams, the Poincaré sections, the phase portraits, and the maximum Lyapunov exponent. The numerical investigation showed that the system has rich complex dynamics including phenomena such as quasiperiodicity, 3-tori, and chaos.

Flutter analysis of an airfoil with multiple nonlinearities and uncertainties

Directory of Open Access Journals (Sweden)

Haitao Liao

2013-09-01

Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

Prediction of pilot induced oscillations

Directory of Open Access Journals (Sweden)

Valentin PANĂ

2011-03-01

Full Text Available An important problem in the design of flight-control systems for aircraft under pilotedcontrol is the determination of handling qualities and pilot-induced oscillations (PIO tendencieswhen significant nonlinearities exist in the vehicle description. The paper presents a method to detectpossible pilot-induced oscillations of Category II (with rate and position limiting, a phenomenonusually due to a misadaptation between the pilot and the aircraft response during some tasks in whichtight closed loop control of the aircraft is required from the pilot. For the analysis of Pilot in the LoopOscillations an approach, based on robust stability analysis of a system subject to uncertainparameters, is proposed. In this analysis the nonlinear elements are substituted by linear uncertainparameters. This approach assumes that PIO are characterized by a limit cycle behavior.

Phase-locked Josephson soliton oscillators

DEFF Research Database (Denmark)

Holst, T.; Hansen, Jørn Bindslev; Grønbech-Jensen, N.

1991-01-01

Detailed experimental characterization of the phase-locking at both DC and at microwave frequencies is presented for two closely spaced Josephson soliton (fluxon) oscillators. In the phase-locked state, the radiated microwave power exhibited an effective gain. With one common bias source......, a frequency tunability of the phase-locked oscillators up to 7% at 10 GHz was observed. The interacting soliton oscillators were modeled by two inductively coupled nonlinear transmission lines...

Electronegative nonlinear oscillating modes in plasmas

Science.gov (United States)

Panguetna, Chérif Souleman; Tabi, Conrad Bertrand; Kofané, Timoléon Crépin

2018-02-01

The emergence of nonlinear modulated waves is addressed in an unmagnetized electronegative plasma made of Boltzmann electrons, Boltzmann negative ions and cold mobile positive ions. The reductive perturbation method is used to reduce the dynamics of the whole system to a cubic nonlinear Schrödinger equation, whose the nonlinear and dispersion coefficients, P and Q, are function of the negative ion parameters, namely the negative ion concentration ratio (α) and the electron-to-negative ion temperature ratio (σn). It is observed that these parameters importantly affect the formation of modulated ion-acoustic waves, either as exact solutions or via the activation of modulational instability. Especially, the theory of modulational instability is used to show the correlation between the parametric analysis and the formation of modulated solitons, obtained here as bright envelopes and kink-wave solitons.

A multi-harmonic generalized energy balance method for studying autonomous oscillations of nonlinear conservative systems

Science.gov (United States)

Balaji, Nidish Narayanaa; Krishna, I. R. Praveen; Padmanabhan, C.

2018-05-01

The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram.

A Conspiracy of Oscillators

DEFF Research Database (Denmark)

Hjorth, Poul G.

2008-01-01

We discuss nonlinear mechanical systems containing several oscillators whose frequecies are all much higher than frequencies associated with the remaining degrees of freedom. In this situation a near constant of the motion, an adiabatic invariant, exists which is the sum of all the oscillator...... actions. The phenomenon is illustrated, and calculations of the small change of the adiabatic invariant is outlined....

Nonlinear analysis on power reactor dynamics

International Nuclear Information System (INIS)

Konno, H.; Hayashi, K.

1997-01-01

We have shown that the origin of intermittent oscillation observed in a BWR can be ascribed to the couplings among the spatial modes starting from a non-linear center manifold equation with a delay-time and a spatial diffusion. We can reduce the problem to the stochastic coupled van der Pol oscillators with non-linear coupling term. This non-linear coupling term plays an important role to break the symmetry of the system and the non-linear damping of the system. The phenomenological generalization of van der Pol oscillator coupled by the linear diffusion term is not appropriate for describing the nuclear power reactors. However, one must start from the coupled partial differential equations by taking into account the two energy group neutrons, the thermo-hydraulic equations including two-phase flow. In this case, the diffusion constant must be a complex number as is demonstrated in a previous paper. The results will be reported in the near future. (J.P.N.)

Propagation of a femtosecond laser pulse with duration of several optical oscillation periods in a medium with a quadratic nonlinearity

International Nuclear Information System (INIS)

Akopyan, A A; Oganesyan, D L

1998-01-01

It is shown that the wave equation can be solved by the method of unidirectional waves for a pulse with a duration of several oscillation periods in a medium with a quadratic nonlinearity, such as a group-3m crystal. The wave equation reduces to a system of two equations for waves with different polarisations. (laser applications and other topics in quantum electronics)

Discontinuous Spirals of Stable Periodic Oscillations

DEFF Research Database (Denmark)

Sack, Achim; Freire, Joana G.; Lindberg, Erik

2013-01-01

We report the experimental discovery of a remarkable organization of the set of self-generated periodic oscillations in the parameter space of a nonlinear electronic circuit. When control parameters are suitably tuned, the wave pattern complexity of the periodic oscillations is found to increase...

Considerations on 'Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring'

International Nuclear Information System (INIS)

Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.

2009-01-01

In a previous short communication [A. Belendez, E. Fernandez, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.

Oscillators and operational amplifiers

OpenAIRE

Lindberg, Erik

2005-01-01

A generalized approach to the design of oscillators using operational amplifiers as active elements is presented. A piecewise-linear model of the amplifier is used so that it make sense to investigate the eigenvalues of the Jacobian of the differential equations. The characteristic equation of the general circuit is derived. The dynamic nonlinear transfer characteristic of the amplifier is investigated. Examples of negative resistance oscillators are discussed.

Chaotic solar oscillations

Energy Technology Data Exchange (ETDEWEB)

Blacher, S; Perdang, J [Institut d' Astrophysique, B-4200 Cointe-Ougree (Belgium)

1981-09-01

A numerical experiment on Hamiltonian oscillations demonstrates the existence of chaotic motions which satisfy the property of phase coherence. It is observed that the low-frequency end of the power spectrum of such motions is remarkably similar in structure to the low-frequency SCLERA spectra. Since the smallness of the observed solar amplitudes is not a sufficient mathematical ground for inefficiency of non-linear effects the possibility of chaos among solar oscillations cannot be discarded a priori.

Asymmetric Collision of Concepts: Why Eigenstates Alone are Not Enough for Neutrino Flavor Oscillations

OpenAIRE

Williams, John Michael

2000-01-01

The symmetry of the problem of the apparent deficit in upward-going atmospheric muon neutrinos reveals two possible, nonexclusive kinds of solution: Nonlinearity in distance or nonlinearity in angle of observation. Nonlinearity in distance leads to the most popular theory for the atmospheric problem, neutrino flavor oscillations. If the observed deficit is caused by oscillations and not, say, flavor-changing or other weak-force scattering, neutrinos must be massive. But, if flavor oscillation...

Memcapacitor model and its application in chaotic oscillator with memristor.

Science.gov (United States)

Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching

2017-01-01

Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.

Hyperchaotic circuit with damped harmonic oscillators

DEFF Research Database (Denmark)

Lindberg, Erik; Murali, K.; Tamasevicius, A.

2001-01-01

A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance, two ideal...... capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...... by means of numerical integration of the appropriate differential equations....

Nonlinear effects on Turing patterns: Time oscillations and chaos

KAUST Repository

Aragó n, J. L.; Barrio, R. A.; Woolley, T. E.; Baker, R. E.; Maini, P. K.

2012-01-01

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

Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

Directory of Open Access Journals (Sweden)

A. M. El-Naggar

2015-11-01

Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.

Robust Nonlinear Regulation of Limit Cycle Oscillations in UAVs Using Synthetic Jet Actuators

Directory of Open Access Journals (Sweden)

Natalie Ramos Pedroza

2014-09-01

Full Text Available In this paper, a synthetic jet actuators (SJA-based nonlinear robust controller is developed, which is capable of completely suppressing limit cycle oscillations (LCO in UAV systems with parametric uncertainty in the SJA dynamics and unmodeled external disturbances. Specifically, the control law compensates for uncertainty in an input gain matrix, which results from the unknown airflow dynamics generated by the SJA. Challenges in the control design include compensation for input-multiplicative parametric uncertainty in the actuator dynamic model. The result was achieved via innovative algebraic manipulation in the error system development, along with a Lyapunov-based robust control law. A rigorous Lyapunov-based stability analysis is utilized to prove asymptotic LCO suppression, considering a detailed dynamic model of the pitching and plunging dynamics. Numerical simulation results are provided to demonstrate the robustness and practical performance of the proposed control law.

Nonlinear dynamic effects in a two-wave CO2 laser

International Nuclear Information System (INIS)

Gorobets, V A; Kozlov, K V; Kuntsevich, B F; Petukhov, V O

1999-01-01

Theoretical and experimental investigations were made of nonlinear dynamic regimes of the operation of a two-wave CO 2 laser with cw excitation in an electric discharge and loss modulation in one of the channels. Nonlinear amplitude - frequency characteristics of each of the laser channels have two low-frequency resonance spikes, associated with forced linear oscillations of two coupled oscillators, and high-frequency spikes, corresponding to doubling of the period of the output radiation oscillations. At low loss-modulation frequencies the intensity oscillations of the output radiation in the coupled channels are in antiphase, whereas at high modulation frequencies the dynamics is cophasal. Nonlinear dynamic effects, such as doubling of the period and of the repetition frequency of the pulses and chaotic oscillations of the output radiation intensity, are observed for certain system parameters. (control of laser radiation parameters)

Modeling of Nonlinear Dynamics and Synchronized Oscillations of Microbial Populations, Carbon and Oxygen Concentrations, Induced by Root Exudation in the Rhizosphere

Science.gov (United States)

Molz, F. J.; Faybishenko, B.; Jenkins, E. W.

2012-12-01

Mass and energy fluxes within the soil-plant-atmosphere continuum are highly coupled and inherently nonlinear. The main focus of this presentation is to demonstrate the results of numerical modeling of a system of 4 coupled, nonlinear ordinary differential equations (ODEs), which are used to describe the long-term, rhizosphere processes of soil microbial dynamics, including the competition between nitrogen-fixing bacteria and those unable to fix nitrogen, along with substrate concentration (nutrient supply) and oxygen concentration. Modeling results demonstrate the synchronized patterns of temporal oscillations of competing microbial populations, which are affected by carbon and oxygen concentrations. The temporal dynamics and amplitude of the root exudation process serve as a driving force for microbial and geochemical phenomena, and lead to the development of the Gompetzian dynamics, synchronized oscillations, and phase-space attractors of microbial populations and carbon and oxygen concentrations. The nonlinear dynamic analysis of time series concentrations from the solution of the ODEs was used to identify several types of phase-space attractors, which appear to be dependent on the parameters of the exudation function and Monod kinetic parameters. This phase space analysis was conducted by means of assessing the global and local embedding dimensions, correlation time, capacity and correlation dimensions, and Lyapunov exponents of the calculated model variables defining the phase space. Such results can be used for planning experimental and theoretical studies of biogeochemical processes in the fields of plant nutrition, phyto- and bio-remediation, and other ecological areas.

Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

Directory of Open Access Journals (Sweden)

Haitao Liao

2013-01-01

Full Text Available In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

Driven, autoresonant three-oscillator interactions

International Nuclear Information System (INIS)

Yaakobi, O.; Friedland, L.; Henis, Z.

2007-01-01

An efficient control scheme of resonant three-oscillator interactions using an external chirped frequency drive is suggested. The approach is based on formation of a double phase-locked (autoresonant) state in the system, as the driving oscillation passes linear resonance with one of the interacting oscillators. When doubly phase locked, the amplitudes of the oscillators increase with time in proportion to the driving frequency deviation from the linear resonance. The stability of this phase-locked state and the effects of dissipation and of the initial three-oscillator frequency mismatch on the autoresonance are analyzed. The associated autoresonance threshold phenomenon in the driving amplitude is also discussed. In contrast to other nonlinear systems, driven, autoresonant three-oscillator excitations are independent of the sign of the driving frequency chirp rate

New Approach for the Analysis of Damped Vibrations of Fractional Oscillators

Directory of Open Access Journals (Sweden)

Yuriy A. Rossikhin

2009-01-01

Full Text Available The dynamic behavior of linear and nonlinear mechanical oscillators with constitutive equations involving fractional derivatives defined as a fractional power of the operator of conventional time-derivative is considered. Such a definition of the fractional derivative enables one to analyse approximately vibratory regimes of the oscillator without considering the drift of its position of equilibrium. The assumption of small fractional derivative terms allows one to use the method of multiple time scales whereby a comparative analysis of the solutions obtained for different orders of low-level fractional derivatives and nonlinear elastic terms is possible to be carried out. The interrelationship of the fractional parameter (order of the fractional operator and nonlinearity manifests itself in full measure when orders of the small fractional derivative term and of the cubic nonlinearity entering in the oscillator's constitutive equation coincide.

Asymptotic representation of relaxation oscillations in lasers

CERN Document Server

Grigorieva, Elena V

2017-01-01

In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.

Electrodynamic soil plate oscillator: Modeling nonlinear mesoscopic elastic behavior and hysteresis in nonlinear acoustic landmine detection

Science.gov (United States)

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

Signatures of nonlinearity in single cell noise-induced oscillations

NARCIS (Netherlands)

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

Exact folded-band chaotic oscillator.

Science.gov (United States)

Corron, Ned J; Blakely, Jonathan N

2012-06-01

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

Engineering high-order nonlinear dissipation for quantum superconducting circuits

Science.gov (United States)

Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

International Nuclear Information System (INIS)

Kurkin, S. A.; Koronovski, A. A.; Hramov, A. E.

2009-01-01

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.

Controllability of nonlinear delay oscillating systems

Directory of Open Access Journals (Sweden)

Chengbin Liang

2017-05-01

Full Text Available In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix.

Suppression and revival of oscillation in indirectly coupled limit cycle oscillators

International Nuclear Information System (INIS)

Sharma, P.R.; Kamal, N.K.; Verma, U.K.; Suresh, K.; Thamilmaran, K.; Shrimali, M.D.

2016-01-01

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.

Location identification of closed crack based on Duffing oscillator transient transition

Science.gov (United States)

Liu, Xiaofeng; Bo, Lin; Liu, Yaolu; Zhao, Youxuan; Zhang, Jun; Deng, Mingxi; Hu, Ning

2018-02-01

The existence of a closed micro-crack in plates can be detected by using the nonlinear harmonic characteristics of the Lamb wave. However, its location identification is difficult. By considering the transient nonlinear Lamb under the noise interference, we proposed a location identification method for the closed crack based on the quantitative measurement of Duffing oscillator transient transfer in the phase space. The sliding short-time window was used to create a window truncation of to-be-detected signal. And then, the periodic extension processing for transient nonlinear Lamb wave was performed to ensure that the Duffing oscillator has adequate response time to reach a steady state. The transient autocorrelation method was used to reduce the occurrence of missed harmonic detection due to the random variable phase of nonlinear Lamb wave. Moreover, to overcome the deficiency in the quantitative analysis of Duffing system state by phase trajectory diagram and eliminate the misjudgment caused by harmonic frequency component contained in broadband noise, logic operation method of oscillator state transition function based on circular zone partition was adopted to establish the mapping relation between the oscillator transition state and the nonlinear harmonic time domain information. Final state transition discriminant function of Duffing oscillator was used as basis for identifying the reflected and transmitted harmonics from the crack. Chirplet time-frequency analysis was conducted to identify the mode of generated harmonics and determine the propagation speed. Through these steps, accurate position identification of the closed crack was achieved.

Analysis of the power flow in nonlinear oscillators driven by random excitation using the first Wiener kernel

Science.gov (United States)

Hawes, D. H.; Langley, R. S.

2018-01-01

Random excitation of mechanical systems occurs in a wide variety of structures and, in some applications, calculation of the power dissipated by such a system will be of interest. In this paper, using the Wiener series, a general methodology is developed for calculating the power dissipated by a general nonlinear multi-degree-of freedom oscillatory system excited by random Gaussian base motion of any spectrum. The Wiener series method is most commonly applied to systems with white noise inputs, but can be extended to encompass a general non-white input. From the extended series a simple expression for the power dissipated can be derived in terms of the first term, or kernel, of the series and the spectrum of the input. Calculation of the first kernel can be performed either via numerical simulations or from experimental data and a useful property of the kernel, namely that the integral over its frequency domain representation is proportional to the oscillating mass, is derived. The resulting equations offer a simple conceptual analysis of the power flow in nonlinear randomly excited systems and hence assist the design of any system where power dissipation is a consideration. The results are validated both numerically and experimentally using a base-excited cantilever beam with a nonlinear restoring force produced by magnets.

Chimera states in two-dimensional networks of locally coupled oscillators

Science.gov (United States)

Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K.; Ghosh, Dibakar; Lakshmanan, M.

2018-02-01

Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera

OSCILLATION OF NONLINEAR DELAY DIFFERENCE EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

This paper deals with the oscillatory properties of a class of nonlinear difference equations with several delays. Sufficient criteria in the form of infinite sum for the equations to be oscillatory are obtained.

Autonomous third-order duffing-holmes type chaotic oscillator

DEFF Research Database (Denmark)

Lindberg, Erik; Tamaseviciute, E; Mykolaitis, G

2009-01-01

feedback loop. In contrast to many other autonomous chaotic oscillators, including linear unstable resonators and nonlinear damping loops, the novel circuit is based on nonlinear resonator and linear damping loop in the negative feedback. SPICE simulation and hardware experimental investigations...

Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators

KAUST Repository

Talukdar, Abdul Hafiz

2011-01-01

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

NONLINEAR DYNAMICS OF A ROTOR WITH CANTILEVERED DISK RESTING ON ANGULAR CONTACT BALL BEARINGS

Directory of Open Access Journals (Sweden)

S. Filipkovskyi

2016-06-01

Full Text Available The mathematical model of nonlinear oscillations of the rotor resting on angular contact ball bearings is developed. The disc is fixed on the console end of the shaft. The deflection of the shaft, and the elastic deformation of the bearings have the same order. Analysis of free oscillations is carried out, using nonlinear normal modes. The modes and backbone curves of rotor nonlinear oscillations are calculated. The system has soft characteristics.

Oscillations in the interactions among multiple solitons in an optical fibre

Energy Technology Data Exchange (ETDEWEB)

Hu, Wen-Qiang; Gao, Yi-Tian; Zhao, Chen; Feng, Yu-Jie; Su, Chuan-Qi [Beijing University of Aeronautics and Astronautics (China). Ministry of Education Key Laboratory of Fluid Mechanics; Beijing University of Aeronautics and Astronautics (China). National Laboratory for Computational Fluid Dynamics

2016-07-01

In this article, under the investigation on the interactions among multiple solitons for an eighth-order nonlinear Schroedinger equation in an optical fibre, oscillations in the interaction zones are observed theoretically. With different coefficients of the operators in this equation, we find that (1) the oscillations in the solitonic interaction zones have different forms with different spectral parameters of this equation; (2) the oscillations in the interactions among the multiple solitons are affected by the choice of spectral parameters, the dispersive effects and nonlinearity of the eighth-order operator; (3) the second-, fifth-, sixth-, and seventh-order operators restrain oscillations in the solitonic interaction zones and the higher-order operators have stronger attenuated effects than the lower ones, while the third- and fourth-order operators stimulate and extend the scope of oscillations.

A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

Directory of Open Access Journals (Sweden)

S.H. Chen

1996-01-01

Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

Nonlinear chaos control in a permanent magnet reluctance machine

International Nuclear Information System (INIS)

Harb, Ahmad M.

2004-01-01

The dynamics of a permanent magnet synchronous machine (PMSM) is analyzed. The study shows that under certain conditions the PMSM is experiencing chaotic behavior. To control these unwanted chaotic oscillations, a nonlinear controller based on the backstepping nonlinear control theory is designed. The objective of the designed control is to stabilize the output chaotic trajectory by forcing it to the nearest constant solution in the basin of attraction. The result is compared with a nonlinear sliding mode controller. The designed controller that based on backstepping nonlinear control was able to eliminate the chaotic oscillations. Also the study shows that the designed controller is mush better than the sliding mode control

Transient and chaotic low-energy transfers in a system with bistable nonlinearity

Energy Technology Data Exchange (ETDEWEB)

Romeo, F., E-mail: francesco.romeo@uniroma1.it [Department of Structural and Geotechnical Engineering, SAPIENZA University of Rome, Rome (Italy); Manevitch, L. I. [Institute of Chemical Physics, RAS, Moscow (Russian Federation); Bergman, L. A.; Vakakis, A. [College of Engineering, University of Illinois at Urbana–Champaign, Champaign, Illinois 61820 (United States)

2015-05-15

The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensional projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.

Nonlinear extraordinary wave in dense plasma

Energy Technology Data Exchange (ETDEWEB)

Krasovitskiy, V. B., E-mail: krasovit@mail.ru [Russian Academy of Sciences, Keldysh Institute of Applied Mathematics (Russian Federation); Turikov, V. A. [Russian University of Peoples’ Friendship (Russian Federation)

2013-10-15

Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.

NR-code: Nonlinear reconstruction code

Science.gov (United States)

Yu, Yu; Pen, Ue-Li; Zhu, Hong-Ming

2018-04-01

NR-code applies nonlinear reconstruction to the dark matter density field in redshift space and solves for the nonlinear mapping from the initial Lagrangian positions to the final redshift space positions; this reverses the large-scale bulk flows and improves the precision measurement of the baryon acoustic oscillations (BAO) scale.

Modulation linearization of a frequency-modulated voltage controlled oscillator, part 3

Science.gov (United States)

Honnell, M. A.

1975-01-01

An analysis is presented for the voltage versus frequency characteristics of a varactor modulated VHF voltage controlled oscillator in which the frequency deviation is linearized by using the nonlinear characteristics of a field effect transistor as a signal amplifier. The equations developed are used to calculate the oscillator output frequency in terms of pertinent circuit parameters. It is shown that the nonlinearity exponent of the FET has a pronounced influence on frequency deviation linearity, whereas the junction exponent of the varactor controls total frequency deviation for a given input signal. A design example for a 250 MHz frequency modulated oscillator is presented.

Superconducting nanowires as nonlinear inductive elements for qubits

Science.gov (United States)

Ku, Jaseung; Manucharyan, Vladimir; Bezryadin, Alexey

2011-03-01

We report microwave transmission measurements of superconducting Fabry-Perot resonators, having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low-quality factor sample exhibits a ``crater'' at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. NSF DMR-1005645, DOE DO-FG02-07ER46453.

Transition from weak to strong measurements by nonlinear quantum feedback control

International Nuclear Information System (INIS)

Zhang Jing; Liu Yuxi; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong

2010-01-01

We find that feedback control may induce 'pseudo'-nonlinear dynamics in a damped harmonic oscillator, whose centroid trajectory in the phase space behaves like a classical nonlinear system. Thus, similar to nonlinear amplifiers (e.g., rf-driven Josephson junctions), feedback control on the harmonic oscillator can induce nonlinear bifurcation, which can be used to amplify small signals and further to measure quantum states of qubits. Using the cavity QED and the circuit QED systems as examples, we show how to apply our method to measuring the states of two-level atoms and superconducting charge qubits.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

Science.gov (United States)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

Science.gov (United States)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Practical design of a nonlinear tuned vibration absorber

DEFF Research Database (Denmark)

Grappasonni, C.; Habib, G.; Detroux, T.

2014-01-01

The aim of the paper is to develop a new nonlinear tuned vibration absorber (NLTVA) capable of mitigating the vibrations of nonlinear systems which are known to exhibit frequency-energy-dependent oscillations. A nonlinear generalization of Den Hartog's equal-peak method is proposed to ensure equa...

A new analytical approximation to the Duffing-harmonic oscillator

International Nuclear Information System (INIS)

Fesanghary, M.; Pirbodaghi, T.; Asghari, M.; Sojoudi, H.

2009-01-01

In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.

Some aspects of floor spectra of 1DOF nonlinear primary structures

International Nuclear Information System (INIS)

Politopoulos, I.; Feau, C.

2007-01-01

In this paper the influence of the nonlinear behaviour of the primary structure on floor spectra is investigated by means of simple models. The general trends of floor spectra for different types of nonlinear behaviour of one degree of freedom (1DOF) primary structure are shown and we point out their common futures and their differences. A special attention is given to the cases of elastoplastic and nonlinear elastic behaviours and methods to determine an equivalent linear oscillator are proposed. The properties (frequency and damping) of this equivalent linear oscillator are quite different from the properties of equivalent linear oscillators commonly considered in practice. In particular, in the case of elastoplastic behaviour, there is no frequency shift and damping is smaller than assumed by other methods commonly used. In the case of nonlinear elastic behaviour, the concept of an equivalent frequency which is a random variable is used. Finally, a design floor spectrum of primary structures, exhibiting energy dissipating nonlinear behaviour is proposed. (authors)

Studies of hydromagnetic waves and oscillations in plasmas

International Nuclear Information System (INIS)

Sawley, M.L.

1980-10-01

Small amplitude magnetoacoustic oscillations in a partially ionized, non-uniform, current carrying plasma column of finite beta are considered. The linearized magnetohydrodynamic equations are used to develop a theory describing both free and forced magnetoacoustic oscillations. The results of numerical calculations are given for the specific case of diffuse pinch equilibrium configurations. In an experimental study the amplitude of the oscillating axial magnetic flux is determined for several frequencies in the vicinity of the first magnetoacoustic resonance. Accurate determination of the plasma density profile is shown to be possible. Finite-amplitude effects on the propagation of axisymmetric hydromagnetic waves are examined. A nonlinear theory is developed which describes the second-order perturbation that accompanies the primary wave. The influence of Hall currents and the presence of neutral atoms on the second-order fields is treated. In an investigation on the propagation of torsional waves the observed second-order fields are shown to exhibit good quantitative agreement with theoretical calculations for moderate primary wave amplitudes. The re-ionization of the plasma by a torsional wave is investigated. A theoretical description is given of the nonlinear excitation of magnetoacoustic oscillations by means of an oscillating axial current

Deterministic nonlinear phase gates induced by a single qubit

Science.gov (United States)

Park, Kimin; Marek, Petr; Filip, Radim

2018-05-01

We propose deterministic realizations of nonlinear phase gates by repeating a finite sequence of non-commuting Rabi interactions between a harmonic oscillator and only a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the ideal cubic phase gate and the quartic phase gate are generated in the harmonic oscillator faithfully by our method. We numerically analyzed the performance of our scheme under realistic imperfections of the oscillator and the two-level system. The methodology is extended further to higher-order nonlinear phase gates. This theoretical proposal completes the set of operations required for continuous-variable quantum computation.

Nonlinear Dynamic Models in Advanced Life Support

Science.gov (United States)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Non-linear Relationship between BOLD Activation and Amplitude of Beta Oscillations in the Supplementary Motor Area during Rhythmic Finger Tapping and Internal Timing

Science.gov (United States)

Gompf, Florian; Pflug, Anja; Laufs, Helmut; Kell, Christian A.

2017-01-01

Functional imaging studies using BOLD contrasts have consistently reported activation of the supplementary motor area (SMA) both during motor and internal timing tasks. Opposing findings, however, have been shown for the modulation of beta oscillations in the SMA. While movement suppresses beta oscillations in the SMA, motor and non-motor tasks that rely on internal timing increase the amplitude of beta oscillations in the SMA. These independent observations suggest that the relationship between beta oscillations and BOLD activation is more complex than previously thought. Here we set out to investigate this rapport by examining beta oscillations in the SMA during movement with varying degrees of internal timing demands. In a simultaneous EEG-fMRI experiment, 20 healthy right-handed subjects performed an auditory-paced finger-tapping task. Internal timing was operationalized by including conditions with taps on every fourth auditory beat, which necessitates generation of a slow internal rhythm, while tapping to every auditory beat reflected simple auditory-motor synchronization. In the SMA, BOLD activity increased and power in both the low and the high beta band decreased expectedly during each condition compared to baseline. Internal timing was associated with a reduced desynchronization of low beta oscillations compared to conditions without internal timing demands. In parallel with this relative beta power increase, internal timing activated the SMA more strongly in terms of BOLD. This documents a task-dependent non-linear relationship between BOLD and beta-oscillations in the SMA. We discuss different roles of beta synchronization and desynchronization in active processing within the same cortical region. PMID:29249950

Non-linear Relationship between BOLD Activation and Amplitude of Beta Oscillations in the Supplementary Motor Area during Rhythmic Finger Tapping and Internal Timing.

Science.gov (United States)

Gompf, Florian; Pflug, Anja; Laufs, Helmut; Kell, Christian A

2017-01-01

Functional imaging studies using BOLD contrasts have consistently reported activation of the supplementary motor area (SMA) both during motor and internal timing tasks. Opposing findings, however, have been shown for the modulation of beta oscillations in the SMA. While movement suppresses beta oscillations in the SMA, motor and non-motor tasks that rely on internal timing increase the amplitude of beta oscillations in the SMA. These independent observations suggest that the relationship between beta oscillations and BOLD activation is more complex than previously thought. Here we set out to investigate this rapport by examining beta oscillations in the SMA during movement with varying degrees of internal timing demands. In a simultaneous EEG-fMRI experiment, 20 healthy right-handed subjects performed an auditory-paced finger-tapping task. Internal timing was operationalized by including conditions with taps on every fourth auditory beat, which necessitates generation of a slow internal rhythm, while tapping to every auditory beat reflected simple auditory-motor synchronization. In the SMA, BOLD activity increased and power in both the low and the high beta band decreased expectedly during each condition compared to baseline. Internal timing was associated with a reduced desynchronization of low beta oscillations compared to conditions without internal timing demands. In parallel with this relative beta power increase, internal timing activated the SMA more strongly in terms of BOLD. This documents a task-dependent non-linear relationship between BOLD and beta-oscillations in the SMA. We discuss different roles of beta synchronization and desynchronization in active processing within the same cortical region.

Nonlinear Entanglement and its Application to Generating Cat States

Science.gov (United States)

Shen, Y.; Assad, S. M.; Grosse, N. B.; Li, X. Y.; Reid, M. D.; Lam, P. K.

2015-03-01

The Einstein-Podolsky-Rosen (EPR) paradox, which was formulated to argue for the incompleteness of quantum mechanics, has since metamorphosed into a resource for quantum information. The EPR entanglement describes the strength of linear correlations between two objects in terms of a pair of conjugate observables in relation to the Heisenberg uncertainty limit. We propose that entanglement can be extended to include nonlinear correlations. We examine two driven harmonic oscillators that are coupled via third-order nonlinearity can exhibit quadraticlike nonlinear entanglement which, after a projective measurement on one of the oscillators, collapses the other into a cat state of tunable size.

Transition to chaos in the damped and forced non-lnear oscillator

International Nuclear Information System (INIS)

Montenegro Joo, J.; Universidad Nacional Mayor de San Marcos, Lima

2009-01-01

A Virtual Lab to study the Transition to Chaos in second order non-linear differential equations has been developed and successfully applied to the search for chaotic behavior in the damped and forced non-linear oscillator. This simulation and visualization software evaluates the equation under investigation at up to one million time-steps, generating in real-time and on the screen, plots like amplitude of oscillation, phase diagram, amplitude oscillation peaks and an animation of an oscillator governed by the problem equation. In this way the investigator not only gets important behavior graphs but he or she also gets a physical visualization of the system under investigation. Visualizing an animation of the system under study is an enormous help because it is not always easy to interpret behavior graphs. (author).

Non-linear time series analysis on flow instability of natural circulation under rolling motion condition

International Nuclear Information System (INIS)

Zhang, Wenchao; Tan, Sichao; Gao, Puzhen; Wang, Zhanwei; Zhang, Liansheng; Zhang, Hong

2014-01-01

Highlights: • Natural circulation flow instabilities in rolling motion are studied. • The method of non-linear time series analysis is used. • Non-linear evolution characteristic of flow instability is analyzed. • Irregular complex flow oscillations are chaotic oscillations. • The effect of rolling parameter on the threshold of chaotic oscillation is studied. - Abstract: Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions were studied by the method of non-linear time series analysis. Experimental flow time series of different dimensionless power and rolling parameters were analyzed based on phase space reconstruction theory. Attractors which were reconstructed in phase space and the geometric invariants, including correlation dimension, Kolmogorov entropy and largest Lyapunov exponent, were determined. Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions was studied based on the results of the geometric invariant analysis. The results indicated that the values of the geometric invariants first increase and then decrease as dimensionless power increases which indicated the non-linear characteristics of the system first enhance and then weaken. The irregular complex flow oscillation is typical chaotic oscillation because the value of geometric invariants is at maximum. The threshold of chaotic oscillation becomes larger as the rolling frequency or rolling amplitude becomes big. The main influencing factors that influence the non-linear characteristics of the natural circulation system under rolling motion are thermal driving force, flow resistance and the additional forces caused by rolling motion. The non-linear characteristics of the natural circulation system under rolling motion changes caused by the change of the feedback and coupling degree among these influencing factors when the dimensionless power or rolling parameters changes

Experimental studies of nonlinear beam dynamics

International Nuclear Information System (INIS)

Caussyn, D.D.; Ball, M.; Brabson, B.; Collins, J.; Curtis, S.A.; Derenchuck, V.; DuPlantis, D.; East, G.; Ellison, M.; Ellison, T.; Friesel, D.; Hamilton, B.; Jones, W.P.; Lamble, W.; Lee, S.Y.; Li, D.; Minty, M.G.; Sloan, T.; Xu, G.; Chao, A.W.; Ng, K.Y.; Tepikian, S.

1992-01-01

The nonlinear beam dynamics of transverse betatron oscillations were studied experimentally at the Indiana University Cyclotron Facility cooler ring. Motion in one dimension was measured for betatron tunes near the third, fourth, fifth, and seventh integer resonances. This motion is described by coupling between the transverse modes of motion and nonlinear field errors. The Hamiltonian for nonlinear particle motion near the third- and fourth-integer-resonance conditions has been deduced

Reconstructing baryon oscillations: A Lagrangian theory perspective

International Nuclear Information System (INIS)

Padmanabhan, Nikhil; White, Martin; Cohn, J. D.

2009-01-01

Recently Eisenstein and collaborators introduced a method to 'reconstruct' the linear power spectrum from a nonlinearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We reformulate this method within the Lagrangian picture of structure formation, to better understand what such a method does, and what the resulting power spectra are. We show that reconstruction does not reproduce the linear density field, at second order. We however show that it does reduce the damping of the oscillations due to nonlinear structure formation, explaining the improvements seen in simulations. Our results suggest that the reconstructed power spectrum is potentially better modeled as the sum of three different power spectra, each dominating over different wavelength ranges and with different nonlinear damping terms. Finally, we also show that reconstruction reduces the mode-coupling term in the power spectrum, explaining why miscalibrations of the acoustic scale are reduced when one considers the reconstructed power spectrum.

Analytical approximations for the amplitude and period of a relaxation oscillator

Directory of Open Access Journals (Sweden)

Golkhou Vahid

2009-01-01

Full Text Available Abstract Background Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. Results We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates, efficiency (2× more efficient, and dynamic range (30 to 60 decibel increase. The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. Conclusion Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.

Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

KAUST Repository

Mansingka, Abhinav S.; Radwan, Ahmed G.; Salama, Khaled N.; Zidan, Mohammed A.

2012-01-01

This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.

Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

KAUST Repository

Mansingka, Abhinav S.

2012-07-29

This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.

Complete solution of the modified Cherry oscillator problem

International Nuclear Information System (INIS)

Pfirsch, D.

1990-04-01

In 1925, T.M. Cherry presented a simple example demonstrating that linear stability analysis will in general not be sufficient for finding out whether a system is stable or not with respect to small-amplitude perturbations. The example consisted of two nonlinearly coupled oscillators, one possessing positive energy, the other negative energy, with frequencies ω 1 =2ω 2 allowing third-order resonance. In a previous paper, the present author reformulated Cherry's example and then generalized it to three coupled oscillators corresponding to three-wave interaction in a continuum theory like that of Maxwell-Vlasov. Cherry was able to present a two-parameter solution set for his example which would, however, allow a four-parameter solution set, and a three-parameter solution set for the resonant three-oscillator case was obtained which, however, would allow a six-parameter solution set. Nonlinear instability could therefore be proven only for a very small part of the phase space of the oscillators. This paper now gives the complete solution for the three-oscillator case and shows that, except for a singular case, all initial conditions, especially those with arbitrarily small amplitudes, lead to explosive behaviour. This is true of the resonant case. The non-resonant oscillators can sometimes also become explosively unstable, but only if the initial amplitudes are not infinitesimally small. (orig.)

Prediction of partial synchronization in delay-coupled nonlinear oscillators, with application to Hindmarsh–Rose neurons

International Nuclear Information System (INIS)

Ünal, Hakkı Ulaş; Michiels, Wim

2013-01-01

The full synchronization of coupled nonlinear oscillators has been widely studied. In this paper we investigate conditions for which partial synchronization of time-delayed diffusively coupled systems arises. The coupling configuration of the systems is described by a directed graph. As a novel quantitative result we first give necessary and sufficient conditions for the presence of forward invariant sets characterized by partially synchronous motion. These conditions can easily be checked from the eigenvalues and eigenvectors of the graph Laplacian. Second, we perform stability analysis of the synchronized equilibria in a (gain,delay) parameter space. For this analysis the coupled nonlinear systems are linearized around the synchronized equilibria and then the resulting characteristic function is factorized. By such a factorization, it is shown that the relation between the behaviour of different agents at the zero of the characteristic function depends on the structure of the eigenvectors of the weighted Laplacian matrix. By determining the structure of the solutions in the unstable manifold, combined with the characterization of invariant sets, we predict which partially synchronous regimes occur and estimate the corresponding coupling gain and delay values. We apply the obtained results to networks of coupled Hindmarsh–Rose neurons and verify the occurrence of the expected partially synchronous regimes by using a numerical simulation. We also make a comparison with an existing approach based on Lyapunov functionals. (paper)

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2016-10-15

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

International Nuclear Information System (INIS)

Chou, Chia-Chun

2016-01-01

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators

DEFF Research Database (Denmark)

Momeni, M.; Jamshidi, j.; Barari, Amin

2011-01-01

In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...... and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems....

Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

KAUST Repository

Abdelkefi, Abdessattar

2013-06-18

In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.

CLIMATE CHANGE: LONG-TERM TRENDS AND SHORT-TERM OSCILLATIONS

Institute of Scientific and Technical Information of China (English)

GAO Xin-quan; ZHANG Xin; QIAN Wei-hong

2006-01-01

Identifying the Northern Hemisphere (NH) temperature reconstruction and instrumental data for the past 1000 years shows that climate change in the last millennium includes long-term trends and various oscillations. Two long-term trends and the quasi-70-year oscillation were detected in the global temperature series for the last 140 years and the NH millennium series. One important feature was emphasized that temperature decreases slowly but it increases rapidly based on the analysis of different series. Benefits can be obtained of climate change from understanding various long-term trends and oscillations. Millennial temperature proxies from the natural climate system and time series of nonlinear model system are used in understanding the natural climate change and recognizing potential benefits by using the method of wavelet transform analysis. The results from numerical modeling show that major oscillations contained in numerical solutions on the interdecadal timescale are consistent with that of natural proxies. It seems that these oscillations in the climate change are not directly linked with the solar radiation as an external forcing. This investigation may conclude that the climate variability at the interdecadal timescale strongly depends on the internal nonlinear effects in the climate system.

Building better oscillators using nonlinear dynamics and pattern ...

Indian Academy of Sciences (India)

Frequency and time references play an essential role in modern technology and in liv- ... of noise and improve the frequency precision of oscillators, with particular ..... signal is cyclostationary (the statistics is periodic rather than stationary) the ...

Integrability and symmetries for the Helmholtz oscillator with friction

International Nuclear Information System (INIS)

Almendral, Juan A; Sanjuan, Miguel A F

2003-01-01

This paper deals with the Helmholtz oscillator, which is a simple nonlinear oscillator whose equation presents a quadratic nonlinearity and the possibility of escape. When a periodic external force is introduced, the width of the stochastic layer, which is a region around the separatrix where orbits may exhibit transient chaos, is calculated. In the absence of friction and external force, it is well known that analytical solutions exist since it is completely integrable. When only friction is included, there is no analytical solution for all parameter values. However, by means of the Lie theory for differential equations we find a relation between parameters for which the oscillator is integrable. This is related to the fact that the system possesses a symmetry group and the corresponding symmetries are computed. Finally, the analytical explicit solutions are shown and related to the basins of attraction

Synchronization of coupled different chaotic FitzHugh-Nagumo neurons with unknown parameters under communication-direction-dependent coupling.

Science.gov (United States)

Iqbal, Muhammad; Rehan, Muhammad; Khaliq, Abdul; Saeed-ur-Rehman; Hong, Keum-Shik

2014-01-01

This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.

First integral method for an oscillator system

Directory of Open Access Journals (Sweden)

Xiaoqian Gong

2013-04-01

Full Text Available In this article, we consider the nonlinear Duffing-van der Pol-type oscillator system by means of the first integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly, we apply the Division Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to explore a quasi-polynomial first integral to an equivalent autonomous system. Then, through solving an algebraic system we derive the first integral of the Duffing-van der Pol-type oscillator system under certain parametric condition.

Modified Legendre Wavelets Technique for Fractional Oscillation Equations

OpenAIRE

Mohyud-Din, Syed; Iqbal, Muhammad; Hassan, Saleh

2015-01-01

Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinea...

Energy flow theory of nonlinear dynamical systems with applications

CERN Document Server

Xing, Jing Tang

2015-01-01

This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...

Bifurcation analysis and spatio-temporal patterns of nonlinear oscillations in a delayed neural network with unidirectional coupling

International Nuclear Information System (INIS)

Song Yongli; Tadé, Moses O; Zhang Tonghua

2009-01-01

In this paper, a delayed neural network with unidirectional coupling is considered which consists of two two-dimensional nonlinear differential equation systems with exponential decay where one system receives a delayed input from the other system. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the centre manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay-differential equations combined with representation theory of Lie groups. Then the global continuation of phase-locked periodic solutions is investigated. Numerical simulations are given to illustrate the results obtained

Nonlinear Dynamics Analysis of the Semiactive Suspension System with Magneto-Rheological Damper

Directory of Open Access Journals (Sweden)

Hailong Zhang

2015-01-01

Full Text Available This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The magneto-rheological (MR suspension system has been established, by employing the modified Bouc-Wen force-velocity (F-v model of magneto-rheological damper (MRD. The possibility of chaotic motions in MR suspension is discovered by employing the method of nonlinear stability analysis. With the bifurcation diagrams and corresponding Lyapunov exponent (LE spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasiperiodic oscillations, and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolutions to chaos through period-doubling bifurcations, saddle-node bifurcations, and reverse period-doubling bifurcations.

Perturbation method of studying the EI Niño oscillation with two parameters by using the delay sea-air oscillator model

International Nuclear Information System (INIS)

Du Zeng-Ji; Lin Wan-Tao; Mo Jia-Qi

2012-01-01

The EI Niño-southern oscillation (ENSO) is an interannual phenomenon involved in tropical Pacific ocean-atmosphere interactions. In this paper, we develop an asymptotic method of solving the nonlinear equation using the ENSO model. Based on a class of the oscillator of the ENSO model, a approximate solution of the corresponding problem is studied employing the perturbation method

Relaxed damage threshold intensity conditions and nonlinear increase in the conversion efficiency of an optical parametric oscillator using a bi-directional pump geometry.

Science.gov (United States)

Norris, G; McConnell, G

2010-03-01

A novel bi-directional pump geometry that nonlinearly increases the nonlinear optical conversion efficiency of a synchronously pumped optical parametric oscillator (OPO) is reported. This bi-directional pumping method synchronizes the circulating signal pulse with two counter-propagating pump pulses within a linear OPO resonator. Through this pump scheme, an increase in nonlinear optical conversion efficiency of 22% was achieved at the signal wavelength, corresponding to a 95% overall increase in average power. Given an almost unchanged measured pulse duration of 260 fs under optimal performance conditions, this related to a signal wavelength peak power output of 18.8 kW, compared with 10 kW using the traditional single-pass geometry. In this study, a total effective peak intensity pump-field of 7.11 GW/cm(2) (corresponding to 3.55 GW/cm(2) from each pump beam) was applied to a 3 mm long periodically poled lithium niobate crystal, which had a damage threshold intensity of 4 GW/cm(2), without impairing crystal integrity. We therefore prove the application of this novel pump geometry provides opportunities for power-scaling of synchronously pumped OPO systems together with enhanced nonlinear conversion efficiency through relaxed damage threshold intensity conditions.

Microwave oscillator based on an intrinsic BSCCO-type Josephson junction

DEFF Research Database (Denmark)

Pedersen, Niels Falsig; Madsen, Søren Peder

2005-01-01

. The resulting model is a set of coupled nonlinear partial differential equations. By direct numerical simulations we have demonstrated that the qualitative behavior of the combined intrinsic Josephson junction and cavity system can be understood on the basis of general concepts of nonlinear oscillators...

Implementing a memristive Van der Pol oscillator coupled to a linear oscillator: synchronization and application to secure communication

International Nuclear Information System (INIS)

Megam Ngouonkadi, E B; Fotsin, H B; Louodop Fotso, P

2014-01-01

This paper investigates the dynamics of a memristor-based Van der Pol oscillator coupled to a linear circuit (VDPCL). This chaotic oscillator is a modification of the classical Van der Pol coupled to a linear circuit, and is obtained by replacing the classical cubic nonlinearity by the memristive one. The memristive VDPCL oscillator, in addition to having a very special stability property, exhibits interesting spectral characteristics, which makes it suitable for chaos-based secure communication applications. The memristor is realized by using off-the-shelf components. The basic properties of the circuit are analyzed by means of bifurcation analysis. Chaotic attractors from numerical and experimental analysis are presented, followed by a comparison of results obtained from the modified VDPCL oscillator and those from the classical VDPCL oscillator. An application to synchronization and chaos secure communication is also presented. (paper)

Oscillating electromagnetic soliton in an anisotropic ferromagnetic medium

Energy Technology Data Exchange (ETDEWEB)

Sathishkumar, P., E-mail: perumal_sathish@yahoo.co.in [Department of Physics, K.S.R. College of Engineering (Autonomous), Tiruchengode 637215, Tamilnadu (India); Senjudarvannan, R. [Department of Physics, Jansons Institute of Technology, Karumathampatty, Coimbatore 641659 (India)

2017-05-01

We investigate theoretically the propagation of electromagnetic oscillating soliton in the form of breather in an anisotropic ferromagnetic medium. The interaction of magnetization with the magnetic field component of the electromagnetic (EM) wave has been studied by solving Maxwell's equations coupled with a Landau–Lifshitz equation for the magnetization of the medium. We made a small perturbation on the magnetization and magnetic field along the direction of propagation of EM wave in the framework of reductive perturbation method and the associated nonlinear magnetization dynamics is governed by a generalized derivative nonlinear Schrödinger (DNLS) equation. In order to understand the dynamics of the concerned system, we employ the Jacobi elliptic function method to solve the DNLS equation and deduce breatherlike soliton modes for the EM wave in the medium. - Highlights: • The propagation of electromagnetic oscillating soliton in an anisotropic ferromagnetic medium is investigated in the presence of varying external magnetic field. • The magnetization and electromagnetic wave modulates in the form of breathing like oscillating solitons. • The governing nonlinear spin dynamical equation is studied through a reductive perturbation method. • The magnetization components of the ferromagnetic medium are derived using Jacobi elliptic functions method with the aid of symbolic computation.

The Duffing oscillator with damping

DEFF Research Database (Denmark)

Johannessen, Kim

2015-01-01

An analytical solution to the differential equation describing the Duffing oscillator with damping is presented. The damping term of the differential equation and the initial conditions satisfy an algebraic equation, and thus the solution is specific for this type of damping. The nonlinear term...... of the differential equation is allowed to be considerable compared to the linear term. The solution is expressed in terms of the Jacobi elliptic functions by including a parameter-dependent elliptic modulus. The analytical solution is compared to the numerical solution, and the agreement is found to be very good....... It is established that the period of oscillation is shorter compared to that of a linearized model but increasing with time and asymptotically approaching the period of oscillation of the linear damped model. An explicit expression for the period of oscillation has been derived, and it is found to be very accurate....

The effect of loss of immunity on noise-induced sustained oscillations in epidemics.

Science.gov (United States)

Chaffee, J; Kuske, R

2011-11-01

The effect of loss of immunity on sustained population oscillations about an endemic equilibrium is studied via a multiple scales analysis of a SIRS model. The analysis captures the key elements supporting the nearly regular oscillations of the infected and susceptible populations, namely, the interaction of the deterministic and stochastic dynamics together with the separation of time scales of the damping and the period of these oscillations. The derivation of a nonlinear stochastic amplitude equation describing the envelope of the oscillations yields two criteria providing explicit parameter ranges where they can be observed. These conditions are similar to those found for other applications in the context of coherence resonance, in which noise drives nearly regular oscillations in a system that is quiescent without noise. In this context the criteria indicate how loss of immunity and other factors can lead to a significant increase in the parameter range for prevalence of the sustained oscillations, without any external driving forces. Comparison of the power spectral densities of the full model and the approximation confirms that the multiple scales analysis captures nonlinear features of the oscillations.

Modal analysis of inter-area oscillations using the theory of normal modes

Energy Technology Data Exchange (ETDEWEB)

Betancourt, R.J. [School of Electromechanical Engineering, University of Colima, Manzanillo, Col. 28860 (Mexico); Barocio, E. [CUCEI, University of Guadalajara, Guadalajara, Jal. 44480 (Mexico); Messina, A.R. [Graduate Program in Electrical Engineering, Cinvestav, Guadalajara, Jal. 45015 (Mexico); Martinez, I. [State Autonomous University of Mexico, Toluca, Edo. Mex. 50110 (Mexico)

2009-04-15

Based on the notion of normal modes in mechanical systems, a method is proposed for the analysis and characterization of oscillatory processes in power systems. The method is based on the property of invariance of modal subspaces and can be used to represent complex power system modal behavior by a set of decoupled, two-degree-of-freedom nonlinear oscillator equations. Using techniques from nonlinear mechanics, a new approach is outlined, for determining the normal modes (NMs) of motion of a general n-degree-of-freedom nonlinear system. Equations relating the normal modes and the physical velocities and displacements are developed from the linearized system model and numerical issues associated with the application of the technique are discussed. In addition to qualitative insight, this method can be utilized in the study of nonlinear behavior and bifurcation analyses. The application of these procedures is illustrated on a planning model of the Mexican interconnected system using a quadratic nonlinear model. Specifically, the use of normal mode analysis as a basis for identifying modal parameters, including natural frequencies and damping ratios of general, linear systems with n degrees of freedom is discussed. Comparisons to conventional linear analysis techniques demonstrate the ability of the proposed technique to extract the different oscillation modes embedded in the oscillation. (author)

Nonlinear response and bistability of driven ion acoustic waves

Science.gov (United States)

Akbari-Moghanjoughi, M.

2017-08-01

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

Nonlinear optical interactions in silicon waveguides

Directory of Open Access Journals (Sweden)

Kuyken B.

2017-03-01

Full Text Available The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.

Chemical event chain model of coupled genetic oscillators.

Science.gov (United States)

Jörg, David J; Morelli, Luis G; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Chemical event chain model of coupled genetic oscillators

Science.gov (United States)

Jörg, David J.; Morelli, Luis G.; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Phase-locking phenomena and excitation of damped and driven nonlinear oscillators

DEFF Research Database (Denmark)

Shagalov, A.G.; Juul Rasmussen, Jens; Naulin, Volker

2009-01-01

Resonant phase-locking phenomena ('autoresonance') in the van der Pol Duffing oscillator forced by a small amplitude periodic driving with slowly varying frequency have been studied. We show that autoresonance occurs for oscillators with sufficiently small damping, when the system may have bi-stable...

Nonlinear behavior of nonradial oscillations in ε Per

International Nuclear Information System (INIS)

Smith, M.A.

1987-01-01

The authors conducted a simultaneous spectroscopic/photometric campaign of ε Per (BO.7 III) during five nights in November, 1984. The spectroscopic data consist of 300 observations of the Si III λλ4552-74 triplet, while the photometric data were obtained at two different observatories. In both sets of data they find a dominant 3.85+-.02 hr. period. The analysis of line profiles in the context of nonradial pulsation (NRP) indicates this oscillation is caused by a -m=iota =4 mode. In this context the line profiles also indicate the presence of a secondary -m=iota =6 mode with a period of 2.25+-.03 hr, an oscillation below the detection threshold in the photometric data. These periodicities and mode identifications have been reported by Penrod on other occasions. They may be considered to be stable except that their amplitudes vary from epoch to epoch

The nonlinear dynamics of the Oklo natural reactor

International Nuclear Information System (INIS)

Bilanovic, Z.; Harms, A.A.

1985-01-01

An analysis of the Oklo natural reactor, a self-sustaining and self-regulating critical assembly that existed some 2 billion years ago in Gabon, Africa, is presented. Nonlinear continuous dif ferential and nonlinear discrete iterative formulations are established and selected parameter characterizations identified. Conceivable power oscillations are calculated and discussed. Some implications of nonlinear mappings for nuclear simulation are suggested

Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations

Directory of Open Access Journals (Sweden)

Rong Haiwu

2014-01-01

Full Text Available The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.

Waves and Oscillations in Plasmas

CERN Document Server

Pecseli, Hans L

2012-01-01

The result of more than 15 years of lectures in plasma sciences presented at universities in Denmark, Norway, and the United States, Waves and Oscillations in Plasmas addresses central issues in modern plasma sciences. The book covers fluid models as well as kinetic plasma models, including a detailed discussion of, for instance, collisionless Landau damping. Offering a clear separation of linear and nonlinear models, the book can be tailored for readers of varying levels of expertise.Designed to provide basic training in linear as well as nonlinear plasma dynamics, and practical in areas as d

Curvature-induced symmetry breaking in nonlinear Schrodinger models

DEFF Research Database (Denmark)

Gaididei, Yuri Borisovich; Mingaleev, S. F.; Christiansen, Peter Leth

2000-01-01

We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states...

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...

Nonlinear optics principles and applications

CERN Document Server

Rottwitt, Karsten

2014-01-01

IntroductionReview of linear opticsInduced polarizationHarmonic oscillator modelLocal field correctionsEstimated nonlinear responseSummaryTime-domain material responseThe polarization time-response functionThe Born-Oppenheimer approximationRaman scattering response function of silicaSummaryMaterial response in the frequency domain, susceptibility tensorsThe susceptibility tensorThe induced polarization in the frequency domainSum of monochromatic fieldsThe prefactor to the induced polarizationThird-order polarization in the Born-Oppenheimer approximation in the frequency domainKramers-Kronig relationsSummarySymmetries in nonlinear opticsSpatial symmetriesSecond-order materialsThird-order nonlinear materialsCyclic coordinate-systemContracted notation for second-order susceptibility tensorsSummaryThe nonlinear wave equationMono and quasi-monochromatic beamsPlane waves - the transverse problemWaveguidesVectorial approachNonlinear birefringenceSummarySecond-order nonlinear effectsGeneral theoryCoupled wave theoryP...

Heartbeat of the Southern Oscillation explains ENSO climatic resonances

Science.gov (United States)

Bruun, John T.; Allen, J. Icarus; Smyth, Timothy J.

2017-08-01

The El Niño-Southern Oscillation (ENSO) nonlinear oscillator phenomenon has a far reaching influence on the climate and human activities. The up to 10 year quasi-period cycle of the El Niño and subsequent La Niña is known to be dominated in the tropics by nonlinear physical interaction of wind with the equatorial waveguide in the Pacific. Long-term cyclic phenomena do not feature in the current theory of the ENSO process. We update the theory by assessing low (>10 years) and high (features. The observational data sets of the Southern Oscillation Index (SOI), North Pacific Index Anomaly, and ENSO Sea Surface Temperature Anomaly, as well as a theoretical model all confirm the existence of long-term and short-term climatic cycles of the ENSO process with resonance frequencies of {2.5, 3.8, 5, 12-14, 61-75, 180} years. This fundamental result shows long-term and short-term signal coupling with mode locking across the dominant ENSO dynamics. These dominant oscillation frequency dynamics, defined as ENSO frequency states, contain a stable attractor with three frequencies in resonance allowing us to coin the term Heartbeat of the Southern Oscillation due to its characteristic shape. We predict future ENSO states based on a stable hysteresis scenario of short-term and long-term ENSO oscillations over the next century.Plain Language SummaryThe Pacific El Niño-Southern Oscillation (ENSO) nonlinear oscillator phenomenon has a far reaching influence on the climate and our human activities. This work can help predict both long-term and short-term future ENSO events and to assess the risk of future climate hysteresis changes: is the elastic band that regulates the ENSO climate breaking? We update the current theory of the ENSO process with a sophisticated analysis approach (Dominant Frequency State Analysis) to include long-term oscillations (up to 200 years) as well as tropical and extratropical interaction dynamics. The analysis uses instrumental and paleoproxy data

Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

Science.gov (United States)

Wu, Jiagui; Huang, Shu-Wei; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Duan, Shukai; Wei Wong, Chee

2017-01-01

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale. PMID:28598426

Energy transfer in coupled nonlinear phononic waveguides: transition from wandering breather to nonlinear self-trapping

International Nuclear Information System (INIS)

Kosevich, Y A; Manevitch, L I; Savin, A V

2007-01-01

We consider, both analytically and numerically, the dynamics of stationary and slowly-moving breathers (localized short-wavelength excitations) in two weakly coupled nonlinear oscillator chains (nonlinear phononic waveguides). We show that there are two qualitatively different dynamical regimes of the coupled breathers: the oscillatory exchange of the low-amplitude breather between the phononic waveguides (wandering breather), and one-waveguide-localization (nonlinear self-trapping) of the high-amplitude breather. We also show that phase-coherent dynamics of the coupled breathers in two weakly linked nonlinear phononic waveguides has a profound analogy, and is described by a similar pair of equations, to the tunnelling quantum dynamics of two weakly linked Bose-Einstein condensates in a symmetric double-well potential (single bosonic Josephson junction). The exchange of phonon energy and excitations between the coupled phononic waveguides takes on the role which the exchange of atoms via quantum tunnelling plays in the case of the coupled condensates. On the basis of this analogy, we predict a new tunnelling mode of the coupled Bose-Einstein condensates in a single bosonic Josephson junction in which their relative phase oscillates around π/2. The dynamics of relative phase of two weakly linked Bose-Einstein condensates can be studied by means of interference, while the dynamics of the exchange of lattice excitations in coupled nonlinear phononic waveguides can be observed by means of light scattering

Linear and nonlinear low-frequency electrostatic waves in a nonuniform pair-ion-dust magnetoplasma

International Nuclear Information System (INIS)

Saleem, H; Shukla, P K; Eliasson, B

2008-01-01

Linear and nonlinear properties of the low-frequency (in comparison with the ion gyrofrequency) electrostatic oscillations in pair-ion-dust magnetoplasma are presented. In the linear limit, the Shukla-Varma mode is coupled with the ion oscillations while the nonlinearly coupled modes appear in the form of a dipolar or a monopolar vortex

Phase locking between Josephson soliton oscillators

DEFF Research Database (Denmark)

Holst, T.; Hansen, Jørn Bindslev; Grønbech-Jensen, N.

1990-01-01

We report observations of phase-locking phenomena between two Josephson soliton (fluxon) oscillators biased in self-resonant modes. The locking strength was measured as a function of bias conditions. A frequency tunability of the phase-locked oscillators up to 7% at 10 GHz was observed. Two coupled...... perturbed sine-Gordon equations were derived from an equivalent circuit consisting of inductively coupled, nonlinear, lossy transmission lines. These equations were solved numerically to find the locking regions. Good qualitative agreement was found between the experimental results and the calculations...

Nonlinear oscillation and interfacial stability of an encapsulated microbubble under dual-frequency ultrasound

Energy Technology Data Exchange (ETDEWEB)

Liu, Yunqiao [MOE Key Laboratory of Hydrodynamics, Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240 (China); Calvisi, Michael L [Department of Mechanical and Aerospace Engineering, University of Colorado, Colorado Springs, CO 80918, United States of America (United States); Wang, Qianxi, E-mail: yunqiaoliu@sjtu.edu.cn [School of Mathematics, University of Birmingham, Birmingham B15 2TT (United Kingdom)

2017-04-15

Encapsulated microbubbles (EMBs) are widely used in medical ultrasound imaging as contrast-enhanced agents. However, the potential damaging effects of violent collapsing EMBs to cells and tissues in clinical settings have remained a concern. Dual-frequency ultrasound is a promising technique for improving the efficacy and safety of sonography. The system modeled consists of the external liquid, membrane and internal gases of an EMB. The microbubble dynamics are simulated using a simple nonlinear interactive theory, considering the compressibility of the internal gas, viscosity of the liquid flow and viscoelasticity of the membrane. The radial oscillation and interfacial stability of an EMB under single- and dual-frequency excitations are compared. The simulation results show that the dual-frequency technique produces larger backscatter pressure at higher harmonics of the primary driving frequency—this enriched acoustic spectrum can enhance blood-tissue contrast and improve the quality of sonographic images. The results further show that the acoustic pressure threshold associated with the onset of shape instability is greater for dual-frequency driving. This suggests that the dual-frequency technique stabilizes the encapsulated bubble, thereby improving the efficacy and safety of contrast-enhanced agents. (paper)

The implications of non-linear biological oscillations on human electrophysiology for electrohypersensitivity (EHS) and multiple chemical sensitivity (MCS).

Science.gov (United States)

Sage, Cindy

2015-01-01

The 'informational content' of Earth's electromagnetic signaling is like a set of operating instructions for human life. These environmental cues are dynamic and involve exquisitely low inputs (intensities) of critical frequencies with which all life on Earth evolved. Circadian and other temporal biological rhythms depend on these fluctuating electromagnetic inputs to direct gene expression, cell communication and metabolism, neural development, brainwave activity, neural synchrony, a diversity of immune functions, sleep and wake cycles, behavior and cognition. Oscillation is also a universal phenomenon, and biological systems of the heart, brain and gut are dependent on the cooperative actions of cells that function according to principles of non-linear, coupled biological oscillations for their synchrony. They are dependent on exquisitely timed cues from the environment at vanishingly small levels. Altered 'informational content' of environmental cues can swamp natural electromagnetic cues and result in dysregulation of normal biological rhythms that direct growth, development, metabolism and repair mechanisms. Pulsed electromagnetic fields (PEMF) and radiofrequency radiation (RFR) can have the devastating biological effects of disrupting homeostasis and desynchronizing normal biological rhythms that maintain health. Non-linear, weak field biological oscillations govern body electrophysiology, organize cell and tissue functions and maintain organ systems. Artificial bioelectrical interference can give false information (disruptive signaling) sufficient to affect critical pacemaker cells (of the heart, gut and brain) and desynchronize functions of these important cells that orchestrate function and maintain health. Chronic physiological stress undermines homeostasis whether it is chemically induced or electromagnetically induced (or both exposures are simultaneous contributors). This can eventually break down adaptive biological responses critical to health

The charged bubble oscillator: Dynamics and thresholds

Indian Academy of Sciences (India)

The nonlinear, forced oscillations of a bubble in a fluid due to an external pressure field are studied theoretically. ... for the system, delineating different dynamics. Keywords. ..... (c) Power spectral density of the charged and uncharged bub-.

Nonlinearity and nonclassicality in a nanomechanical resonator

Energy Technology Data Exchange (ETDEWEB)

Teklu, Berihu [Clermont Universite, Blaise Pascal University, CNRS, PHOTON-N2, Institut Pascal, Aubiere Cedex (France); Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy); Ferraro, Alessandro; Paternostro, Mauro [Queen' s University, Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Belfast (United Kingdom); Paris, Matteo G.A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy)

2015-12-15

We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems. (orig.)

Nonlinear magnetohydrodynamics of edge localized mode precursors

Energy Technology Data Exchange (ETDEWEB)

Guo, Z. B., E-mail: guozhipku@gmail.com [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China); WCI Center for Fusion Theory, NFRI, Gwahangno 113, Yusung-gu, Daejeon 305-333 (Korea, Republic of); Wang, Lu [SEEE, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Wang, X. G. [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China)

2015-02-15

A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ω{sub pre}∼x{sup 1/3}ξ{sup ^}{sub ψ,in}{sup 2/3}n, with x position in radial direction, ξ{sup ^}{sub ψ,in} strength of initial perturbation, and n toroidal mode number.

Non-linear stochastic response of a shallow cable

DEFF Research Database (Denmark)

Larsen, Jesper Winther; Nielsen, Søren R.K.

2004-01-01

The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two...

Synchronization of delay-coupled nonlinear oscillators: an approach based on the stability analysis of synchronized equilibria.

Science.gov (United States)

Michiels, Wim; Nijmeijer, Henk

2009-09-01

We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the paper starts from an exact stability analysis in a (gain, delay) parameter space of a synchronized equilibrium and extracts insights from an analysis of its bifurcations and from the corresponding emerging behavior. Instrumental to this analysis a factorization of the characteristic equation is employed that not only facilitates the analysis and reduces computational cost but also allows to determine the precise role of the individual agents and the topology of the network in the (in)stability mechanisms. The study provides an algorithm to perform a stability and bifurcation analysis of synchronized equilibria. Furthermore, it reveals fundamental limitations to synchronization and it explains under which conditions on the topology of the network and on the characteristics of the coupling the systems are expected to synchronize. In the second part of the paper the results are applied to coupled Lorenz systems. The main results show that for sufficiently large coupling gains, delay-coupled Lorenz systems exhibit a generic behavior that does not depend on the number of systems and the topology of the network, as long as some basic assumptions are satisfied, including the strong connectivity of the graph. Here the linearized stability analysis is strengthened by a nonlinear stability analysis which confirms the predictions based on the linearized stability and bifurcation analysis. This illustrates the usefulness of the exact linearized analysis in a situation where a direct nonlinear stability analysis is not possible or where it yields conservative conditions from which it is hard to get qualitative insights in the synchronization mechanisms and their scaling properties

Relaxation oscillations induced by amplitude-dependent frequency in dissipative trapped electron mode turbulence

International Nuclear Information System (INIS)

Terry, P.W.; Ware, A.S.; Newman, D.E.

1994-01-01

A nonlinear frequency shift in dissipative trapped electron mode turbulence is shown to give rise to a relaxation oscillation in the saturated power density spectrum. A simple non-Markovian closure for the coupled evolution of ion momentum and electron density response is developed to describe the oscillations. From solutions of a nonlinear oscillator model based on the closure, it is found that the oscillation is driven by the growth rate, as modified by the amplitude-dependent frequency shift, with inertia provided by the memory of the growth rate of prior amplitudes. This memory arises from time-history integrals common to statistical closures. The memory associated with a finite time of energy transfer between coupled spectrum components does not sustain the oscillation in the simple model. Solutions of the model agree qualitatively with the time-dependent numerical solutions of the original dissipative trapped electron model, yielding oscillations with the proper phase relationship between the fluctuation energy and the frequency shift, the proper evolution of the wave number spectrum shape and particle flux, and a realistic period

Mode competition and hopping in optomechanical nano-oscillators

Science.gov (United States)

Zhang, Xingwang; Lin, Tong; Tian, Feng; Du, Han; Zou, Yongchao; Chau, Fook Siong; Zhou, Guangya

2018-04-01

We investigate the inter-mode nonlinear interaction in the multi-mode optomechanical nano-oscillator which consists of coupled silicon nanocantilevers, where the integrated photonic crystal nanocavities provide the coupling between the optical and mechanical modes. Due to the self-saturation and cross-saturation of the mechanical gain, the inter-mode competition is observed, which leads to the bistable operation of the optomechanical nano-oscillator: only one of the mechanical modes can oscillate at any one time, and the oscillation of one mode extremely suppresses that of the other with a side mode suppression ratio (SMSR) up to 40 dB. In the meantime, mode hopping, i.e., the optomechanical oscillation switches from one mode to the other, is also observed and found to be able to be provoked by excitation laser fluctuations.

Nonlinear effects on Turing patterns: Time oscillations and chaos

KAUST Repository

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.

A probabilistic analysis of the crystal oscillator behavior at low drive levels

Science.gov (United States)

Shmaliy, Yuriy S.; Brendel, Rémi

2008-03-01

The paper discusses a probabilistic model of a crystal oscillator at low drive levels where the noise intensity is comparable with the oscillation amplitude. The stationary probability density of the oscillations envelope is derived and investigated for the nonlinear resonator loses. A stochastic explanation is given for the well-known phenomenon termed sleeping sickness associated with losing a facility of self-excitation by a crystal oscillator after a long storage without a power supply. It is shown that, with low drive levels leading to an insufficient feedback, a crystal oscillator generates the noise-induced oscillations rather than it absolutely "falls in sleep".

Nonlinear Dynamics in Spear Wigglers

International Nuclear Information System (INIS)

2002-01-01

BL11, the most recently installed wiggler in the SPEAR storage ring at SSRL, produces a large nonlinear perturbation of the electron beam dynamics, which was not directly evident in the integrated magnetic field measurements. Measurements of tune shifts with betatron oscillation amplitude and with closed orbit shifts were used to characterize the nonlinear fields of the SPEAR insertion devices (IDs). Because of the narrow pole width in BL11, the nonlinear fields seen along the wiggling electron trajectory are dramatically different than the flip coil measurements made along a straight line. This difference explains the tune shift measurements and the observed degradation in dynamic aperture. Corrector magnets to cancel the BL11 nonlinear fields are presently under construction

Dynamics of nonlinear oscillators with time-varying conjugate coupling

Indian Academy of Sciences (India)

oscillators. We analyze the behavior of coupled systems with respect to the coupling switching frequency using ..... are of potential utility in appropriate design strategies and/or understanding of complex systems with dynamic interaction ...

Nonlinear dynamics of the human lumbar intervertebral disc.

Science.gov (United States)

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J

2015-02-05

Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated. Copyright © 2014 Elsevier Ltd. All rights reserved.

International Conference on Applications in Nonlinear Dynamics

CERN Document Server

Longhini, Patrick; Palacios, Antonio

2017-01-01

This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

Nonlinear bias compensation of ZiYuan-3 satellite imagery with cubic splines

Science.gov (United States)

Cao, Jinshan; Fu, Jianhong; Yuan, Xiuxiao; Gong, Jianya

2017-11-01

Like many high-resolution satellites such as the ALOS, MOMS-2P, QuickBird, and ZiYuan1-02C satellites, the ZiYuan-3 satellite suffers from different levels of attitude oscillations. As a result of such oscillations, the rational polynomial coefficients (RPCs) obtained using a terrain-independent scenario often have nonlinear biases. In the sensor orientation of ZiYuan-3 imagery based on a rational function model (RFM), these nonlinear biases cannot be effectively compensated by an affine transformation. The sensor orientation accuracy is thereby worse than expected. In order to eliminate the influence of attitude oscillations on the RFM-based sensor orientation, a feasible nonlinear bias compensation approach for ZiYuan-3 imagery with cubic splines is proposed. In this approach, no actual ground control points (GCPs) are required to determine the cubic splines. First, the RPCs are calculated using a three-dimensional virtual control grid generated based on a physical sensor model. Second, one cubic spline is used to model the residual errors of the virtual control points in the row direction and another cubic spline is used to model the residual errors in the column direction. Then, the estimated cubic splines are used to compensate the nonlinear biases in the RPCs. Finally, the affine transformation parameters are used to compensate the residual biases in the RPCs. Three ZiYuan-3 images were tested. The experimental results showed that before the nonlinear bias compensation, the residual errors of the independent check points were nonlinearly biased. Even if the number of GCPs used to determine the affine transformation parameters was increased from 4 to 16, these nonlinear biases could not be effectively compensated. After the nonlinear bias compensation with the estimated cubic splines, the influence of the attitude oscillations could be eliminated. The RFM-based sensor orientation accuracies of the three ZiYuan-3 images reached 0.981 pixels, 0.890 pixels, and 1

Vibrational mechanics nonlinear dynamic effects, general approach, applications

CERN Document Server

Blekhman, Iliya I

2000-01-01

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat

Synchronization of Coupled Different Chaotic FitzHugh-Nagumo Neurons with Unknown Parameters under Communication-Direction-Dependent Coupling

Directory of Open Access Journals (Sweden)

Muhammad Iqbal

2014-01-01

Full Text Available This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN neurons with unknown parameters under external electrical stimulation (EES. The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.

Relation of deformed nonlinear algebras with linear ones

International Nuclear Information System (INIS)

Nowicki, A; Tkachuk, V M

2014-01-01

The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator. (paper)

On the theory of internal kink oscillations

International Nuclear Information System (INIS)

Breizman, B.N.; Candy, J.; Berk, H.L.

1997-12-01

In this paper the authors derive a time evolution equation for internal kink oscillations which is valid for both stable and unstable plasma regimes, and incorporates the nonlinear response of an energetic particle population. A linear analysis reveals a parallel between (i) the time evolution of the spatial derivative of the internal kink radial displacement and (ii) the time evolution of the perturbed particle distribution function in the field of an electrostatic wave (Landau problem). They show that diamagnetic drift effects make the asymptotic decay of internal kink perturbations in a stable plasma algebraic rather than exponential. However, under certain conditions the stable root of the dispersion relation can dominate the response of the on-axis displacement for a significant period of time. The form of the evolution equation naturally allows one to include a nonlinear, fully toroidal treatment of energetic particles into the theory of internal kink oscillations

Modeling of termokinetic oscillations at partial oxidation of methane

Science.gov (United States)

Arutyunov, A. V.; Belyaev, A. A.; Inovenkov, I. N.; Nefedov, V. V.

2017-12-01

Partial oxidation of natural gas at moderate temperatures below 1500 K has significant interest for a number of industrial applications. But such processes can proceed at different unstable regimes including oscillating modes. Nonlinear phenomena at partial oxidation of methane were observed at different conditions. The investigation of the complex nonlinear system of equations that describes this process is a real method to insure its stability at industrial conditions and, at the same time, is an effective tool for its further enhancement. Numerical analysis of methane oxidation kinetics in the continuous stirred-tank reactor, with the use of detailed kinetic model has shown the possibility of the appearance of oscillating modes in the appropriate range of reaction parameters that characterize the composition, pressure, reagents flow, thermophysical features of the system, and geometry of the reactor. The appearance of oscillating modes is connected both with the reaction kinetics, heat release and sink and reagents introduction and removing. At that, oscillations appear only at a limited range of parameters, but can be accompanied by significant change in the yield of products. We have determined the range of initial temperature and pressure at which oscillations can be observed, if all other parameters remained fixed. The boundaries of existence of oscillations on the phase plane were calculated. It was shown that depending on the position inside the oscillation region the oscillations have different frequency and amplitude. It was reviled the role of heat exchange with the environment: at the absence of heat exchange the oscillating modes are impossible. In the vicinity of the boundary of phase range, where oscillations exist, significant change of concentration of some products were observed, for example, that of CO2, which in this case one of the principal products is. At that, insignificant increase in pressure not only change the character of CO2 behaving

Nonlinear von Neumann equations for quantum dissipative systems

International Nuclear Information System (INIS)

Messer, J.; Baumgartner, B.

1978-01-01

For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)

Nonlinear von Neumann equations for quantum dissipative systems

International Nuclear Information System (INIS)

Messer, J.; Baumgartner, B.

For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)

Chimera States in Neural Oscillators

Science.gov (United States)

Bahar, Sonya; Glaze, Tera

2014-03-01

Chimera states have recently been explored both theoretically and experimentally, in various coupled nonlinear oscillators, ranging from phase-oscillator models to coupled chemical reactions. In a chimera state, both coherent and incoherent (or synchronized and desynchronized) states occur simultaneously in populations of identical oscillators. We investigate chimera behavior in a population of neural oscillators using the Huber-Braun model, a Hodgkin-Huxley-like model originally developed to characterize the temperature-dependent bursting behavior of mammalian cold receptors. One population of neurons is allowed to synchronize, with each neuron receiving input from all the others in its group (global within-group coupling). Subsequently, a second population of identical neurons is placed under an identical global within-group coupling, and the two populations are also coupled to each other (between-group coupling). For certain values of the coupling constants, the neurons in the two populations exhibit radically different synchronization behavior. We will discuss the range of chimera activity in the model, and discuss its implications for actual neural activity, such as unihemispheric sleep.

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.

Time-averaged second-order pressure and velocity measurements in a pressurized oscillating flow prime mover

Energy Technology Data Exchange (ETDEWEB)

Paridaens, Richard [DynFluid, Arts et Metiers, 151 boulevard de l' Hopital, Paris (France); Kouidri, Smaine [LIMSI-CNRS, Orsay Cedex (France)

2016-11-15

Nonlinear phenomena in oscillating flow devices cause the appearance of a relatively minor secondary flow known as acoustic streaming, which is superimposed on the primary oscillating flow. Knowledge of control parameters, such as the time-averaged second-order velocity and pressure, would elucidate the non-linear phenomena responsible for this part of the decrease in the system's energetic efficiency. This paper focuses on the characterization of a travelling wave oscillating flow engine by measuring the time-averaged second order pressure and velocity. Laser Doppler velocimetry technique was used to measure the time-averaged second-order velocity. As streaming is a second-order phenomenon, its measurement requires specific settings especially in a pressurized device. Difficulties in obtaining the proper settings are highlighted in this study. The experiments were performed for mean pressures varying from 10 bars to 22 bars. Non-linear effect does not constantly increase with pressure.

Quantum synchronization of quantum van der Pol oscillators with trapped ions.

Science.gov (United States)

Lee, Tony E; Sadeghpour, H R

2013-12-06

The van der Pol oscillator is the prototypical self-sustained oscillator and has been used to model nonlinear behavior in biological and other classical processes. We investigate how quantum fluctuations affect phase locking of one or many van der Pol oscillators. We find that phase locking is much more robust in the quantum model than in the equivalent classical model. Trapped-ion experiments are ideally suited to simulate van der Pol oscillators in the quantum regime via sideband heating and cooling of motional modes. We provide realistic experimental parameters for 171Yb+ achievable with current technology.

Tuning chaos in network sharing common nonlinearity

Science.gov (United States)

Paul Asir, M.; Jeevarekha, A.; Philominathan, P.

2016-06-01

In this paper, a novel type of network called network sharing common nonlinearity comprising both autonomous and non-autonomous oscillators have been investigated. We propose that these networks are robust for operating at desired modes i.e., chaotic or periodic by altering the v-i characteristics of common nonlinear element alone. The dynamics of these networks were examined through numerical, analytical, experimental and Multisim simulations.

Monlinear fish-scale metamaterial via coupled duffing oscillators

OpenAIRE

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

Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

Directory of Open Access Journals (Sweden)

Kun Wei

Full Text Available In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE. Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

Science.gov (United States)

Wei, Kun; Gao, Shilong; Zhong, Suchuan; Ma, Hong

2012-01-01

In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

Science.gov (United States)

Gopal, R.; Chandrasekar, V. K.; Senthilkumar, D. V.; Venkatesan, A.; Lakshmanan, M.

2018-06-01

A complex collective emerging behavior characterized by coexisting coherent and incoherent domains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators driven by a common dynamic environment. The latter facilitates the onset of phase-flip bifurcation/transitions among the coupled oscillators of the ensemble, while the nonlocal coupling induces a partial asynchronization among the out-of-phase synchronized oscillators at this onset. This leads to the manifestation of coexisting out-of-phase synchronized coherent domains interspersed by asynchronous incoherent domains elucidating the existence of a different type of chimera state. In addition to this, a rich variety of other collective behaviors such as clusters with phase-flip transition, conventional chimera, solitary state and complete synchronized state which have been reported using different coupling architectures are found to be induced by the employed couplings for appropriate coupling strengths. The robustness of the resulting dynamics is demonstrated in ensembles of two paradigmatic models, namely Rössler oscillators and Stuart-Landau oscillators.

The benefits of noise and nonlinearity: Extracting energy from random vibrations

Energy Technology Data Exchange (ETDEWEB)

Gammaitoni, Luca, E-mail: luca.gammaitoni@pg.infn.it [NiPS Laboratory, Universita di Perugia, I-06100 Perugia (Italy); Neri, Igor; Vocca, Helios [NiPS Laboratory, Universita di Perugia, I-06100 Perugia (Italy)

2010-10-05

Nonlinear behavior is the ordinary feature of the vast majority of dynamical systems and noise is commonly present in any finite temperature physical and chemical system. In this article we briefly review the potentially beneficial outcome of the interplay of noise and nonlinearity by addressing the novel field of vibration energy harvesting. The role of nonlinearity in a piezoelectric harvester oscillator dynamics is modeled with nonlinear stochastic differential equation.

Nonlinear electrostatic ion-acoustic "oscilliton" waves driven by charge non-neutrality effects

Directory of Open Access Journals (Sweden)

J. Z. G. Ma

2011-01-01

Full Text Available Nonlinear "oscilliton" structures features a low-frequency (LF solitary envelope, the amplitude of which is modulated violently by superimposed high-frequency (HF oscillations. We have studied the charge non-neutrality effects on the excitation of electrostatic ion-acoustic (IA oscillitons. A two-fluid, warm plasma model is employed, and a set of nonlinear self-similar equations is solved in a cylindrical geometry. Under charge-neutrality conditions, three conventional IA structures (namely, sinusoidal, sawtooth, and spicky/bipolar are obtained. By contrast, under charge non-neutrality conditions, oscilliton structures are excited, where the LF envelope is in the sound-wave (SW mode, while the HF ingredients include the IA mode and the ion-Langmiur (IL mode. The amplitudes of the SW wave are violently modulated by the IA oscillations, whereas the upward sides of the IA amplitudes are modulated by the IL oscillations of smaller amplitudes, and the downward sides are modulated by hybrid IA/IL oscillations. The nonlinear oscillitons are found to be dependent not only upon the input parameters (e.g., the Mach number, the Debye length, and the initial temperature of particles, but on initial conditions as well.

Large time behaviour of oscillatory nonlinear solute transport in porous media

NARCIS (Netherlands)

Duijn, van C.J.; Zee, van der S.E.A.T.M.

2018-01-01

Oscillations in flow occur under many different situations in natural porous media, due to tidal, daily or seasonal patterns. In this paper, we investigate how such oscillations in flow affect the transport of an initially sharp solute front, if the solute undergoes nonlinear sorption and,

Comparison of heaving buoy and oscillating flap wave energy converters

Science.gov (United States)

Abu Bakar, Mohd Aftar; Green, David A.; Metcalfe, Andrew V.; Najafian, G.

2013-04-01

Waves offer an attractive source of renewable energy, with relatively low environmental impact, for communities reasonably close to the sea. Two types of simple wave energy converters (WEC), the heaving buoy WEC and the oscillating flap WEC, are studied. Both WECs are considered as simple energy converters because they can be modelled, to a first approximation, as single degree of freedom linear dynamic systems. In this study, we estimate the response of both WECs to typical wave inputs; wave height for the buoy and corresponding wave surge for the flap, using spectral methods. A nonlinear model of the oscillating flap WEC that includes the drag force, modelled by the Morison equation is also considered. The response to a surge input is estimated by discrete time simulation (DTS), using central difference approximations to derivatives. This is compared with the response of the linear model obtained by DTS and also validated using the spectral method. Bendat's nonlinear system identification (BNLSI) technique was used to analyze the nonlinear dynamic system since the spectral analysis was only suitable for linear dynamic system. The effects of including the nonlinear term are quantified.

Coupled large earthquakes in the Baikal rift system: Response to bifurcations in nonlinear resonance hysteresis

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.

Chaos Noise on Phase of Van Der Pol Oscillator

Directory of Open Access Journals (Sweden)

Xian He Huang

2010-12-01

Full Text Available Phase noise is the most important parameter in many oscillators. In this paper, based on nonlinear stochastic differential equation for phase noise analysis approach is proposed. And then discusses and compares the influence of two different sources of noise in the Van Der Pol oscillator adopted this method. One source of noise is a white noise process, which is a genuinely stochastic process; the other source of noise is actually a deterministic system, which exhibits chaotic behavior in some regions. The behavior of the oscillator under different conditions is investigated numerically. It is shown that the phase noise of the oscillator is affected more by noise arising from chaos than by noise arising from the genuine stochastic process at the same noise intensity.

Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification

International Nuclear Information System (INIS)

Fotsin, H.B.; Daafouz, J.

2005-01-01

This Letter uses systematic tools from recent papers to design non-linear observers for synchronization of a chaotic colpitts oscillator both in the non adaptive and adaptive cases. It is shown that all parameters of a totally uncertain model of the oscillator can be estimated through adaptive synchronization. A strategy for practical implementation of a secure communication strategy is also discussed

Oscillation and chaos in physiological control systems.

Science.gov (United States)

Mackey, M C; Glass, L

1977-07-15

First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.

Acoustic Pressure Oscillations Induced in I-Burner

Science.gov (United States)

Matsui, Kiyoshi

Iwama et al. invented the I-burner to investigate acoustic combustion instability in solid-propellant rockets (Proceedings of ICT Conference, 1994, pp. 26-1 26-14). Longitudinal pressure oscillations were induced in the combustion chamber of a thick-walled rocket by combustion of a stepped-perforation grain (I-burner). These oscillations were studied here experimentally. Two I-burners with an internal diameter of 80 mm and a length of 1208 mm or 2240 mm were made. The grain had stepped perforations (20 and 42 mm in diameter and 657 and 160 mm in length, respectively). Longitudinal pressure oscillations always occur in two stages when an HTPB (hydroxyl-terminated polybutadiene)/AP (ammonium perchlorate)/aluminum-powder propellant burns (54 tests; the highest average pressure in the combustion chamber was 9.5 29 MPa), but no oscillations occur when an HTPB/AP propellant burns (29 tests). The pressure oscillations are essentially linear, but dissipation adds a nonlinear nature to them. In the first stage, the amplitudes are small and the first wave group predominates. In the next stage, the amplitudes are large and many wave groups are present. The change in the grain form accompanying the combustion affects the pressure oscillations.

Phase multistability of self-modulated oscillations

DEFF Research Database (Denmark)

Sosnovtseva, Olga; Postnov, D.E.; Nekrasov, A.M.

2002-01-01

The paper examines the type of multistability that one can observe in the synchronization of two oscillators when the systems individually display self-modulation or other types of multicrest wave forms. The investigation is based on a phase reduction method and on the calculation of phase maps...... nonlinearity and a biologically motivated model of nephron autoregulation are presented....

Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?

NARCIS (Netherlands)

Wit, Hero P.; van Dijk, Pim

Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of

Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?

Science.gov (United States)

Wit, Hero P; van Dijk, Pim

2012-08-01

Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of SOAEs.

Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts

International Nuclear Information System (INIS)

Emans, Joseph; Wiercigroch, Marian; Krivtsov, Anton M.

2005-01-01

The nonlinear analysis of a common beam system was performed, and the method for such, outlined and presented. Nonlinear terms for the governing dynamic equations were extracted and the behaviour of the system was investigated. The analysis was carried out with and without physically realistic parameters, to show the characteristics of the system, and the physically realistic responses. Also, the response as part of a more complex system was considered, in order to investigate the cumulative effects of nonlinearities. Chaos, as well as periodic motion was found readily for the physically unrealistic parameters. In addition, nonlinear behaviour such as co-existence of attractors was found even at modest oscillation levels during investigations with realistic parameters. When considered as part of a more complex system with further nonlinearities, comparisons with linear beam theory show the classical approach to be lacking in accuracy of qualitative predictions, even at weak oscillations

Excitation of high numbers harmonics by flows of oscillators in a periodic potential

International Nuclear Information System (INIS)

Buts, V.A.; Marekha, V.I.; Tolstoluzhsky, A.P.

2005-01-01

It is shown that the maximum of radiation spectrum of nonrelativistic oscillators, which move into a periodically inhomogeneous potential, can be in the region of high numbers harmonics. Spectrum of such oscillators radiation becomes similar to the radiation spectrum of relativistic oscillators. The equations, describing the non-linear self-consistent theory of excitations, of high numbers harmonics by ensemble of oscillators are formulated and its numerical analysis is conducted. The numerical analysis has confirmed the capability of radiation of high numbers of harmonics. Such peculiarity of radiation allows t expect of creation of nonrelativistic FEL

Measurement of nonlinear mode coupling of tearing fluctuations

International Nuclear Information System (INIS)

Assadi, S.; Prager, S.C.; Sidikman, K.L.

1992-03-01

Three-wave nonlinear coupling of spatial Fourier modes is measured in the MST reversed field pinch by applying bi-spectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 polodial modes and 32 toroidal modes. Comparison to bi-spectra predicted by MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomittant with a broadened (presumably nonlinearly generated) k-spectrum

Spatial xenon oscillation control with expert systems

International Nuclear Information System (INIS)

Alten, S.; Danofsky, R.A.

1993-01-01

Spatial power oscillations were attributed to the xenon transients in a reactor core in 1958 by Randall and St. John. These transients are usually initiated by a local reactivity insertion and lead to divergent axial flux oscillations in the core at constant power. Several heuristic manual control strategies and automatic control methods were developed to damp the xenon oscillations at constant power operations. However, after the load-follow operation of the reactors became a necessity of life, a need for better control strategies arose. Even though various advanced control strategies were applied to solve the xenon oscillation control problem for the load-follow operation, the complexity of the system created difficulties in modeling. The strong nonlinearity of the problem requires highly sophisticated analytical approaches that are quite inept for numerical solutions. On the other hand, the complexity of a system and heuristic nature of the solutions are the basic reasons for using artificial intelligence techniques such as expert systems

Frequency and amplitude stabilization in MEMS and NEMS oscillators

Science.gov (United States)

Chen, Changyao; Lopez, Omar Daniel; Czaplewski, David A.

2017-06-14

This invention comprises a nonlinear micro- and nano-mechanical resonator that can maintain frequency of operation and amplitude of operation for a period of time after all external power has been removed from the device. Utilizing specific nonlinear dynamics of the micromechanical resonator, mechanical energy at low frequencies can be input and stored in higher frequencies modes, thus using the multiple degrees of freedom of the resonator to extend its energy storage capacity. Furthermore, the energy stored in multiple vibrational modes can be used to maintain the resonator oscillating for a fixed period of time, even without an external power supply. This is the first demonstration of an "autonomous" frequency source that can maintain a constant frequency and vibrating amplitude when no external power is provided, making it ideal for applications requiring an oscillator in low power, or limited and intermittent power supplies.

Effects of phase lag on the information rate of a bistable Duffing oscillator

International Nuclear Information System (INIS)

Perkins, Edmon; Balachandran, Balakumar

2015-01-01

To utilize noise for systems, which are transmitting or receiving information, the information rate is a necessary metric to consider. The phase lag, which is the difference between the sender (applied forcing) and receiver (the oscillator) phases, has a significant effect on the information rate. However, this phase lag is a nonlinear function of the noise level. Here, the effects of phase lag on the information rate for a Duffing oscillator are examined and comparative discussions are made with phase lag from linear response theory. The phase lag is shown to be an important variable in calculating the information rate. - Highlights: • Simulations and Fokker–Planck analysis for Duffing oscillator response are performed. • The phase lag is found to be a nonlinear function of the noise level. • The phase lag is shown to be important for calculating the information rate metric

Effects of phase lag on the information rate of a bistable Duffing oscillator

Energy Technology Data Exchange (ETDEWEB)

Perkins, Edmon, E-mail: edmon@umd.edu; Balachandran, Balakumar, E-mail: balab@umd.edu

2015-02-06

To utilize noise for systems, which are transmitting or receiving information, the information rate is a necessary metric to consider. The phase lag, which is the difference between the sender (applied forcing) and receiver (the oscillator) phases, has a significant effect on the information rate. However, this phase lag is a nonlinear function of the noise level. Here, the effects of phase lag on the information rate for a Duffing oscillator are examined and comparative discussions are made with phase lag from linear response theory. The phase lag is shown to be an important variable in calculating the information rate. - Highlights: • Simulations and Fokker–Planck analysis for Duffing oscillator response are performed. • The phase lag is found to be a nonlinear function of the noise level. • The phase lag is shown to be important for calculating the information rate metric.

Supersymmetric construction of exactly solvable potentials and nonlinear algebras

International Nuclear Information System (INIS)

Junker, G.; Roy, P.

1998-01-01

Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and lowering operators of these harmonic oscillators and the SUSY operators we construct ladder operators for these new conditionally solvable systems. It is found that these ladder operators together with the Hamilton operator form a nonlinear algebra which is of quadratic and cubic type for the SUSY partners of the linear and radial harmonic oscillator

Steady-state mechanical squeezing and ground-state cooling of a Duffing anharmonic oscillator in an optomechanical cavity assisted by a nonlinear medium

Science.gov (United States)

Momeni, F.; Naderi, M. H.

2018-05-01

In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric nonlinearity can be exploited to drive the system toward the multistability region. We also show that for appropriate values of the mechanical anharmonicity strength the steady-state mechanical squeezing and the ground-state cooling of the mechanical resonator can be achieved. Moreover, we find that the presence of the nonlinear gain medium can lead to the improvement of the mechanical anharmonicity-induced cooling of the mechanical motion, as well as to the mechanical squeezing beyond the standard quantum limit of 3 dB.

Oscillations-free PID control of anesthetic drug delivery in neuromuscular blockade.

Science.gov (United States)

Medvedev, Alexander; Zhusubaliyev, Zhanybai T; Rosén, Olov; Silva, Margarida M

2016-07-25

The PID-control of drug delivery or the neuromuscular blockade (NMB) in closed-loop anesthesia is considered. The NMB system dynamics portrayed by a Wiener model can exhibit sustained nonlinear oscillations under realistic PID gains and for physiologically feasible values of the model parameters. Such oscillations, also repeatedly observed in clinical trials, lead to under- and over-dosing of the administered drug and undermine patient safety. This paper proposes a tuning policy for the proportional PID gain that via bifurcation analysis ensures oscillations-free performance of the control loop. Online estimates of the Wiener model parameters are needed for the controller implementation and monitoring of the closed-loop proximity to oscillation. The nonlinear dynamics of the PID-controlled NMB system are studied by bifurcation analysis. A database of patient models estimated under PID-controlled neuromuscular blockade during general anesthesia is utilized, along with the corresponding clinical measurements. The performance of three recursive algorithms is compared in the application at hand: an extended Kalman filter, a conventional particle filter (PF), and a PF making use of an orthonormal basis to estimate the probability density function from the particle set. It is shown that with a time-varying proportional PID gain, the type of equilibria of the closed-loop system remains the same as in the case of constant controller gains. The recovery time and frequency of oscillations are also evaluated in simulation over the database of patient models. Nonlinear identification techniques based on model linearization yield biased parameter estimates and thus introduce superfluous uncertainty. The bias and variance of the estimated models are related to the computational complexity of the identification algorithms, highlighting the superiority of the PFs in this safety-critical application. The study demonstrates feasibility of the proposed oscillation-free control

Superconducting Nanowires as Nonlinear Inductive Elements for Qubits

OpenAIRE

Ku, Jaseung; Manucharyan, Vladimir; Bezryadin, Alexey

2010-01-01

We report microwave transmission measurements of superconducting Fabry-Perot resonators (SFPR), having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonl...

New Oscillation Criteria for Second-Order Forced Quasilinear Functional Differential Equations

Directory of Open Access Journals (Sweden)

Mervan Pašić

2013-01-01

or delay-advanced types. The nonlinear terms are of superlinear or supersublinear (mixed types. Consequences and examples are shown to illustrate the novelty and simplicity of our oscillation criteria.

Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping

International Nuclear Information System (INIS)

Raghavan, S.; Smerzi, A.; Fantoni, S.; Shenoy, S.R.

2001-03-01

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 3 He-B and the internal Josephson effect in 3 He-A are also discussed. (author)

Bloch oscillations and accelerated Bose–Einstein condensates in an optical lattice

Energy Technology Data Exchange (ETDEWEB)

Sacchetti, Andrea, E-mail: andrea.sacchetti@unimore.it

2017-01-30

Highlights: • Discrete nonlinear Schrödinger model for accelerated BECs in optical lattices. • Numerical computation of wavefunction BECs dynamics. • Correlation between nonlinearity and the oscillating period of the BEC's center of mass. • Discussion of the validity of the Bloch Theorem for accelerated BECs in an optical lattice. - Abstract: We discuss the method for the measurement of the gravity acceleration g by means of Bloch oscillations of an accelerated BEC in an optical lattice. This method has a theoretical critical point due to the fact that the period of the Bloch oscillations depends, in principle, on the initial shape of the BEC wavepacket. Here, by making use of the nearest-neighbor model for the numerical analysis of the BEC wavefunction, we show that in real experiments the period of the Bloch oscillations does not really depend on the shape of the initial wavepacket and that the relative uncertainty, due to the fact that the initial shape of the wavepacket may be asymmetrical, is smaller than the one due to experimental errors. Furthermore, we also show that the relation between the oscillation period and the scattering length of the BEC's atoms is linear; this fact suggests us a new experimental procedure for the measurement of the scattering length of atoms.

Theory of oscillators

CERN Document Server

Andronov, Aleksandr Aleksandrovich; Vitt, Aleksandr Adolfovich

1966-01-01

Theory of Oscillators presents the applications and exposition of the qualitative theory of differential equations. This book discusses the idea of a discontinuous transition in a dynamic process. Organized into 11 chapters, this book begins with an overview of the simplest type of oscillatory system in which the motion is described by a linear differential equation. This text then examines the character of the motion of the representative point along the hyperbola. Other chapters consider examples of two basic types of non-linear non-conservative systems, namely, dissipative systems and self-

Nonlinear dynamics and stability of boiling water reactors: qualitative and quantitative analyses

International Nuclear Information System (INIS)

March-Leuba, J.; Cacuci, D.G.; Perez, R.B.

1985-01-01

A phenomenological model has been developed to simulate the qualitative behavior of boiling water reactors (BWRs) in the nonlinear regime under deterministic and stochastic excitations. After the linear stability threshold is crossed, limit cycle oscillations appear due to interactions between two unstable equilibrium points and the phase-space trajectories. This limit cycle becomes unstable when the feedback gain exceeds a certain critical value. Subsequent limit cycle instabilities produce a cascade of period-doubling bifurcations that leads to a periodic pulsed behavior. Under stochastic excitations, BWRs exhibit a single characteristic resonance, at approx.0.5 Hz, in the linear regime. By contrast, this work shows that harmonics of this characteristic frequency appear in the nonlinear regime. Furthermore, this work also demonstrates that amplitudes of the limit cycle oscillations do not depend on the variance of the stochastic excitation and remain bounded at all times. A physical model of nonlinear BWR dynamics has also been developed and employed to calculate the amplitude of limit cycle oscillations and their effects on fuel integrity over a wide range of operating conditions in the Vermont Yankee reactor. These calculations have confirmed that, beyond the threshold for linear stability, the reactor's state variable undergo limit cycle oscillations

High-data-transfer-rate read heads composed of spin-torque oscillators

International Nuclear Information System (INIS)

Mizushima, K; Kudo, K; Nagasawa, T; Sato, R

2011-01-01

The signal-to-noise ratios (SNRs) of the high-data-transfer-rate read heads beyond 3 Gbits/s composed of spin-torque oscillators (STOs) are calculated under the thermal magnetization fluctuations by using the recent nonlinear theories. The STO head senses the media field as a modulation in the oscillation frequency, enabling high signal transfer rates beyond the limit of ferromagnetic relaxation. The output (digital) signal is obtained by FM (frequency modulation) detection, which is commonly used in communication technologies. As the problem of rapid phase diffusion in STOs caused by the thermal fluctuations is overcome by employing a delay detection method, the sufficiently large SNRs are obtained even in nonlinear STOs less than 30 x 30 nm 2 in size.

Controllability in tunable chains of coupled harmonic oscillators

DEFF Research Database (Denmark)

Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David

2018-01-01

any desired Gaussian state requires at most 3 N ( N −1)/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can......We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N −1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach...... be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides....

Controllability in tunable chains of coupled harmonic oscillators

Science.gov (United States)

Buchmann, L. F.; Mølmer, K.; Petrosyan, D.

2018-04-01

We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N -1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach any desired Gaussian state requires at most 3 N (N -1 )/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides.

Controllability in tunable chains of coupled harmonic oscillators

DEFF Research Database (Denmark)

Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David

2018-01-01

We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N −1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach...... any desired Gaussian state requires at most 3 N ( N −1)/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can...... be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides....

Even and odd combinations of nonlinear coherent states

International Nuclear Information System (INIS)

De los Santos-Sanchez, O; Recamier, J

2011-01-01

In this work we present some statistical properties of even and odd combinations of nonlinear coherent states associated with two nonlinear potentials; one supporting a finite number of bound states and the other supporting an infinite number of bound states, within the framework of an f-deformed algebra. We calculate their normalized variance and the temporal evolution of their dispersion relations using nonlinear coherent states defined as (a) eigensates of the deformed annihilation operator and (b) those states created by the application of a deformed displacement operator upon the ground state of the oscillator.

The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection

Science.gov (United States)

Franzen, J.

1994-01-01

The superposition of higher order multipole fields on the basic quadrupole field in ion traps generates a non-harmonic oscillator system for the ions. Fourier analyses of simulated secular oscillations in non-linear ion traps, therefore, not only reveal the sideband frequencies, well-known from the Mathieu theory, but additionally a commonwealth of multipole-specific overtones (or higher harmonics), and corresponding sidebands of overtones. Non-linear resonances occur when the overtone frequencies match sideband frequencies. It can be shown that in each of the resonance conditions, not just one overtone matches one sideband, instead, groups of overtones match groups of sidebands. The generation of overtones is studied by Fourier analysis of computed ion oscillations in the direction of thez axis. Even multipoles (octopole, dodecapole, etc.) generate only odd orders of higher harmonics (3, 5, etc.) of the secular frequency, explainable by the symmetry with regard to the planez = 0. In contrast, odd multipoles (hexapole, decapole, etc.) generate all orders of higher harmonics. For all multipoles, the lowest higher harmonics are found to be strongest. With multipoles of higher orders, the strength of the overtones decreases weaker with the order of the harmonics. Forz direction resonances in stationary trapping fields, the function governing the amplitude growth is investigated by computer simulations. The ejection in thez direction, as a function of timet, follows, at least in good approximation, the equation wheren is the order of multipole, andC is a constant. This equation is strictly valid for the electrically applied dipole field (n = 1), matching the secular frequency or one of its sidebands, resulting in a linear increase of the amplitude. It is valid also for the basic quadrupole field (n = 2) outside the stability area, giving an exponential increase. It is at least approximately valid for the non-linear resonances by weak superpositions of all higher odd

A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations

International Nuclear Information System (INIS)

Ge, Gen; Li, ZePeng

2016-01-01

A modified stochastic averaging method on single-degree-of-freedom (SDOF) oscillators under white noise excitations with strongly nonlinearity was proposed. Considering the existing approach dealing with strongly nonlinear SDOFs derived by Zhu and Huang [14, 15] is quite time consuming in calculating the drift coefficient and diffusion coefficients and the expressions of them are considerable long, the so-called He's energy balance method was applied to overcome the minor defect of the Zhu and Huang's method. The modified method can offer more concise approximate expressions of the drift and diffusion coefficients without weakening the accuracy of predicting the responses of the systems too much by giving an averaged frequency beforehand. Three examples, a cubic and quadratic nonlinearity coexisting oscillator, a quadratic nonlinear oscillator under external white noise excitations and an externally excited Duffing–Rayleigh oscillator, were given to illustrate the approach we proposed. The three examples were excited by the Gaussian white noise and the Gaussian colored noise separately. The stationary responses of probability density of amplitudes and energy, together with joint probability density of displacement and velocity are studied to verify the presented approach. The reliability of the systems were also investigated to offer further support. Digital simulations were carried out and the output of that are coincide with the theoretical approximations well.

Explanation of the Inverse Doppler Effect Observed in Nonlinear Transmission Lines

International Nuclear Information System (INIS)

Kozyrev, Alexander B.; Weide, Daniel W. van der

2005-01-01

The theory of the inverse Doppler effect recently observed in magnetic nonlinear transmission lines is developed. We explain the crucial role of the backward spatial harmonic in the occurrence of an inverse Doppler effect and draw analogies of the magnetic nonlinear transmission line to the backward wave oscillator

Nonlinear dynamics of boiling water reactors

International Nuclear Information System (INIS)

March-Leuba, J.; Cacuci, D.G.; Perez, R.B.

1983-01-01

Recent stability tests in Boiling Water Reactors (BWRs) have indicated that these reactors can exhibit the special nonlinear behavior of following a closed trajectory called limit cycle. The existence of a limit cycle corresponds to an oscillation of fixed amplitude and period. During these tests, such oscillations had their amplitudes limited to about +- 15% of the operating power. Since limit cycles are fairly insensitive to parameter variations, it is possible to operate a BWR under conditions that sustain a limit cycle (of fixed amplitude and period) over a finite range of reactor parameters

Chimera states in an ensemble of linearly locally coupled bistable oscillators

Science.gov (United States)

Shchapin, D. S.; Dmitrichev, A. S.; Nekorkin, V. I.

2017-11-01

Chimera states in a system with linear local connections have been studied. The system is a ring ensemble of analog bistable self-excited oscillators with a resistive coupling. It has been shown that the existence of chimera states is not due to the nonidentity of oscillators and noise, which is always present in real experiments, but is due to the nonlinear dynamics of the system on invariant tori with various dimensions.

Non-linear Vibration of Oscillation Systems using Frequency-Amplitude Formulation

DEFF Research Database (Denmark)

Fereidoon, A.; Ghadimi, M.; Barari, Amin

2012-01-01

In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifthorder 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 t...... 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....

Basin stability measure of different steady states in coupled oscillators

Science.gov (United States)

Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar

2017-04-01

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.

Applications of Nonlinear Dynamics Model and Design of Complex Systems

CERN Document Server

In, Visarath; Palacios, Antonio

2009-01-01

This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

Experiments in nonlinear dynamics using control-based continuation: Tracking stable and unstable response curves

DEFF Research Database (Denmark)

Bureau, Emil; Schilder, Frank; Santos, Ilmar

2014-01-01

We show how to implement control-based continuation in a nonlinear experiment using existing and freely available software. We demonstrate that it is possible to track the complete frequency response, including the unstable branches, for a harmonically forced impact oscillator.......We show how to implement control-based continuation in a nonlinear experiment using existing and freely available software. We demonstrate that it is possible to track the complete frequency response, including the unstable branches, for a harmonically forced impact oscillator....

Higher-order chaotic oscillator using active bessel filter

DEFF Research Database (Denmark)

Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra

2010-01-01

A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending...

Image processing with a cellular nonlinear network

International Nuclear Information System (INIS)

Morfu, S.

2005-01-01

A cellular nonlinear network (CNN) based on uncoupled nonlinear oscillators is proposed for image processing purposes. It is shown theoretically and numerically that the contrast of an image loaded at the nodes of the CNN is strongly enhanced, even if this one is initially weak. An image inversion can be also obtained without reconfiguration of the network whereas a gray levels extraction can be performed with an additional threshold filtering. Lastly, an electronic implementation of this CNN is presented

Predicting chaos in memristive oscillator via harmonic balance method.

Science.gov (United States)

Wang, Xin; Li, Chuandong; Huang, Tingwen; Duan, Shukai

2012-12-01

This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.

Nonlinear Quantum Optical Springs and Their Nonclassical Properties

International Nuclear Information System (INIS)

Faghihi, M.J.; Tavassoly, M.K.

2011-01-01

The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in the Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its frequency) depends on the quantum states of another system. Recently, it is realized that by the assumption of frequency modulation of ω to ω√1+μa † a the mentioned idea can be established. In the present paper, we generalize the approach of quantum optical spring with particular attention to the dependence of frequency to the intensity of radiation field that naturally observes in the nonlinear coherent states, from which we arrive at a physical system has been called by us as nonlinear quantum optical spring. Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters, as particular quantum features, will be revealed. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Estimation of airway smooth muscle stiffness changes due to length oscillation using artificial neural network.

Science.gov (United States)

Al-Jumaily, Ahmed; Chen, Leizhi

2012-10-07

This paper presents a novel approach to estimate stiffness changes in airway smooth muscles due to external oscillation. Artificial neural networks are used to model the stiffness changes due to cyclic stretches of the smooth muscles. The nonlinear relationship between stiffness ratios and oscillation frequencies is modeled by a feed-forward neural network (FNN) model. The structure of the FNN is selected through the training and validation using literature data from 11 experiments with different muscle lengths, muscle masses, oscillation frequencies and amplitudes. Data pre-processing methods are used to improve the robustness of the neural network model to match the non-linearity. The validation results show that the FNN model can predict the stiffness ratio changes with a mean square error of 0.0042. Copyright © 2012 Elsevier Ltd. All rights reserved.

Study of chaotic oscillations in practical work on radio physics

International Nuclear Information System (INIS)

Ezdov, A.A.; Il'in, V.A.; Petrova, E.B.

1995-01-01

A description is given of a laboratory study of chaotic oscillations in deterministic dynamical systems. This work utilizes mathematical modeling and a computer experiment, as well as a direct study of the chaotic behavior of nonlinear electrical circuits

Relationship Between the Parameters of the Linear and Nonlinear Wave Generation Stages in a Magnetospheric Cyclotron Maser in the Backward-Wave Oscillator Regime

Science.gov (United States)

Demekhov, A. G.

2017-03-01

By using numerical simulations we generalize certain relationships between the parameters of quasimonochromatic whistler-mode waves generated at the linear and nonlinear stages of the cyclotron instability in the backward-wave oscillator regime. One of these relationships is between the wave amplitude at the nonlinear stage and the linear growth rate of the cyclotron instability. It was obtained analytically by V.Yu.Trakhtengerts (1984) for a uniform medium under the assumption of constant frequency and amplitude of the generated wave. We show that a similar relationship also holds for the signals generated in a nonuniform magnetic field and having a discrete structure in the form of short wave packets (elements) with fast frequency drift inside each element. We also generalize the formula for the linear growth rate of absolute cyclotron instability in a nonuniform medium and analyze the relationship between the frequency drift rate in the discrete elements and the wave amplitude. These relationships are important for analyzing the links between the parameters of chorus emissions in the Earth's and planetary magnetospheres and the characteristics of the energetic charged particles generating these signals.

Nonlinear dynamics in integrated coupled DFB lasers with ultra-short delay.

Science.gov (United States)

Liu, Dong; Sun, Changzheng; Xiong, Bing; Luo, Yi

2014-03-10

We report rich nonlinear dynamics in integrated coupled lasers with ultra-short coupling delay. Mutually stable locking, period-1 oscillation, frequency locking, quasi-periodicity and chaos are observed experimentally. The dynamic behaviors are reproduced numerically by solving coupled delay differential equations that take the variation of both frequency detuning and coupling phase into account. Moreover, it is pointed out that the round-trip frequency is not involved in the above nonlinear dynamical behaviors. Instead, the relationship between the frequency detuning Δν and the relaxation oscillation frequency νr under mutual injection are found to be critical for the various observed dynamics in mutually coupled lasers with very short delay.

Synchronization of muscular oscillations between two subjects during isometric interaction

Directory of Open Access Journals (Sweden)

Laura V. Schaefer

2014-05-01

Full Text Available Muscles oscillate with a frequency around 10 Hz. But what happens with myofascial oscillations, if two neuromuscular systems interact? The purpose of this study was to examine this question, initially, on the basis of a case study. Oscillations of the triceps brachii muscles of two subjects were determined through mechanomyography (MMG during isometric interaction. The MMG-signals were analyzed concerning the interaction of the two subjects with algorithms of nonlinear dynamics. In this case study it could be shown, that the muscles of both neuromuscular systems also oscillate with the known frequency (here 12 Hz during interaction. Furthermore, both subjects were able to adapt their oscillations against each other. This adjustment induced a significant ( < .05 coherent behavior, which was characterized by a phase shifting of approximately 90°. The authors draw the conclusion, that the complementary neuromuscular partners potentially have the ability of mutual synchronization.

Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations

KAUST Repository

Carles, Ré mi; Dumas, Eric; Sparber, Christof

2010-01-01

We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrödinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation of the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrödinger equation on the torus in negative order Sobolev spaces. © 2010 Society for Industrial and Applied Mathematics.

PERFORMANCE IMPROVEMENT OF A CHEMICAL REACTOR BY NONLINEAR NATURAL OSCILLATIONS

NARCIS (Netherlands)

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

The dynamics of two linearly coupled Goodwin oscillators

Science.gov (United States)

Antonova, A. O.; Reznik, S. N.; Todorov, M. D.

2017-10-01

In this paper the Puu model of the interaction of Goodwin's business cycles for two regions is reconsidered. We investigated the effect of the accelerator coefficients and the Hicksian 'ceiling' and 'floor' parameters on the time dynamics of incomes for different values of marginal propensity to import. The cases when the periods of isolated Goodwin's cycles are close, and when they differ approximately twice are considered. By perturbation theory we obtained the formulas for slowly varying amplitudes and phase difference of weakly nonlinear coupled Goodwin oscillations. The coupled oscillations of two Goodwin's cycles with piecewise linear accelerators with only 'floor' are considered.

Control of Limit Cycle Oscillations of a Two-Dimensional Aeroelastic System

Directory of Open Access Journals (Sweden)

M. Ghommem

2010-01-01

Full Text Available Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO. It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be effciently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.

Deep saturated Free Electron Laser oscillators and frozen spikes

Energy Technology Data Exchange (ETDEWEB)

Ottaviani, P.L. [ENEA - Centro Ricerche Bologna, via Martiri di Monte Sole, 4, IT 40129, Bologna (Italy); Pagnutti, S., E-mail: simonetta.pagnutti@enea.it [ENEA - Centro Ricerche Bologna, via Martiri di Monte Sole, 4, IT 40129, Bologna (Italy); Dattoli, G., E-mail: giuseppe.dattoli@enea.it [ENEA - Centro Ricerche Frascati, via E. Fermi, 45, IT 00044, Frascati, Roma (Italy); Sabia, E., E-mail: elio.sabia@enea.it [ENEA - Centro Ricerche Frascati, via E. Fermi, 45, IT 00044, Frascati, Roma (Italy); Petrillo, V., E-mail: vittoria.petrillo@mi.infn.it [Universita' degli Studi di Milano, via Celoria 16, IT 20133, Milano (Italy); INFN - Mi, via Celoria 16, IT 20133, Milano (Italy); Slot, P.J.M. van der, E-mail: p.j.m.vanderslot@utwente.nl [Mesa+ Institute for Nanotechnology, University of Twente, P.O.Box 217, 7500 AE, Enschede (Netherlands); Biedron, S., E-mail: sandra.biedron@colostate.edu [Department of Electrical and Computer Engineering Colorado State University (United States); Milton, S., E-mail: milton@engr.colostate.edu [Department of Electrical and Computer Engineering Colorado State University (United States)

2016-10-21

We analyze the behavior of Free Electron Laser (FEL) oscillators operating in the deep saturated regime and point out the formation of sub-peaks of the optical pulse. These are very stable configurations and the sub-peaks are found to have a duration corresponding to the coherence length. We speculate on the physical mechanisms underlying their growth and attempt an identification with natural mode-locked structures in FEL oscillators. Their impact on the intra-cavity nonlinear harmonic generation is also discussed along with the possibility of exploiting them as cavity out-coupler.

Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit

International Nuclear Information System (INIS)

Wang Jinzhi; Duan Zhisheng; Huang Lin

2006-01-01

In this Letter a new method of chaos control for Chua's circuit and the modified canonical Chua's electrical circuit is proposed by using the results of dichotomy in nonlinear systems. A linear feedback control based on linear matrix inequality (LMI) is given such that chaos oscillation or hyperchaos phenomenon of circuit systems injected control signal disappear. Numerical simulations are presented to illustrate the efficiency of the proposed method

Simulations of oscillatory systems with award-winning software, physics of oscillations

CERN Document Server

Butikov, Eugene I

2015-01-01

Deepen Your Students' Understanding of Oscillations through Interactive Experiments Simulations of Oscillatory Systems: with Award-Winning Software, Physics of Oscillations provides a hands-on way of visualizing and understanding the fundamental concepts of the physics of oscillations. Both the textbook and software are designed as exploration-oriented supplements for courses in general physics and the theory of oscillations. The book is conveniently structured according to mathematical complexity. Each chapter in Part I contains activities, questions, exercises, and problems of varying levels of difficulty, from straightforward to quite challenging. Part II presents more sophisticated, highly mathematical material that delves into the serious theoretical background for the computer-aided study of oscillations. The software package allows students to observe the motion of linear and nonlinear mechanical oscillatory systems and to obtain plots of the variables that describe the systems along with phase diagram...

Potential role of the glycolytic oscillator in acute hypoxia in tumors

International Nuclear Information System (INIS)

Fru, Leonard Che; Adamson, Erin B; Campos, David D; Fain, Sean B; Song, Chihwa; Kissick, Michael W; Jacques, Steven L; Van der Kogel, Albert J; Nickel, Kwang P; Kimple, Randall J

2015-01-01

Tumor acute hypoxia has a dynamic component that is also, at least partially, coherent. Using blood oxygen level dependent magnetic resonance imaging, we observed coherent oscillations in hemoglobin saturation dynamics in cell line xenograft models of head and neck squamous cell carcinoma. We posit a well-established biochemical nonlinear oscillatory mechanism called the glycolytic oscillator as a potential cause of the coherent oscillations in tumors. These data suggest that metabolic changes within individual tumor cells may affect the local tumor microenvironment including oxygen availability and therefore radiosensitivity. These individual cells can synchronize the oscillations in patches of similar intermediate glucose levels. These alterations have potentially important implications for radiation therapy and are a potential target for optimizing the cancer response to radiation. (paper)

The effect of the dust’s electric dipole moment on transverse oscillations of the one dimensional dusty crystals

Directory of Open Access Journals (Sweden)

S Karimi

2013-10-01

Full Text Available In this paper, we investigated the effect of dipole-dipole interaction between the dust particles on the transverse oscillation of one dimensional dusty crystal. We used the Boltzmann distribution for the electrons and ions density and assumed that dust particles are negatively charged. The equation of motion for dust particles in this one dimensional chain was obtained. It is shown that the direction of dipoles plays an important role in the motion of dusts and significantly changes the oscillation frequency. Also, in the long wavelength approximation, a nonlinear Schrödinger equation for the evolution of the amplitude of the nonlinear oscillations was derived, showing that both the bright solitons and the dark solitons could exist.

Extreme Nonlinear Optics An Introduction

CERN Document Server

Wegener, Martin

2005-01-01

Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged. Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself. This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The followi...

Halo Mitigation Using Nonlinear Lattices

CERN Document Server

Sonnad, Kiran G

2005-01-01

This work shows that halos in beams with space charge effects can be controlled by combining nonlinear focusing and collimation. The study relies on Particle-in-Cell (PIC) simulations for a one dimensional, continuous focusing model. The PIC simulation results show that nonlinear focusing leads to damping of the beam oscillations thereby reducing the mismatch. It is well established that reduced mismatch leads to reduced halo formation. However, the nonlinear damping is accompanied by emittance growth causing the beam to spread in phase space. As a result, inducing nonlinear damping alone cannot help mitigate the halo. To compensate for this expansion in phase space, the beam is collimated in the simulation and further evolution of the beam shows that the halo is not regenerated. The focusing model used in the PIC is analysed using the Lie Transform perturbation theory showing that by averaging over a lattice period, one can reuduce the focusing force to a form that is identical to that used in the PIC simula...

Extraction and prediction of indices for monsoon intraseasonal oscillations: an approach based on nonlinear Laplacian spectral analysis

Science.gov (United States)

Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.

2017-11-01

An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜3 weeks.

Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

Science.gov (United States)

Vasconcellos, Rui; Abdelkefi, Abdessattar

2015-01-01

The effects of a multi-segmented nonlinearity in the pitch degree of freedom on the behavior of a two-degree of freedom aeroelastic system are investigated. The aeroelastic system is free to plunge and pitch and is supported by linear translational and nonlinear torsional springs and is subjected to an incoming flow. The unsteady representation based on the Duhamel formulation is used to model the aerodynamic loads. Using modern method of nonlinear dynamics, a nonlinear characterization is performed to identify the system's response when increasing the wind speed. It is demonstrated that four sudden transitions take place with a change in the system's response. It is shown that, in the first transition, the system's response changes from simply periodic (only main oscillating frequency) to two periods (having the main oscillating frequency and its superharmonic of order 2). In the second transition, the response of the system changes from two periods (having the main oscillating frequency and its superharmonic of order 2) to a period-1. The results also show that the third transition is accompanied by a change in the system's response from simply periodic to two periods (having the main oscillating frequency and its superharmonic of order 3). After this transition, chaotic responses take place and then the fourth transition is accompanied by a sudden change in the system's response from chaotic to two periods (having the main oscillating frequency and its superharmonic of order 3). The results show that these transitions are caused by the tangential contact between the trajectory and the multi-segmented nonlinearity boundaries and with a zero-pitch speed incidence. This observation is associated with the definition of grazing bifurcation.

Classical plasma dynamics of Mie-oscillations in atomic clusters

Science.gov (United States)

Kull, H.-J.; El-Khawaldeh, A.

2018-04-01

Mie plasmons are of basic importance for the absorption of laser light by atomic clusters. In this work we first review the classical Rayleigh-theory of a dielectric sphere in an external electric field and Thomson’s plum-pudding model applied to atomic clusters. Both approaches allow for elementary discussions of Mie oscillations, however, they also indicate deficiencies in describing the damping mechanisms by electrons crossing the cluster surface. Nonlinear oscillator models have been widely studied to gain an understanding of damping and absorption by outer ionization of the cluster. In the present work, we attempt to address the issue of plasmon relaxation in atomic clusters in more detail based on classical particle simulations. In particular, we wish to study the role of thermal motion on plasmon relaxation, thereby extending nonlinear models of collective single-electron motion. Our simulations are particularly adopted to the regime of classical kinetics in weakly coupled plasmas and to cluster sizes extending the Debye-screening length. It will be illustrated how surface scattering leads to the relaxation of Mie oscillations in the presence of thermal motion and of electron spill-out at the cluster surface. This work is intended to give, from a classical perspective, further insight into recent work on plasmon relaxation in quantum plasmas [1].

Nonlinear ordinary differential equations analytical approximation and numerical methods

CERN Document Server

Hermann, Martin

2016-01-01

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

Beam-beam interaction and pacman effects in the SSC with momentum oscillation

International Nuclear Information System (INIS)

Mahale, N.K.; Ohnuma, S.

1989-01-01

In order to find the combined effects of beam-beam interaction (head-on and long-range) and random nonlinear multipoles in dipole magnets, the transverse oscillations of ''regular'' as well as ''pacman'' particles are traced for 256 synchrotron oscillation periods (corresponding to 135K revolutions) in the proposed SSC. Results obtained in this study do not show any obvious reduction of dynamic or linear apertures for pacman particles when compared with regular particles for (Δp/p) = 0. There are some indications of possible sudden or gradual increases in the oscillation amplitude, for pacman as well as regular particles, when the amplitude of momentum oscillation is as large as 3σ. 4 refs., 7 figs

Dynamical Jumps in a Shape Memory Alloy Oscillator

Directory of Open Access Journals (Sweden)

H. S. Oliveira

2014-01-01

Full Text Available The dynamical response of systems with shape memory alloy (SMA elements presents a rich behavior due to their intrinsic nonlinear characteristic. SMA’s nonlinear response is associated with both adaptive dissipation related to hysteretic behavior and huge changes in properties caused by phase transformations. These characteristics are attracting much technological interest in several scientific and engineering fields, varying from medical to aerospace applications. An important characteristic associated with dynamical response of SMA system is the jump phenomenon. Dynamical jumps result in abrupt changes in system behavior and its analysis is essential for a proper design of SMA systems. This paper discusses the nonlinear dynamics of a one degree of freedom SMA oscillator presenting pseudoelastic behavior and dynamical jumps. Numerical simulations show different aspects of this kind of behavior, illustrating its importance for a proper understanding of nonlinear dynamics of SMA systems.

The chimera state in colloidal phase oscillators with hydrodynamic interaction

Science.gov (United States)

Hamilton, Evelyn; Bruot, Nicolas; Cicuta, Pietro

2017-12-01

The chimera state is the incongruous situation where coherent and incoherent populations coexist in sets of identical oscillators. Using driven non-linear oscillators interacting purely through hydrodynamic forces at low Reynolds number, previously studied as a simple model of motile cilia supporting waves, we find concurrent incoherent and synchronised subsets in small arrays. The chimeras seen in simulation display a "breathing" aspect, reminiscent of uniformly interacting phase oscillators. In contrast to other systems where chimera has been observed, this system has a well-defined interaction metric, and we know that the emergent dynamics inherit the symmetry of the underlying Oseen tensor eigenmodes. The chimera state can thus be connected to a superposition of eigenstates, whilst considering the mean interaction strength within and across subsystems allows us to make a connection to more generic (and abstract) chimeras in populations of Kuramoto phase oscillators. From this work, we expect the chimera state to emerge in experimental observations of oscillators coupled through hydrodynamic forces.

A novel method combining cellular neural networks and the coupled nonlinear oscillators' paradigm involving a related bifurcation analysis for robust image contrast enhancement in dynamically changing difficult visual environments

International Nuclear Information System (INIS)

Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere

2010-01-01

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 been derived, which are capable of determining the various

Spiral intensity patterns in the internally pumped optical parametric oscillator

DEFF Research Database (Denmark)

Lodahl, Peter; Bache, Morten; Saffman, Mark

2001-01-01

We describe a nonlinear optical system that supports spiral pattern solutions in the field intensity. This new spatial structure is found to bifurcate above a secondary instability in the internally pumped optical parametric oscillator. The analytical predictions of threshold and spatial scale...

Analytical solution for Van der Pol-Duffing oscillators

International Nuclear Information System (INIS)

Kimiaeifar, A.; Saidi, A.R.; Bagheri, G.H.; Rahimpour, M.; Domairry, D.G.

2009-01-01

In this paper, the problem of single-well, double-well and double-hump Van der Pol-Duffing oscillator is studied. Governing equation is solved analytically using a new kind of analytic technique for nonlinear problems namely the 'Homotopy Analysis Method' (HAM), for the first time. Present solution gives an expression which can be used in wide range of time for all domain of response. Comparisons of the obtained solutions with numerical results show that this method is effective and convenient for solving this problem. This method is a capable tool for solving this kind of nonlinear problems.

Applied nonlinear optics in the journal 'Quantum Electronics'

International Nuclear Information System (INIS)

Grechin, Sergei G; Dmitriev, Valentin G; Chirkin, Anatolii S

2011-01-01

A brief historical review of the experimental and theoretical works on nonlinear optical frequency conversion (generation of harmonics, up- and down-conversion, parametric oscillation), which have been published in the journal 'Quantum Electronics' for the last 40 years, is presented.

On One Means of Hard Excitation of Oscillations in Nonlinear Flutter Systems

Directory of Open Access Journals (Sweden)

S. D. Glyzin

2014-01-01

Full Text Available Considered are so-called finite-dimensional flutter systems, i.e. systems of ordinary differential equations, arising from Galerkin approximations of certain boundary value problems of aeroelasticity theory as well as from a number of radiophysics applications. We study small oscillations of these equations in case of 1 : 3 resonance. By combining analytical and numerical methods, it is concluded that the mentioned resonance can cause a hard excitation of oscillations. Namely, for flutter systems shown is the possibility of coexistence, along with the stable zero state, of stable invariant tori of arbitrary finite dimension as well as chaotic attractors.

Damped nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Nicholson, D.R.; Goldman, M.V.

1976-01-01

High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time

Simple Chaotic Oscillator: From Mathematical Model to Practical Experiment

Directory of Open Access Journals (Sweden)

S. Hanus

2006-04-01

Full Text Available This paper shows the circuitry implementation and practical verification of the autonomous nonlinear oscillator. Since it is described by a single third-order differential equation, its state variables can be considered as the position, velocity and acceleration and thus have direct connection to a real physical system. Moreover, for some specific configurations of internal system parameters, it can exhibit a period doubling bifurcation leading to chaos. Two different structures of the nonlinear element were verified by a comparison of numerically integrated trajectory with the oscilloscope screenshots .

Flame oscillations in tubes with nonslip at the walls

Energy Technology Data Exchange (ETDEWEB)

Akkerman, V' yacheslav; Bychkov, Vitaly; Petchenko, Arkady [Institute of Physics, Umeaa University, SE-901 87 Umeaa (Sweden); Eriksson, Lars-Erik [Department of Applied Mechanics, Chalmers University of Technology, 412 96 Goeteborg (Sweden)

2006-06-15

A laminar premixed flame front propagating in a two-dimensional tube is considered with nonslip at the walls and with both ends open. The problem of flame propagation is solved using direct numerical simulations of the complete set of hydrodynamic equations including thermal conduction, diffusion, viscosity, and chemical kinetics. As a result, it is shown that flame interaction with the walls leads to the oscillating regime of burning. The oscillations involve variations of the curved flame shape and the velocity of flame propagation. The oscillation parameters depend on the characteristic tube width, which controls the Reynolds number of the flow. In narrow tubes the oscillations are rather weak, while in wider tubes they become stronger with well-pronounced nonlinear effects. The period of oscillations increases for wider tubes, while the average flame length scaled by the tube diameter decreases only slightly with increasing tube width. The average flame length calculated in the present work is in agreement with that obtained in the experiments. Numerical results reduce the gap between the theory of turbulent flames and the experiments on turbulent combustion in tubes. (author)

Multiple sine wave excitation of a hard spring oscillator

International Nuclear Information System (INIS)

Curreri, J.R.; Bezler, P.

1976-06-01

The vibration testing of non-linear systems has not received much attention in the literature. Frequently, linear procedures are used in the hope that large differences between the linear and non-linear responses will not occur. This may be valid for certain small ranges of the non-linearity and for a single harmonic component excitation. However, for multi-component periodic inputs, there is very little guidance in the literature for even a qualitative evaluation of the probable response. With multi-component periodic inputs, it has been shown that sub-combination frequencies can occur in cubic non-linear systems. Under these conditions, large responses can develop. The critical nature of the development of the large response has not been discussed. This is the subject of this paper. The qualitative response of a two component sine wave applied to a hard spring oscillator is shown

Control of xenon oscillations in Advanced Heavy Water Reactor via two-stage decomposition

International Nuclear Information System (INIS)

Munje, R.K.; Parkhe, J.G.; Patre, B.M.

2015-01-01

Highlights: • Singularly perturbed model of Advanced Heavy Water Reactor is explored. • Composite controller is designed using slow subsystem alone, which achieves asymptotic stability. • Nonlinear simulations are carried out under different transient conditions. • Performance of the controller is found to be satisfactory. - Abstract: Xenon induced spatial oscillations developed in large nuclear reactors, like Advanced Heavy Water Reactor (AHWR) need to be controlled for safe operation. Otherwise, a serious situation may arise in which different regions of the core may undergo variations in neutron flux in opposite phase. If these oscillations are left uncontrolled, the power density and rate of change of power at some locations in the reactor core may exceed their respective thermal limits, resulting in fuel failure. In this paper, a state feedback based control strategy is investigated for spatial control of AHWR. The nonlinear model of AHWR including xenon and iodine dynamics is characterized by 90 states, 5 inputs and 18 outputs. The linear model of AHWR, obtained by linearizing the nonlinear equations is found to be highly ill-conditioned. This higher order model of AHWR is first decomposed into two comparatively lower order subsystems, namely, 73rd order ‘slow’ subsystem and 17th order ‘fast’ subsystem using two-stage decomposition. Composite control law is then derived from individual subsystem feedback controls and applied to the vectorized nonlinear model of AHWR. Through the dynamic simulations it is observed that the controller is able to suppress xenon induced spatial oscillations developed in AHWR and the overall performance is found to be satisfactory

Synchronization of modified Colpitts oscillators with structural perturbations

Energy Technology Data Exchange (ETDEWEB)

Kammogne, Soup Tewa; Fotsin, H B, E-mail: hbfotsin@yahoo.fr [Laboratoire d' electronique, Departement de Physique, Faculte des sciences, Universite de Dschang, PO Box 067, Dschang (Cameroon)

2011-06-01

This paper deals with the problem of the synchronization of uncertain modified Colpitts oscillators. Considering the effect of external disturbances on the system parameters and nonlinear control inputs, a robust controller based on Lyapunov theory is designed for the output synchronization between a slave system and a master system in order to ensure the synchronization of uncertain modified Colpitts oscillator systems. This approach was chosen not only to guarantee a stable synchronization but also to reduce the effect of external perturbation. Nonadaptive feedback synchronization with only one controller for the system is investigated. Numerical simulations are performed to confirm the efficiency of the proposed control scheme.

Some contributions to non-linear physic: Mathematical problems

International Nuclear Information System (INIS)

1981-01-01

The main results contained in this report are the following: i ) Lagrangian universality holds in a precisely defined weak sense. II ) Isolation of 5th order polynomial evolution equations having high order conservation laws. III ) Hamiltonian formulation of a wide class of non-linear evolution equations. IV) Some properties of the symmetries of Gardner-like systems. v) Characterization of the range and Kernel of ζ/ζ u α , |α | - 1. vi) A generalized variational approach and application to the anharmonic oscillator. v II ) Relativistic correction and quasi-classical approximation to the anechoic oscillator. VII ) Properties of a special class of 6th-order anharmonic oscillators. ix) A new method for constructing conserved densities In PDE. (Author) 97 refs

Laser beam propagation in nonlinear optical media

CERN Document Server

Guha, Shekhar

2013-01-01

""This is very unique and promises to be an extremely useful guide to a host of workers in the field. They have given a generalized presentation likely to cover most if not all situations to be encountered in the laboratory, yet also highlight several specific examples that clearly illustrate the methods. They have provided an admirable contribution to the community. If someone makes their living by designing lasers, optical parametric oscillators or other devices employing nonlinear crystals, or designing experiments incorporating laser beam propagation through linear or nonlinear media, then

Bifurcation of forced periodic oscillations for equations with Preisach hysteresis

International Nuclear Information System (INIS)

Krasnosel'skii, A; Rachinskii, D

2005-01-01

We study oscillations in resonant systems under periodic forcing. The systems depend on a scalar parameter and have the form of simple pendulum type equations with ferromagnetic friction represented by the Preisach hysteresis nonlinearity. If for some parameter value the period of free oscillations of the principal linear part of the system coincides with the period of the forcing term, then one may expect the existence of unbounded branches of periodic solutions for nearby parameter values. We present conditions for the existence and nonexistence of such branches and estimates of their number

Spin–orbit coupling induced magnetoresistance oscillation in a dc biased two-dimensional electron system

International Nuclear Information System (INIS)

Wang, C M; Lei, X L

2014-01-01

We study dc-current effects on the magnetoresistance oscillation in a two-dimensional electron gas with Rashba spin-orbit coupling, using the balance-equation approach to nonlinear magnetotransport. In the weak current limit the magnetoresistance exhibits periodical Shubnikov-de Haas oscillation with changing Rashba coupling strength for a fixed magnetic field. At finite dc bias, the period of the oscillation halves when the interbranch contribution to resistivity dominates. With further increasing current density, the oscillatory resistivity exhibits phase inversion, i.e., magnetoresistivity minima (maxima) invert to maxima (minima) at certain values of the dc bias, which is due to the current-induced magnetoresistance oscillation. (paper)

Analysis of diffusivity of the oscillating reaction components in a microreactor system

Directory of Open Access Journals (Sweden)

Martina Šafranko

2017-01-01

Full Text Available When performing oscillating reactions, periodical changes in the concentrations of reactants, intermediaries, and products take place. Due to the mentioned periodical changes of the concentrations, the information about the diffusivity of the components included into oscillating reactions is very important for the control of the oscillating reactions. Non-linear dynamics makes oscillating reactions very interesting for analysis in different reactor systems. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor, with the aim of identifying the limiting component. The geometry of the microreactor microchannel and a well defined flow profile ensure optimal conditions for the diffusion phenomena analysis, because diffusion profiles in a microreactor depend only on the residence time. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor equipped with 2 Y-shape inlets and 2 Y-shape outlets, with active volume of V = 4 μL at different residence times.

Stochastic modeling of kHz quasi-periodic oscillation light curves

DEFF Research Database (Denmark)

Vio, R.; Rebusco, P.; Andreani, P.

2006-01-01

Kluzniak & Abramowicz explain the high frequency, double peak, "3:2" QPOs observed in neutron star and black hole sources in terms of a non-linear parametric resonance between radial and vertical epicyclic oscillations of an almost Keplerian accretion disk. The 3:2 ratio of epicyclic frequencies ...

Nonlinear Bloch waves in metallic photonic band-gap filaments

International Nuclear Information System (INIS)

Kaso, Artan; John, Sajeev

2007-01-01

We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10-50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell's equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament

Nonlinear Bloch waves in metallic photonic band-gap filaments

Science.gov (United States)

Kaso, Artan; John, Sajeev

2007-11-01

We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10 50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.

Critical fluctuations and the rates of interstate switching near the excitation threshold of a quantum parametric oscillator.

Science.gov (United States)

Lin, Z R; Nakamura, Y; Dykman, M I

2015-08-01

We study the dynamics of a nonlinear oscillator near the critical point where period-two vibrations are first excited with the increasing amplitude of parametric driving. Above the threshold, quantum fluctuations induce transitions between the period-two states over the quasienergy barrier. We find the effective quantum activation energies for such transitions and their scaling with the difference of the driving amplitude from its critical value. We also find the scaling of the fluctuation correlation time with the quantum noise parameters in the critical region near the threshold. The results are extended to oscillators with nonlinear friction.

Chaotic synchronization of three coupled oscillators with ring connection

International Nuclear Information System (INIS)

Kyprianidis, I.M.; Stouboulos, I.N.

2003-01-01

We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional)

Chaotic synchronization of three coupled oscillators with ring connection

CERN Document Server

Kyprianidis, I M

2003-01-01

We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional).

Parameter-Independent Dynamical Behaviors in Memristor-Based Wien-Bridge Oscillator

Directory of Open Access Journals (Sweden)

Ning Wang

2017-01-01

Full Text Available This paper presents a novel memristor-based Wien-bridge oscillator and investigates its parameter-independent dynamical behaviors. The newly proposed memristive chaotic oscillator is constructed by linearly coupling a nonlinear active filter composed of memristor and capacitor to a Wien-bridge oscillator. For a set of circuit parameters, phase portraits of a double-scroll chaotic attractor are obtained by numerical simulations and then validated by hardware experiments. With a dimensionless system model and the determined system parameters, the initial condition-dependent dynamical behaviors are explored through bifurcation diagrams, Lyapunov exponents, and phase portraits, upon which the coexisting infinitely many attractors and transient chaos related to initial conditions are perfectly offered. These results are well verified by PSIM circuit simulations.

Dipole oscillations of a Bose-Einstein condensate in the presence of defects and disorder.

Science.gov (United States)

Albert, M; Paul, T; Pavloff, N; Leboeuf, P

2008-06-27

We consider dipole oscillations of a trapped dilute Bose-Einstein condensate in the presence of a scattering potential consisting either in a localized defect or in an extended disordered potential. In both cases the breaking of superfluidity and the damping of the oscillations are shown to be related to the appearance of a nonlinear dissipative flow. At supersonic velocities the flow becomes asymptotically dissipationless.

Nonlinear effects on the rotor driven by a motor with limited power

Czech Academy of Sciences Publication Activity Database

Půst, Ladislav

2007-01-01

Roč. 1, č. 2 (2007), s. 603-612 ISSN 1802-680X. [Computational Mechanics 2007. Hrad Nečtiny, 05.11.2007-07.11.2007] R&D Projects: GA ČR GA101/06/0063 Institutional research plan: CEZ:AV0Z20760514 Keywords : rotor dynamics * nonlinear oscillations * weak energy source * nonlinear magnetic flux Subject RIV: BI - Acoustics

Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction

Science.gov (United States)

Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.

2005-03-01

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

Theory of quasi-biennial and some other oscillations in meteorological parameters

International Nuclear Information System (INIS)

Njau, E.C.

1990-11-01

We show that quasi-biennial and several other oscillations in meteorological parameters are caused by ''foldover distortions'' in the physical processes represented by the formulations contained in our recent theory. The periods of all these oscillations extend from about 50 days up to over 200,000 years. Additional oscillations within and outside this periodicity range are correspondingly generated primarily as a result of non-linearities in the earth-atmosphere system. Our analysis agrees quite well with past observations as well as results of analyses on climatic records from different locations on the earth and can, therefore, be useful in attempts to make climatic predictions as briefly indicated in the text. (author). 15 refs, 4 figs, 2 tabs

Energy localization in the phi4 oscillator chain.

Science.gov (United States)

Ponno, A; Ruggiero, J; Drigo, E; De Luca, J

2006-05-01

We study energy localization in a finite one-dimensional phi(4) oscillator chain with initial energy in a single oscillator of the chain. We numerically calculate the effective number of degrees of freedom sharing the energy on the lattice as a function of time. We find that for energies smaller than a critical value, energy equipartition among the oscillators is reached in a relatively short time. On the other hand, above the critical energy, a decreasing number of particles sharing the energy is observed. We give an estimate of the effective number of degrees of freedom as a function of the energy. Our results suggest that localization is due to the appearance, above threshold, of a breather-like structure. Analytic arguments are given, based on the averaging theory and the analysis of a discrete nonlinear Schrödinger equation approximating the dynamics, to support and explain the numerical results.

Nonlinear generation of the fundamental radiation in plasmas: the influence of induced ion-acoustic and Langmuir waves

International Nuclear Information System (INIS)

Rizzato, F.B.

1992-01-01

A nonlinear emission mechanism of electromagnetic waves at the fundamental plasma frequency has been examined. This mechanism is based on the electromagnetic oscillating two-stream instability driven by two oppositely propagating Langmuir waves. The excitation of the electromagnetic oscillating two-stream instability is due to nonlinear wave-wave coupling involving Langmuir waves, low-frequency density waves and electromagnetic waves. The Chian and Alves model is improved using the generalized Zakharov equations. Attention is directed toward the influence of induced low-frequency and Langmuir waves on the properties of the electromagnetic oscillating two-stream instability. Presumably, the properties derived in the present context may be relevant to both space and laboratory plasmas. (author)

Modeling of Coupled Chaotic Oscillators

International Nuclear Information System (INIS)

Lai, Y.; Grebogi, C.

1999-01-01

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 1999 The American Physical Society

Effect of Magnetic Twist on Nonlinear Transverse Kink Oscillations of Line-tied Magnetic Flux Tubes

Science.gov (United States)

Terradas, J.; Magyar, N.; Van Doorsselaere, T.

2018-01-01

Magnetic twist is thought to play an important role in many structures of the solar atmosphere. One of the effects of twist is to modify the properties of the eigenmodes of magnetic tubes. In the linear regime standing kink solutions are characterized by a change in polarization of the transverse displacement along the twisted tube. In the nonlinear regime, magnetic twist affects the development of shear instabilities that appear at the tube boundary when it is oscillating laterally. These Kelvin–Helmholtz instabilities (KHI) are produced either by the jump in the azimuthal component of the velocity at the edge of the sharp boundary between the internal and external part of the tube or by the continuous small length scales produced by phase mixing when there is a smooth inhomogeneous layer. In this work the effect of twist is consistently investigated by solving the time-dependent problem including the process of energy transfer to the inhomogeneous layer. It is found that twist always delays the appearance of the shear instability, but for tubes with thin inhomogeneous layers the effect is relatively small for moderate values of twist. On the contrary, for tubes with thick layers, the effect of twist is much stronger. This can have some important implications regarding observations of transverse kink modes and the KHI itself.

Nonlinear Aeroelastic Study of Stall Induced Oscillation in a Symmetric Airfoil

NARCIS (Netherlands)

Sarkar, S.; Bijl, H.

2006-01-01

In this paper the aeroelastic stability of a wind turbine rotor in the dynamic stall regime is investigated. Increased flexibility of modern turbine blades makes them more susceptible to aeroelastic instabilities. Complex oscillation modes like flap/lead-lag are of particular concern, which give way

Limit cycle analysis of nuclear coupled density wave oscillations

International Nuclear Information System (INIS)

Ward, M.E.

1985-01-01

An investigation of limit cycle behavior for the nuclear-coupled density wave oscillation (NCDWO) in a boiling water reactor (BWR) was performed. A simplified nonlinear model of BWR core behavior was developed using a two-region flow channel representation, coupled with a form of the point-kinetics equation. This model has been used to investigate the behavior of large amplitude NCDWO's through conventional time-integration solutions and through application of a direct relaxation-oscillation limit cycle solution in phase space. The numerical solutions demonstrate the potential for severe global power and flow oscillations in a BWR core at off-normal conditions, such as might occur during Anticipated Transients without Scram. Because of the many simplifying assumptions used, it is felt that the results should not be interpreted as an absolute prediction of core behavior, but as an indication of the potential for large oscillations and a demonstration of the corresponding limit cycle mechanisms. The oscillations in channel density drive the core power variations, and are reinforced by heat flux variations due to the changing fuel temperature. A global temperature increase occurs as energy is accumulated in the fuel, and limits the magnitude of the oscillations because as the average channel density decreases, the amplitude and duration of positive void reactivity at a given oscillation amplitude is lessened

Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder

Energy Technology Data Exchange (ETDEWEB)

Nono Dueyou Buckjohn, C., E-mail: bucknono@yahoo.f [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Siewe Siewe, M., E-mail: martinsiewesiewe@yahoo.f [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Tchawoua, C., E-mail: ctchawa@yahoo.f [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Kofane, T.C., E-mail: tckofane@yahoo.co [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon)

2010-08-02

In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.

Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder

International Nuclear Information System (INIS)

Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.; Kofane, T.C.

2010-01-01

In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.

Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder

Science.gov (United States)

Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.; Kofane, T. C.

2010-08-01

In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.

Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

Science.gov (United States)

Bogdan, V. M.; Bond, V. B.

1980-01-01

The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

Magma chamber interaction giving rise to asymmetric oscillations

Science.gov (United States)

Walwer, D.; Ghil, M.; Calais, E.

2017-12-01

Geodetic time series at four volcanoes (Okmok, Akutan, Shishaldin, and Réunion) are processed using Multi-channel Singular Spectrum Analysis (M-SSA) and reveal sawtooth-shaped oscillations ; the latter are characterized by short intervals of fast inflations followed by longer intervals of slower deflations. At Okmok and Akutan, the oscillations are first damped and then accentuated. At Okmok, the increase in amplitude of the oscillations is followed by an eruption. We first show that the dynamics of these four volcanoes bears similarities with that of a simple nonlinear, dissipative oscillator, indicating that the inflation-deflation episodes are relaxation oscillations. These observations imply that ab initio dynamical models of magma chambers should possess an asymmetric oscillatory regime. Next, based on the work of Whitehead and Helfrich [1991], we show that a model of two magma chambers — connected by a cylindrical conduit in which the magma viscosity depends on temperature — gives rise to asymmetric overpressure oscillations in the magma reservoirs. These oscillations lead to surface deformations that are consistent with those observed at the four volcanoes in this study. This relaxation oscillation regime occurs only when the vertical temperature gradient in the host rock between the two magma chambers is large enough and when the magma flux entering the volcanic system is sufficiently high. The magma being supplied by a deeper source region, the input flux depends on the pressure difference between the source and the deepest reservoir. When this difference is not sufficiently high, the magma flux exponentially decreases, leading to damped oscillations as observed at Akutan and Okmok. The combination of observational and modeling results clearly supports the role of relaxation oscillations in the dynamics of volcanic systems.

Picone-type inequalities for nonlinear elliptic equations and their applications

Directory of Open Access Journals (Sweden)

Takaŝi Kusano

2001-01-01

Full Text Available Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.

Extreme nonlinearities in InAs/InP nanowire gain media: the two-photon induced laser

DEFF Research Database (Denmark)

Capua, Amir; Kami, Ouri; Eisenstein, Gadi

2012-01-01

We demonstrate a novel laser oscillation scheme in an InAs / InP wire-like quantum dash gain medium. A short optical pulse excites carriers by two photon absorption which relax to the energy levels providing gain thereby enabling laser oscillations. The nonlinear dynamic interaction is analyzed a...

An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method