arXiv: Chaotic Dynamics最新文献_第2页

Multifaceted nonlinear dynamics in $$mathcal {PT}$$-symmetric coupled Liénard oscillators $$mathcal {PT}$$ -对称耦合lisamadard振荡器的多面非线性动力学

arXiv: Chaotic Dynamics Pub Date : 2018-12-25 DOI: 10.1007/s11071-020-05585-8

J. Deka, A. Sarma, A. Govindarajan, M. Kulkarni

引用次数: 4

Stability and chaos in the classical three rotor problem 经典三转子问题的稳定性和混沌性

arXiv: Chaotic Dynamics Pub Date : 2018-10-02 DOI: 10.29195/iascs.02.01.0020

G. Krishnaswami, Himalaya Senapati

{"title":"Stability and chaos in the classical three rotor problem","authors":"G. Krishnaswami, Himalaya Senapati","doi":"10.29195/iascs.02.01.0020","DOIUrl":"https://doi.org/10.29195/iascs.02.01.0020","url":null,"abstract":"We study the equal-mass classical three rotor problem, a variant of the three body problem of celestial mechanics. The quantum $N$-rotor problem has been used to model chains of coupled Josephson junctions and also arises via a partial continuum limit of the Wick-rotated XY model. In units of the coupling, the energy serves as a control parameter. We find periodic 'pendulum' and 'breather' orbits at all energies and choreographies at relatively low energies. They furnish analogs of the Euler-Lagrange and figure-8 solutions of the planar three body problem. Integrability at very low energies gives way to a rather marked transition to chaos at $E_c approx 4$, followed by a gradual return to regularity as $E to infty$. We find four signatures of this transition: (a) the fraction of the area of Poincare surfaces occupied by chaotic sections rises sharply at $E_c$, (b) discrete symmetries are spontaneously broken at $E_c$, (c) $E=4$ is an accumulation point of stable to unstable transitions in pendulum solutions and (d) the Jacobi-Maupertuis curvature goes from being positive to having both signs above $E=4$. Moreover, Poincare plots also reveal a regime of global chaos slightly above $E_c$.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125515337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Unraveling the Chaos-Land and Its Organization in the Rabinovich System 拉宾诺维奇体系中的混沌之地及其组织解析

arXiv: Chaotic Dynamics Pub Date : 2018-06-04 DOI: 10.1007/978-3-319-53673-6_4

K. Pusuluri, A. Pikovsky, A. Shilnikov

引用次数: 8

Partial control of chaos: how to avoid undesirable behaviors with small controls in presence of noise 混沌的局部控制:如何在存在噪声的情况下用小控制避免不良行为

arXiv: Chaotic Dynamics Pub Date : 2018-03-22 DOI: 10.3934/dcdsb.2018241

Rubén Capeáns, J. F. Sanjuan

{"title":"Partial control of chaos: how to avoid undesirable behaviors with small controls in presence of noise","authors":"Rubén Capeáns, J. F. Sanjuan","doi":"10.3934/dcdsb.2018241","DOIUrl":"https://doi.org/10.3934/dcdsb.2018241","url":null,"abstract":"The presence of a nonattractive chaotic set, also called chaotic saddle, in phase space implies the appearance of a finite time kind of chaos that is known as transient chaos. For a given dynamical system in a certain region of phase space with transient chaos, trajectories eventually abandon the chaotic region escaping to an external attractor, if no external intervention is done on the system. In some situations, this attractor may involve an undesirable behavior, so the application of a control in the system is necessary to avoid it. Both, the nonattractive nature of transient chaos and eventually the presence of noise may hinder this task. Recently, a new method to control chaos called emph{partial control} has been developed. The method is based on the existence of a set, called the safe set, that allows to sustain transient chaos by only using a small amount of control. The surprising result is that the trajectories can be controlled by using an amount of control smaller than the amount of noise affecting it. We present here a broad survey of results of this control method applied to a wide variety of dynamical systems. We also review here all the variations of the partial control method that have been developed so far. In all the cases various systems of different dimensionality are treated in order to see the potential of this method. We believe that this method is a step forward in controlling chaos in presence of disturbances.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"199 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125263280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

On the Keldysh Problem of Flutter Suppression. 颤振抑制的Keldysh问题。

arXiv: Chaotic Dynamics Pub Date : 2018-03-14 DOI: 10.1063/1.5034578

N. Kuznetsov, G. Leonov

引用次数: 6

A globally stable attractor that is locally unstable everywhere 一个全局稳定的吸引子到处都是局部不稳定的

arXiv: Chaotic Dynamics Pub Date : 2017-12-02 DOI: 10.1063/1.5016214

Phanindra Tallapragada, S. Sudarsanam

引用次数: 4

Construction,sensitivity index, and synchronization speed of optimal networks 最优网络的构造、灵敏度指数和同步速度

arXiv: Chaotic Dynamics Pub Date : 2017-11-29 DOI: 10.1166/jcsmd.2017.1121

Jeremie Fish, Jie Sun

{"title":"Construction,sensitivity index, and synchronization speed of optimal networks","authors":"Jeremie Fish, Jie Sun","doi":"10.1166/jcsmd.2017.1121","DOIUrl":"https://doi.org/10.1166/jcsmd.2017.1121","url":null,"abstract":"The stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can be measured by the range of coupling strength that admits stable synchronization, can be optimized for a given number of nodes and links. Depending on the geometric degeneracy of the Laplacian eigenvectors, optimal networks can be classified into different sensitivity levels, which we define as a network's sensitivity index. We introduce an efficient and explicit way to construct optimal networks of arbitrary size over a wide range of sensitivity and link densities. Using coupled chaotic oscillators, we study synchronization dynamics on optimal networks, showing that cospectral optimal networks can have drastically different speed of synchronization. Such difference in dynamical stability is found to be closely related to the different structural sensitivity of these networks: generally, networks with high sensitivity index are slower to synchronize, and, surprisingly, may not synchronize at all, despite being theoretically stable under linear stability analysis.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116624934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Belykh attractor in Zaslavsky map and its transformation under smoothing Zaslavsky映射中的Belykh吸引子及其平滑下的变换

arXiv: Chaotic Dynamics Pub Date : 2017-10-21 DOI: 10.18500/0869-6632-2018-26-1-64-79

S. Kuznetsov

{"title":"Belykh attractor in Zaslavsky map and its transformation under smoothing","authors":"S. Kuznetsov","doi":"10.18500/0869-6632-2018-26-1-64-79","DOIUrl":"https://doi.org/10.18500/0869-6632-2018-26-1-64-79","url":null,"abstract":"If we allow non-smooth or discontinuous functions in definition of an evolution operator for dynamical systems, then situations of quasi-hyperbolic chaotic dynamics often occur like, for example, on attractors in model Lozi map and in Belykh map. The present article deals with the quasihyperbolic attractor of Belykh in a map describing a rotator with dissipation driven by periodic kicks, the intensity of which depends on the instantaneous angular coordinate of the rotator as a sawtooth-like function, and also the transformation of the attractor under smoothing of that function is considered. Reduction of the equations to the standard form of the Belykh map is provided. Results of computations illustrating the dynamics of the system with continuous time on the Belykh attractor are presented. Also, results for the model with the smoothed sawtooth function are considered depending on the parameter characterizing the smoothing scale. On graphs of Lyapunov exponents versus a parameter, the smoothing of the sawtooth implies appearance of periodicity windows, which indicates violation of the quasi-hyperbolic nature of the attractor. Charts of dynamic regimes on the parameter plane of the system are also plotted, where regions of periodic motions (\"Arnold's tongues\") are present, which decrease in size with the decrease in the characteristic scale of the smoothing, and disappear in the limit case of the sawtooth function with a break. Since the Belykh attractor was originally introduced in the radiophysical context (phase-locked loops), the analysis undertaken here is of interest from the point of view of possible exploiting the chaotic dynamics on this attractor in electronic devices.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130200483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Chaos in three coupled rotators: From Anosov dynamics to hyperbolic attractors 三个耦合旋转器的混沌:从安诺索夫动力学到双曲吸引子

arXiv: Chaotic Dynamics Pub Date : 2017-08-15 DOI: 10.29195/iascs.01.01.0017

S. Kuznetsov

引用次数: 1

Coexistence of attractors in a coupled nonlinear delayed system modelling El Ni~no Southern Oscillations 模拟厄尔尼诺南方涛动的耦合非线性延迟系统中吸引子的共存

arXiv: Chaotic Dynamics Pub Date : 2017-07-28 DOI: 10.29195/iascs.01.01.0006

C. Meena, E. Surovyatkina, S. Sinha

{"title":"Coexistence of attractors in a coupled nonlinear delayed system modelling El Ni~no Southern Oscillations","authors":"C. Meena, E. Surovyatkina, S. Sinha","doi":"10.29195/iascs.01.01.0006","DOIUrl":"https://doi.org/10.29195/iascs.01.01.0006","url":null,"abstract":"We study the dynamics of the sea surface temperature (SST) anomaly using a model of the temporal patterns of two sub-regions, mimicking behaviour similar to El Ni~no Southern Oscillations (ENSO). Specifically, we present the existence, stability, and basins of attraction of the solutions arising in the model system in the space of these parameters: self delay, delay and inter-region coupling strengths. The emergence or suppression of oscillations in our models is a dynamical feature of utmost relevance, as it signals the presence or absence of ENSO-like oscillations. In contrast to the well-known low order model of ENSO, where the influence of the neighbouring regions on the region of interest is modelled as external noise, we consider neighbouring regions as a coupled deterministic dynamical systems. Different parameters yield a rich variety of dynamical patterns in our model, ranging from steady states and homogeneous oscillations to irregular oscillations and coexistence of oscillatory attractors, without explicit inclusion of noise. Interestingly, if we take the self-delay coupling strengths of the two sub-regions to be such that the temperature of one region goes to a fixed point regime when uncoupled, while the other system is in the oscillatory regime, then on coupling both systems show oscillations. We explicitly obtain the basins of attraction for the different steady states and oscillatory states in the model. Our results might be helpful for forecasting of El Ni~no (or La Ni~na) progress, as it indicates the combination of initial SST anomalies in the sub-regions that can result in a El Ni~no/La Ni~na episodes. In particular, the result suggests using an interval as a criterion to estimate the El-Ni~no or La-Ni~na progress instead of the currently used the single value criterion.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131240246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0