scholarly journals Modulation of nonlinear coupling on the synchronization induced by linear coupling

2012 ◽  
Vol 61 (24) ◽  
pp. 240501
Author(s):  
Li Fan ◽  
Jin Wu-Yin ◽  
Ma Jun
Keyword(s):  
Nonlinear Coupling ◽  
Linear Coupling

PHASE SYNCHRONIZATION OF LINEARLY AND NONLINEARLY COUPLED OSCILLATORS WITH INTERNAL RESONANCE

2009 ◽  
Vol 23 (30) ◽  
pp. 5715-5726
Author(s):  
YONG LIU
Keyword(s):  
Coupling Strength ◽  
Coupled Oscillators ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Phase Synchronization ◽  
Coupled Systems ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Phase Dynamics ◽  
Diffuse Clouds

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, it demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase in the linear coupling strength, the effect of phase synchronization between two sub-systems was enhanced, while increased firstly, and then decayed as nonlinear coupling strength increases. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the Lyapunov exponents, which can also be explained by the diffuse clouds.

QUANTUM TELEPORTATION VIA 1D OPTICAL LATTICE CHAINS WITH NONLINEAR COUPLING

2008 ◽  
Vol 06 (06) ◽  
pp. 1213-1222
Author(s):  
JIN-LIANG GUO ◽  
JIE SONG ◽  
HE-SHAN SONG
Keyword(s):  
Magnetic Field ◽  
Optical Lattice ◽  
Quantum Teleportation ◽  
Uniform Magnetic Field ◽  
Communication Protocol ◽  
Nonlinear Coupling ◽  
Classical Communication ◽  
Average Fidelity ◽  
Linear Coupling ◽  
External Uniform Magnetic Field

We study quantum teleportation by using 1D optical lattice for two particles with nonlinear coupling in an external uniform magnetic field as resources via the standard teleportation protocol T0. The effects of linear coupling J, nonlinear coupling K and magnetic field B on the average fidelity are investigated in detail. It is found that increasing |K| is not only very helpful for enhancing the average fidelity, but also beneficial to improving the critical temperature Tf and magnetic field Bf, beyond which quantum teleportation is inferior to classical communication protocol.

TRACKING PHASE SYNCHRONIZATION OF TWO COUPLED RÖSSLER OSCILLATORS WITH INTERNAL RESONANCE

2009 ◽  
Vol 23 (23) ◽  
pp. 4809-4816 ◽  
Author(s):  
YONG LIU
Keyword(s):  
Coupling Strength ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Phase Synchronization ◽  
Coupling Parameter ◽  
Primary Resonance ◽  
Coupled Systems ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Phase Dynamics

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, we tune the linear coupling parameter to obtain the two Rössler oscillators in a synchronized regime and analyze the effect of a nonlinear coupling on the phase synchronized state. It demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase of the nonlinear coupling strength, for the primary resonance, the effect of phase synchronization between two sub-systems was decayed, while increasing with frequency ratio 1:2. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the nonlinear coupling strength.

scholarly journals Modulation of nonlinear coupling on the synchronization induced by linear coupling

2013 ◽  
Vol 62 (2) ◽  
pp. 028701
Author(s):  
Zhao Long ◽  
Yang Ji-Ping ◽  
Zheng Yan-Hong
Keyword(s):  
Nonlinear Coupling ◽  
Linear Coupling

scholarly journals Reconstructing coupled time series in climate systems using three kinds of machine-learning methods

2020 ◽  
Vol 11 (3) ◽  
pp. 835-853
Author(s):  
Yu Huang ◽  
Lichao Yang ◽  
Zuntao Fu
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Time Series ◽  
Explanatory Variable ◽  
The Other ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Explanatory Variables ◽  
Machine Learning Methods ◽  
Reconstruction Quality

Abstract. Despite the great success of machine learning, its application in climate dynamics has not been well developed. One concern might be how well the trained neural networks could learn a dynamical system and what will be the potential application of this kind of learning. In this paper, three machine-learning methods are used: reservoir computer (RC), backpropagation-based (BP) artificial neural network, and long short-term memory (LSTM) neural network. It shows that the coupling relations or dynamics among variables in linear or nonlinear systems can be inferred by RC and LSTM, which can be further applied to reconstruct one time series from the other. Specifically, we analyzed the climatic toy models to address two questions: (i) what factors significantly influence machine-learning reconstruction and (ii) how do we select suitable explanatory variables for machine-learning reconstruction. The results reveal that both linear and nonlinear coupling relations between variables do influence the reconstruction quality of machine learning. If there is a strong linear coupling between two variables, then the reconstruction can be bidirectional, and both of these two variables can be an explanatory variable for reconstructing the other. When the linear coupling among variables is absent but with the significant nonlinear coupling, the machine-learning reconstruction between two variables is direction dependent, and it may be only unidirectional. Then the convergent cross mapping (CCM) causality index is proposed to determine which variable can be taken as the reconstructed one and which as the explanatory variable. In a real-world example, the Pearson correlation between the average tropical surface air temperature (TSAT) and the average Northern Hemisphere SAT (NHSAT) is weak (0.08), but the CCM index of NHSAT cross mapped with TSAT is large (0.70). And this indicates that TSAT can be well reconstructed from NHSAT through machine learning. All results shown in this study could provide insights into machine-learning approaches for paleoclimate reconstruction, parameterization scheme, and prediction in related climate research.Highlights: i The coupling dynamics learned by machine learning can be used to reconstruct time series. ii Reconstruction quality is direction dependent and variable dependent for nonlinear systems. iii The CCM index is a potential indicator to choose reconstructed and explanatory variables. iv The tropical average SAT can be well reconstructed from the average Northern Hemisphere SAT.

scholarly journals NONLINEAR INTERACTION BETWEEN DIURNAL TIDAL AND 2-DAY WAVE IN THE METEOR WINDS OBSERVED AT CACHOEIRA PAULISTA-SP AND SÃO JOÃO DO CARIRI-PB, BRAZIL: A CASE STUDY

2013 ◽  
Vol 31 (3) ◽  
pp. 403 ◽  
Author(s):  
Edvaldo De Oliveira Alves ◽  
Lourivaldo Mota Lima ◽  
Amauri Fragoso De Medeiros ◽  
Ricardo Arlen Buriti ◽  
Paulo Prado Batista ◽  
...  
Keyword(s):  
Spectral Energy ◽  
Secondary Wave ◽  
Nonlinear Coupling ◽  
Meteor Radar ◽  
Bispectral Analysis ◽  
Atmospheric Tide ◽  
Linear Coupling ◽  
Atmospheric Wave ◽  
June July

ABSTRACT. Simultaneous measurements of meteor winds obtained in S˜ao Jo˜ao do Cariri-PB and Cachoeira Paulista-SP, Brazil, during June-July 2008 were used to investigate the occurrence of nonlinear coupling between atmospheric wave modes. The wind spectrum showed the quasi simultaneous presence of spectral energy peaks in the periods near 16, 24 and 48 hours, consistent with the occurrence of interaction between 48-h and 24-h waves, and the generation of 16-h waves. From the bispectral analysis, it was possible to confirm the occurrence of a 16-hour secondary wave generated by non-linear coupling between the 2-day and diurnal tide primary waves.Keywords: atmospheric tide, bispectral analysis, meteor radar. RESUMO. Medidas simultâneas de ventos meteóricos obtidos em São João do Cariri-PB e Cachoeira Paulista-SP, Brasil, durante os meses de junho e julho de 2008, foram usadas para investigar a ocorrência de acoplamento não linear entre modos de ondas atmosféricas. Os espectros dos ventos evidenciaram a presença quase simultânea de picos de energia espectral nos períodos de ∼ 16, ∼ 24 e ∼ 48 horas, compatíveis com a ocorrência de interação entre as ondas de 48 e 24 horas, e a geraçao da onda de 16 horas. Através de análise biespectral foi possível confirmar que a onda secundária de 16 horas foi gerada pelo acoplamento não linear entre as ondas primárias de 2 dias e a maré diurna.Palavras-chave: maré atmosférica, análise biespectral, radar meteórico.

scholarly journals A Novel Method for Constructing Grid Multi-Wing Butterfly Chaotic Attractors via Nonlinear Coupling Control

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Yun Huang
Keyword(s):  
Piecewise Linear ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Piecewise Linear Function ◽  
Chaotic Attractors ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
First Order ◽  
Novel Method ◽  
Chaotic Characteristic

A new method is presented to construct grid multi-wing butterfly chaotic attractors. Based on the three-dimensional Lorenz system, two first-order differential equations are added along with one linear coupling controller, respectively. And a piecewise linear function, which is taken into the linear coupling controller, is designed to form a nonlinear coupling controller; thus a five-dimensional chaotic system is produced, which is able to generate gird multi-wing butterfly chaotic attractors. Through the analysis of the equilibrium points, Lyapunov exponent spectrums, bifurcation diagrams, and Poincaré mapping in this system, the chaotic characteristic of the system is verified. Apart from the research above, an electronic circuit is designed to implement the system. The circuit experimental results are in accordance with the results of numerical simulation, which verify the availability and feasibility of this method.

scholarly journals Cluster Synchronization in a Network of Nonlinear Systems with Directed Topology and Competitive Relationships

2021 ◽  
Author(s):  
Xin Wang ◽  
Shidong Zhai ◽  
Guoqiang Luo ◽  
Tao Huang
Keyword(s):  
Nonlinear Systems ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Cluster Synchronization ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Directed Topology ◽  
Cooperative Relationships ◽  
Synchronization Problem ◽  
Strongly Connected

Abstract This paper studies the cluster synchronization problem of coupled nonlinear systems with directed topology and competitive relationships. We assume that nodes within the same cluster have the same intrinsic dynamics, whereas node dynamics between different clusters differ. In the same cluster, there only exist cooperative relationships, and there may have competitive relationships among nodes belonging to different clusters. Under the assumptions that each node satisfies one-sided Lipschitz condition, and the digraphs of each cluster are strongly connected, some sufficient conditions for cluster synchronization in the cases of linear coupling and nonlinear coupling are obtained respectively. The obtained conditions are presented as some algebraic conditions which are easy to solve. Finally, our results are validated by two numerical simulations.

Linear coupling of electromagnetic waves in inhomogeneous weakly-ionized media

1983 ◽  
Vol 141 (10) ◽  
pp. 257 ◽  
Author(s):  
V.V. Zheleznyakov ◽  
Vit V. Kocharovskii ◽  
Vlad V. Kocharovskii
Keyword(s):  
Electromagnetic Waves ◽  
Linear Coupling ◽  
Weakly Ionized
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