EXPERIMENTAL TRACKING OF UNSTABLE ORBITS IN DRIVEN DIODE RESONATOR BY WEAK COUPLING

1996 ◽  
Vol 06 (04) ◽  
pp. 769-774 ◽  
Author(s):  
JONG CHEOL SHIN ◽  
SOOK-IL KWUN ◽  
YOUNGTAE KIM
Keyword(s):  
Feedback Control ◽  
Weak Coupling ◽  
Control Parameter ◽  
Chaotic Regime ◽  
Coupling Method ◽  
Generic Properties ◽  
Wide Range ◽  
Resonator System ◽  
Weak Coupling Method

The weak coupling method is demonstrated to stabilize and track the unstable orbits in the diode resonator system. Continuous tracking of the unstable orbits could be achieved over a wide range from the periodic down to the deep chaotic regime as the control parameter is varied continuously without changing the feedback control parameter. During the tracking of unstable orbits, hysteresis as well as switching of the attractors are observed and these are supposed to be the generic properties of continuous tracking.

A weak coupling method between the dynamics code HOST and the 3D unsteady Euler code WAVES

2001 ◽  
Vol 5 (6) ◽  
pp. 397-408 ◽  
Author(s):  
Gaëlle Servera ◽  
Philippe Beaumier ◽  
Michel Costes
Keyword(s):  
Weak Coupling ◽  
Coupling Method ◽  
Weak Coupling Method

scholarly journals Parametrization of stochastic multiscale triads

2016 ◽  
Author(s):  
Jeroen Wouters ◽  
Stamen I. Dolaptchiev ◽  
Valerio Lucarini ◽  
Ulrich Achatz
Keyword(s):  
Model Reduction ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Coupling Model ◽  
Linear Response Theory ◽  
Coupling Method ◽  
Scale Separation ◽  
Time Scale Separation ◽  
Weakly Coupled ◽  
Weak Coupling Method

Abstract. We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction method results in general in a non-Markovian system, we therefore discuss the Markovianization of the system to allow for straightforward numerical integration. We compare the applied method to the equations obtained through homogenization in the limit of large time scale separation between slow and fast degrees of freedom. We numerically compare the ensemble spread from a fixed initial condition, correlation functions and exit times from a domain. The weak coupling method gives more accurate results in all test cases, albeit with a higher numerical cost.

The investigation on anomalous isotope effect coefficient of LaSrCuO superconductor

2019 ◽  
Vol 33 (31) ◽  
pp. 1950379
Author(s):  
P. Mycharoen ◽  
P. Udomsamuthirun
Keyword(s):  
Experimental Data ◽  
Critical Temperature ◽  
Temperature Dependence ◽  
Isotope Effect ◽  
Weak Coupling ◽  
Numerical Results ◽  
Coupling Method ◽  
Density Of State ◽  
Van Hove Singularity ◽  
Weak Coupling Method

In this research, the anomalous isotope effect coefficient of LaSrCuO superconductor was investigated in the weak-coupling method. The constant and van Hove singularity density of state, pseudogap, and the form of pseudogap temperature dependence on critical temperature are included in our calculation. Finally, the numerical results are shown in comparison with the experimental data of LaSrCuO superconductor. We found that the van Hove singularity density of state and the inversely relation of pseudogap temperature and critical temperature can fit well with the anomalous isotope effect coefficient data of LaSrCuO superconductor.

scholarly journals Parameterization of stochastic multiscale triads

2016 ◽  
Vol 23 (6) ◽  
pp. 435-445 ◽  
Author(s):  
Jeroen Wouters ◽  
Stamen Iankov Dolaptchiev ◽  
Valerio Lucarini ◽  
Ulrich Achatz
Keyword(s):  
Model Reduction ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Coupling Model ◽  
Linear Response Theory ◽  
Coupling Method ◽  
Test Cases ◽  
Weakly Coupled ◽  
Weak Coupling Method ◽  
Markovian System

Abstract. We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction method results in general in a non-Markovian system; we therefore discuss the Markovianization of the system to allow for straightforward numerical integration. We compare the applied method to the equations obtained through homogenization in the limit of large timescale separation between slow and fast degrees of freedom. We numerically compare the ensemble spread from a fixed initial condition, correlation functions and exit times from a domain. The weak coupling method gives more accurate results in all test cases, albeit with a higher numerical cost.

scholarly journals Asynchronous Chaos and Bifurcations in a Model of Two Coupled Identical Hindmarsh – Rose Neurons

2021 ◽  
Vol 17 (3) ◽  
pp. 307-320
Author(s):  
I. R. Garashchuk ◽  
Keyword(s):  
Chaotic Attractor ◽  
Control Parameter ◽  
Single Neuron ◽  
Chaotic Regime ◽  
The Other ◽  
Linear Coupling ◽  
Minimal Network ◽  
Chaotic Bursting ◽  
Wide Range ◽  
Dynamical Regimes

We study a minimal network of two coupled neurons described by the Hindmarsh – Rose model with a linear coupling. We suppose that individual neurons are identical and study whether the dynamical regimes of a single neuron would be stable synchronous regimes in the model of two coupled neurons. We find that among synchronous regimes only regular periodic spiking and quiescence are stable in a certain range of parameters, while no bursting synchronous regimes are stable. Moreover, we show that there are no stable synchronous chaotic regimes in the parameter range considered. On the other hand, we find a wide range of parameters in which a stable asynchronous chaotic regime exists. Furthermore, we identify narrow regions of bistability, when synchronous and asynchronous regimes coexist. However, the asynchronous attractor is monostable in a wide range of parameters. We demonstrate that the onset of the asynchronous chaotic attractor occurs according to the Afraimovich – Shilnikov scenario. We have observed various asynchronous firing patterns: irregular quasi-periodic and chaotic spiking, both regular and chaotic bursting regimes, in which the number of spikes per burst varied greatly depending on the control parameter.

scholarly journals Importance of $${{d}}_{{{xy}}}$$ orbital and electron correlation in iron-based superconductors revealed by phase diagram for 1111-system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tsuyoshi Kawashima ◽  
Shigeki Miyasaka ◽  
Hirokazu Tsuji ◽  
Takahiro Yamamoto ◽  
Masahiro Uekubo ◽  
...  
Keyword(s):  
Electron Correlation ◽  
Weak Coupling ◽  
Structural Parameters ◽  
Structural Flexibility ◽  
Superconducting Transition ◽  
Iron Based Superconductors ◽  
Wide Range ◽  
Band Filling ◽  
Iron Based ◽  
Correlation Strength

AbstractThe structural flexibility at three substitution sites in LaFeAsO enabled investigation of the relation between superconductivity and structural parameters over a wide range of crystal compositions. Substitutions of Nd for La, Sb or P for As, and F or H for O were performed. All these substitutions modify the local structural parameters, while the F/H-substitution also changes band filling. It was found that the superconducting transition temperature $$T_{\text{c}}$$ T c is strongly affected by the pnictogen height $$h_{Pn}$$ h Pn from the Fe-plane that controls the electron correlation strength and the size of the $$d_{xy}$$ d xy hole Fermi surface (FS). With increasing $$h_{Pn}$$ h Pn , weak coupling BCS superconductivity switches to the strong coupling non-BCS one where electron correlations and the $$d_{xy}$$ d xy hole FS may be important.

Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Licai Wang ◽  
Yudong Chen ◽  
Chunyan Pei ◽  
Lina Liu ◽  
Suhuan Chen
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Critical Point ◽  
Control Parameter ◽  
Eigenvalue Problems ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
State Matrix ◽  
Aeroelastic System ◽  
Center Manifold Reduction

Abstract The feedback control of Hopf bifurcation of nonlinear aeroelastic systems with asymmetric aerodynamic lift force and nonlinear elastic forces of the airfoil is discussed. For the Hopf bifurcation analysis, the eigenvalue problems of the state matrix and its adjoint matrix are defined. The Puiseux expansion is used to discuss the variations of the non-semi-simple eigenvalues, as the control parameter passes through the critical value to avoid the difficulty for computing the derivatives of the non-semi-simple eigenvalues with respect to the control parameter. The method of multiple scales and center-manifold reduction are used to deal with the feedback control design of a nonlinear system with non-semi-simple eigenvalues at the critical point of the Hopf bifurcation. The first order approximate solutions are developed, which include gain vector and input. The presented methods are based on the Jordan form which is the simplest one. Finally, an example of an airfoil model is given to show the feasibility and for verification of the present method.

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