scholarly journals Small amplitude chimeras for coupled clocks

2020 ◽  
Vol 102 (3) ◽  
pp. 1541-1552
Author(s):  
Dawid Dudkowski ◽  
Patrycja Jaros ◽  
Krzysztof Czołczyński ◽  
Tomasz Kapitaniak
Keyword(s):  
Energy Balance ◽  
Small Amplitude ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Energy Balance Method ◽  
Chimera States ◽  
Additional Degree ◽  
Energy Flows

AbstractWe report the arise of small amplitude chimera states in three coupled pendulum clocks suspended on an oscillating base. Two types of chimeras are identified and described by the character of the behaviour of particular units (which can be both regular or irregular). The regions of the appearance of the dynamical patterns are determined and the scenarios of their coexistence with typical synchronization states are discussed. We investigate the chimeras’ basins of attraction, showing that the arise of complex dynamics is not straightforward and highly depends on the system’s parameters and the initial conditions. The latter is confirmed by the probability analysis, exhibiting the rare character of the observed attractors. The scenarios of bifurcations between the chimeric patterns are studied and supported using the energy balance method, which allows to describe the changes of the energy flows between particular nodes of the system. The results presented in this paper confirm the ones obtained for the previous models, extending the analysis with an additional degree of freedom.

Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System

2012 ◽  
Author(s):  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Fractal Boundary ◽  
Final State ◽  
Potential Wells ◽  
Mechanical Coupling ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.

517 Study on Seismic Evaluation for Multiple Degree of Freedom Models by Energy Balance Method

2011 ◽  
Vol 2011 (0) ◽  
pp. _517-1_-_517-8_
Author(s):  
Takahiro YAMANAKA ◽  
Satoshi FUJITA ◽  
Keisuke MINAGAWA ◽  
Rokurou ENDOU ◽  
Mitsuhiko AMAMIYA
Keyword(s):  
Energy Balance ◽  
Degree Of Freedom ◽  
Balance Method ◽  
Seismic Evaluation ◽  
Energy Balance Method

HIGHER-ORDER ENERGY BALANCE METHOD FOR A SERIES OF NONLINEAR OSCILLATORY SYSTEMS

2013 ◽  
Vol 06 (04) ◽  
pp. 1350054 ◽  
Author(s):  
Z. Saadatnia ◽  
N. Safaie ◽  
M. A. Ahmadpour ◽  
H. Askari
Keyword(s):  
Energy Balance ◽  
Natural Frequencies ◽  
Initial Conditions ◽  
Nonlinear Problems ◽  
Solution Procedure ◽  
Higher Order ◽  
Balance Method ◽  
Energy Balance Method ◽  
Oscillatory Systems ◽  
Order Energy

The aim of this paper is to use higher-order energy balance method as a novel solution procedure for investigation the nonlinear oscillation of various systems. The method is associated with collocation method and employed for a group of nonlinear problems including pure cubic nonlinearity, fractional elastic force and duffing harmonic terms. Obtained results are evaluated by comparing with the classical balance method and also the exact solutions computed numerically. It is shown our solution procedure achieves more accurate results versus the classical solution and higher agreement are observed between the newer solutions and the exact ones for the systems. Effect of initial conditions in the nonlinear natural frequencies are carried out for a range of small and large values and it is proved the proposed method is not only simple but also more reliable for analysis of such systems.

scholarly journals AUXILIARY QUANTIZATION CONSTRAINTS ON THE VON ROOS ORDERING-AMBIGUITY AT ZERO BINDING ENERGIES; AZIMUTHALLY SYMMETRIZED CYLINDRICAL COORDINATES

2013 ◽  
Vol 28 (19) ◽  
pp. 1350082
Author(s):  
OMAR MUSTAFA
Keyword(s):  
Binding Energies ◽  
Degree Of Freedom ◽  
Zero Energy ◽  
Cylindrical Coordinates ◽  
Additional Degree ◽  
Quantum Numbers ◽  
Dependent Mass ◽  
Position Dependent Mass

Using azimuthally symmetrized cylindrical coordinates, we report the consequences of zero-energy quantal states on the von Roos Hamiltonian. A position-dependent mass (PDM) M(ρ, φ, z) = bzjρ2υ+1/2 is used. We show that the zero-energy setting not only offers an additional degree of freedom toward feasible separability for the von Roos Hamiltonian, but also manifestly yields auxiliary quantized ambiguity parametric constraints (i.e. the ambiguity parameters are given in terms of quantum numbers).

BASIN CONFIGURATION OF A SIX-DIMENSIONAL MODEL OF AN ELECTRIC POWER SYSTEM

2002 ◽  
Vol 12 (06) ◽  
pp. 1333-1356 ◽  
Author(s):  
YOSHISUKE UEDA ◽  
HIROYUKI AMANO ◽  
RALPH H. ABRAHAM ◽  
H. BRUCE STEWART
Keyword(s):  
Power Systems ◽  
Power System ◽  
Initial Conditions ◽  
Electrical Power ◽  
Practical Importance ◽  
Intervention Strategy ◽  
Basins Of Attraction ◽  
Electric Power System ◽  
Point Of View ◽  
Electrical Power System

As part of an ongoing project on the stability of massively complex electrical power systems, we discuss the global geometric structure of contacts among the basins of attraction of a six-dimensional dynamical system. This system represents a simple model of an electrical power system involving three machines and an infinite bus. Apart from the possible occurrence of attractors representing pathological states, the contacts between the basins have a practical importance, from the point of view of the operation of a real electrical power system. With the aid of a global map of basins, one could hope to design an intervention strategy to boot the power system back into its normal state. Our method involves taking two-dimensional sections of the six-dimensional state space, and then determining the basins directly by numerical simulation from a dense grid of initial conditions. The relations among all the basins are given for a specific numerical example, that is, choosing particular values for the parameters in our model.

3D Printing — The Basins of Tristability in the Lorenz System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750128 ◽  
Author(s):  
Anda Xiong ◽  
Julien C. Sprott ◽  
Jingxuan Lyu ◽  
Xilu Wang
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Symmetric Pair ◽  
State Space Approach ◽  
3D Printers ◽  
The Lorenz System ◽  
Almost All ◽  
Space Approach

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

Three degree of freedom description of movement of the human chest wall

1986 ◽  
Vol 60 (3) ◽  
pp. 928-934 ◽  
Author(s):  
J. C. Smith ◽  
J. Mead
Keyword(s):  
Chest Wall ◽  
Lung Volume ◽  
Pubic Symphysis ◽  
Degree Of Freedom ◽  
Rib Cage ◽  
Additional Degree ◽  
Wall Movement ◽  
Surface Displacements ◽  
Flexion Extension ◽  
Three Degree Of Freedom

A three degree of freedom description of movement of the human chest wall is presented. In addition to the standard variables representing surface displacements of the rib cage and abdominal wall in transverse planes, the description includes a variable representing axial displacements of the chest wall associated with postural movements of the spine and pelvis. A simple technique was developed for quantifying the axial displacements using a single measurement by magnetometry of changes in the distance between a point on the anterior surface of the rib cage near the xiphisternum and a point on the abdominal surface near the pubic symphysis. It was found that axial displacements produced by either flexion-extension of the spine or rotation of the pelvis in the standing postures can be treated as a single degree of freedom. The chest wall displacements induced over the range of axial displacement examined were as large as those normally accompanying a change in lung volume on the order of 30–50% of the vital capacity. It is concluded, however, that although this additional degree of freedom can cause large chest wall displacements, it probably cannot independently change lung volume. This implies that the system is constrained so that there are only a limited number of independent modes of chest wall movement that are capable of producing significant changes in lung volume. It also suggests that the system is constructed so that lung volume can be relatively independent of certain postural distortions of the chest wall.

Experimental and Numerical Investigation Into the Effects of Initial Conditions on a Three Degree of Freedom Capsize Model

2006 ◽  
Vol 50 (01) ◽  
pp. 63-84
Author(s):  
Young-Woo Lee ◽  
Leigh McCue ◽  
Michael Obar ◽  
Armin Troesch
Keyword(s):  
Numerical Model ◽  
Numerical Investigation ◽  
Initial Conditions ◽  
Degree Of Freedom ◽  
Transient Effects ◽  
Ultimate State ◽  
Extreme Behavior ◽  
Three Degree Of Freedom ◽  
Physical Phenomena ◽  
Ship Capsizing

The dynamics and hydrodynamics of ship capsizing include strong nonlinearities, transient effects, and physical phenomena that have not been fully identified or studied. This paper presents a study of some of the various mechanisms associated with this extreme behavior. A quasi-nonlinear three degree of freedom numerical model is employed to examine the effects of initial conditions on the ultimate state of a box barge model. The numerical results are then used to provide structure and understanding to otherwise seemingly inconsistent and ambiguous experiments.

Dynamics research of Fangzhu’s nanoscale surface

2021 ◽  
pp. 146134842110527
Author(s):  
Pinxia Wu ◽  
Weiwei Ling ◽  
Xiumei Li ◽  
Xichun He ◽  
Liangjin Xie
Keyword(s):  
Energy Balance ◽  
Analytical Solutions ◽  
Numerical Experiments ◽  
Fractal Model ◽  
Balance Method ◽  
Transform Method ◽  
Energy Balance Method ◽  
Collection Rate ◽  
Fractal Derivative ◽  
Approximate Analytical Solutions

In this paper, we mainly focus on a fractal model of Fangzhu’s nanoscale surface for water collection which is established through He’s fractal derivative. Based on the fractal two-scale transform method, the approximate analytical solutions are obtained by the energy balance method and He’s frequency–amplitude formulation method with average residuals. Some specific numerical experiments of the model show that these two methods are simple and effective and can be adopted to other nonlinear fractal oscillators. In addition, these properties of the obtained solution reveal how to enhance the collection rate of Fangzhu by adjusting the smoothness of its surfaces.

Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps

2021 ◽  
Vol 29 (6) ◽  
pp. 943-952
Author(s):  
Vasiliy Nechaev ◽  
◽  
Elena Rybalova ◽  
Galina Strelkova ◽  
◽  
...  
Keyword(s):  
Coupling Strength ◽  
Noise Intensity ◽  
Initial Conditions ◽  
Random Variable ◽  
Inhomogeneous Distribution ◽  
Control Parameters ◽  
Chimera States ◽  
Intensity Parameters ◽  
Different Characteristics ◽  
Ring Elements

The aim of the research is to study the influence of inhomogeneity in a control parameter of all partial elements in a ring of nonlocally coupled chaotic maps on the possibility of observing chimera states in the system and to compare the changes in regions of chimera realization using different methods of introducing the inhomogeneity. Methods. In this paper, snapshots of the system dynamics are constructed for various values of the parameters, as well as spatial distributions of cross-correlation coefficient values, which enable us to determine the regime observed in the system for these parameters. To improve the accuracy of the obtained results, the numerical studies are carried out for fifty different realizations of initial conditions of the ring elements. Results. It is shown that a fixed inhomogeneous distribution of the control parameters with increasing noise intensity leads to an increase in the range of the coupling strength where chimera states are observed. With this, the boundary lying in the region of strong coupling changes more significantly as compared with the case of weak coupling strength. The opposite effect is provided when the control parameters are permanently affected by noise. In this case increasing the noise intensity leads to a decrease in the interval of existence of chimera states. Additionally, the nature of the random variable distribution (normal or uniform one) does not strongly influence the observed changes in the ring dynamics. The regions of existence of chimera states are constructed in the plane of «coupling strength – noise intensity» parameters. Conclusion. We have studied how the region of existence of chimeras changes when the coupling strength between the ring elements is varied and when different characteristics of the inhomogeneous distribution of the control parameters are used. It has been shown that in order to increase the region of observing chimera states, the control parameters of the elements must be distributed inhomogeneously over the entire ensemble. To reduce this region, a constant noise effect on the control parameters should be used.

Sign in / Sign up

Export Citation Format

Share Document