Impact of Nonlocal Interaction on Chimera States in Nonlocally Coupled Stuart–Landau Oscillators

2021 ◽  
Vol 30 (4) ◽  
pp. 513-524
Author(s):  
K. Premalatha ◽  
◽  
R. Amuda ◽  
V. K. Chandrasekar ◽  
M. Senthilvelan ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Coupled System ◽  
Nonlocal Interaction ◽  
Coupling Term ◽  
Nonlocal Coupling ◽  
Wave State ◽  
Chimera States ◽  
Chimera State ◽  
Death State ◽  
The Given

We investigate the existence of collective dynamical states in nonlocally coupled Stuart–Landau oscillators with symmetry breaking included in the coupling term. We find that the radius of nonlocal interaction and nonisochronicity parameter play important roles in identifying the swing of synchronized states through amplitude chimera states. Collective dynamical states are distinguished with the help of strength of incoherence. Different transition routes to multi-chimera death states are analyzed with respect to the nonlocal coupling radius. In addition, we investigate the existence of collective dynamical states including traveling wave state, amplitude chimera state and multi-chimera death state by introducing higher-order nonlinear terms in the system. We also verify the robustness of the given notable properties for the coupled system.

Generalized Darboux transformation and asymptotic analysis on the degenerate dark-bright solitons for a coupled nonlinear Schrödinger system

2021 ◽  
Author(s):  
He-yuan Tian ◽  
Bo Tian ◽  
Yan Sun ◽  
Su-Su Chen
Keyword(s):  
Asymptotic Analysis ◽  
Darboux Transformation ◽  
Coupled System ◽  
Bound State ◽  
Bright Soliton ◽  
Spectral Parameters ◽  
Nonlinear Superposition ◽  
Bright Solitons ◽  
Generalized Darboux Transformation ◽  
The Given

Abstract In this paper, our work is based on a coupled nonlinear Schr ̈odinger system in a two-mode nonlinear fiber. A (N,m)-generalized Darboux transformation is constructed to derive the Nth-order solutions, where the positive integers N and m denote the numbers of iterative times and of distinct spectral parameters, respectively. Based on the Nth-order solutions and the given steps to perform the asymptotic analysis, it is found that a degenerate dark-bright soliton is the nonlinear superposition of several asymptotic dark-bright solitons possessing the same profile. For those asymptotic dark-bright solitons, their velocities are z-dependent except that one of those velocities could become z-independent under the certain condition, where z denotes the evolution dimension. Those asymptotic dark-bright solitons are reflected during the interaction. When a degenerate dark-bright soliton interacts with a nondegenerate/degenerate dark-bright soliton, the interaction is elastic, and the asymptotic bound-state dark-bright soliton with z-dependent or z-independent velocity could take place under certain conditions. Our study extends the investigation on the degenerate solitons from the bright soliton case for the scalar equations to the dark-bright soliton case for a coupled system.

Spatio-Temporal Pattern Formation in Holling–Tanner Type Model with Nonlocal Consumption of Resources

2019 ◽  
Vol 29 (01) ◽  
pp. 1930002 ◽  
Author(s):  
Swadesh Pal ◽  
Malay Banerjee ◽  
S. Ghorai
Keyword(s):  
Wave Front ◽  
Traveling Wave ◽  
Traveling Wave Solution ◽  
Nonlocal Interaction ◽  
Nonlocal Term ◽  
Generalist Predator ◽  
Nonlocal Model ◽  
Traveling Wave Front ◽  
Temporal Models ◽  
Spatio Temporal

A wide variety of spatio-temporal models are available in literature which are unable to generate stationary patterns through Turing bifurcation. Introduction of nonlocal terms to the same model can produce Turing patterns and this is true even for a single species population model. In this paper, we consider a prey–predator model of Holling–Tanner type with a generalist predator and a nonlocal interaction in the intra-specific competition term of the prey population. Nonmonotonic functional response is assumed to describe consumption rate of the prey by the predator. The Turing instability condition has been studied for the model without the nonlocal term around coexisting steady states. We also determine the Turing domain in the presence of nonlocal interaction term. The spatial-Hopf bifurcation has been studied and it plays an important role to find the pure Turing domain for the nonlocal model. Furthermore, in the presence of nonlocal interaction, the nonlocal model produces traveling wave solution. Using linear stability analysis, we have obtained the wave speed for the traveling wave front analytically. With the help of numerical simulation, we have verified that the speed of the traveling wave front for the complete nonlinear nonlocal model matches with the analytical approximation. The emergence of wave trains has also been established for higher range of nonlocal interaction.

Unstable Sloshing Vibration in a Thin Cylindrical Weir

1997 ◽  
Vol 119 (1) ◽  
pp. 68-73 ◽  
Author(s):  
M. Chiba ◽  
H. Kiuchi ◽  
J. Tani
Keyword(s):  
Traveling Wave ◽  
Coupled System ◽  
Stationary Wave ◽  
Baffle Plate ◽  
Annular Gap ◽  
Unstable Vibration

Traveling unstable sloshing modes have been observed in experiments on the fluidstructure coupled system in a thin cylindrical weir. The unstable vibration was found to be classified into three types: i.e., traveling wave which travels along one circumference direction; traveling wave which travels in the clockwise and counterclockwise directions alternately; and stationary wave. Influences of the outer and the inner annular gap widths, the height of weir, the elastic rigidity of weir, and baffle plate on the characteristics of the unstable sloshing vibration were clarified.

scholarly journals Cascades of Multiheaded Chimera States for Coupled Phase Oscillators

2014 ◽  
Vol 24 (08) ◽  
pp. 1440014 ◽  
Author(s):  
Yuri L. Maistrenko ◽  
Anna Vasylenko ◽  
Oleksandr Sudakov ◽  
Roman Levchenko ◽  
Volodymyr L. Maistrenko
Keyword(s):  
Periodic Orbit ◽  
Coupled Oscillators ◽  
Phase Oscillators ◽  
Invariant Circle ◽  
Saddle Node Bifurcation ◽  
Chimera States ◽  
Chimera State ◽  
Self Organized ◽  
Saddle Node ◽  
Different Types

Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of coexisting coherence and incoherence. We discuss the appearance of the chimera states in networks of phase oscillators with attractive and with repulsive interactions, i.e. when the coupling respectively favors synchronization or works against it. By systematically analyzing the dependence of the spatiotemporal dynamics on the level of coupling attractivity/repulsivity and the range of coupling, we uncover that different types of chimera states exist in wide domains of the parameter space as cascades of the states with increasing number of intervals of irregularity, so-called chimera's heads. We report three scenarios for the chimera birth: (1) via saddle-node bifurcation on a resonant invariant circle, also known as SNIC or SNIPER, (2) via blue-sky catastrophe, when two periodic orbits, stable and saddle, approach each other creating a saddle-node periodic orbit, and (3) via homoclinic transition with complex multistable dynamics including an "eight-like" limit cycle resulting eventually in a chimera state.

scholarly journals Influence of Bearing Stiffness on the Nonlinear Dynamics of a Shaft-Final Drive System

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Xu Jinli ◽  
Wan Lei ◽  
Luo Wenxin
Keyword(s):  
Coupled System ◽  
Torque Ripple ◽  
Vibration Characteristics ◽  
Vibration Response ◽  
Drive System ◽  
Lumped Mass ◽  
Driving Speed ◽  
Bearing Stiffness ◽  
Final Drive ◽  
The Given

The bearing stiffness has a considerable influence on the nonlinear coupling vibration characteristics of the shaft-final drive system. A 14-DOF nonlinear coupled vibration model was established by employing the lumped mass method so as to identify the coupling effects of the bearing stiffness to the vibration response of the shaft-final drive system. The engine’s torque ripple, the alternating load from the universal joint (U-joint), and the time-varying mesh parameters of hypoid gear of the shaft-final drive system were also considered for accurate quantitative analysis. The numerical analysis of the vibration response of the coupled system was performed and the experimental measurements were carried out for the validation test. Results show that, at the given driving speed, improving the bearing stiffness can reduce the vibration response of the given coupled system; however, when the bearing stiffness increases to a critical value, the effects of bearing stiffness on the vibration reduction become insignificant; when the driving speed changes, the resonance regions of the coupled system vary with the bearing stiffness. The results are helpful to determine the proper bearing stiffness and the optimum control strategy for the shaft-final drive system. It is hoped that the optimal shaft-final drive system can provide good vibration characteristics to achieve the energy saving and noise reduction for the vehicle application.

scholarly journals Pattern selection in multi-layer network with adaptive coupling

2021 ◽  
Author(s):  
Peihua Feng ◽  
Ying Wu
Keyword(s):  
Adaptive Dynamics ◽  
Transient State ◽  
Neuron Network ◽  
Neuron System ◽  
Feed Forward ◽  
Chimera States ◽  
Chimera State ◽  
Narrow Region ◽  
Multiple Network ◽  
Full Synchronization

Abstract Feed-forward effect modulates collective behavior of a multiple neuron network and facilitates strongly synchronization of their firing in deep layers. However, full synchronization of neuron system corresponds to functional disorder. In this work, we investigate coexistence of synchronized and incoherent neurons in deeper layer (called chimera state) in order to avoid the contradiction between facilitation of full synchronization and complete functional failure of neuron system. We focus on a multiple network containing two layers and confirm that chimera state in layer 1 could also induce that in layer 2 when the feed-forward effect is strong enough. Cluster also is discovered as a transient state which separates full synchronization and chimera state and occupy a narrow region. Both feed-forward and back-forward effect together emerge of chimera states in both layer 1 and 2 under same parameter in large range of parameters selection. Further, we introduce adaptive dynamics into inter-layer rather than intra-layer couplings. Under this circumstance chimera state still can be induced and coupling matrix will be self-organized under suitable phase parameter to guarantee chimera formation. Indeed, chimera states exist and transit to deeper layer in a regular multiple network with very strict parameter selection. The results helps understanding better the neuron firing propagating and encoding scheme in a multi-layer neuron network.

scholarly journals Chimera state in coupled map lattice of matrices

2021 ◽  
Vol 62 ◽  
pp. 57-63
Author(s):  
Kotryna Mačernytė ◽  
Rasa Šmidtaitė
Keyword(s):  
Initial Conditions ◽  
State Parameter ◽  
Coupled Map Lattice ◽  
Supplementary Variable ◽  
Chimera States ◽  
Chimera State ◽  
Nilpotent Matrix ◽  
Wide Range ◽  
The Matrix ◽  
Iterative Maps

In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks. Chimera states have wide-range applications in many disciplines including biology, chemistry, physics, or engineering. The object of research in this paper is a coupled map lattice of matrices when each node is described by an iterative map of matrices of order two. A regular topology network of iterative maps of matrices was formed by replacing the scalar iterative map with the iterative map of matrices in each node. The coupled map of matrices is special in a way where we can observe the effect of divergence. This effect can be observed when the matrix of initial conditions is a nilpotent matrix. Also, the evolution of the derived network is investigated. It is found that the network of the supplementary variable $\mu$ can evolve into three different modes: the quiet state, the state of divergence, and the formation of divergence chimeras. The space of parameters of node coupling including coupling strength $\varepsilon$ and coupling range $r$ is also analyzed in this study. Image entropy is applied in order to identify chimera state parameter zones.

scholarly journals Solving Systems of Singularly Perturbed Convection Diffusion Problems via Initial Value Method

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Wondwosen Gebeyaw Melesse ◽  
Awoke Andargie Tiruneh ◽  
Getachew Adamu Derese
Keyword(s):  
Approximate Solution ◽  
Coupled System ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Initial Value ◽  
Convection Diffusion ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
The Given ◽  
Diffusion Problems

In this paper, an initial value method for solving a weakly coupled system of two second-order singularly perturbed Convection–diffusion problems exhibiting a boundary layer at one end is proposed. In this approach, the approximate solution for the given problem is obtained by solving, a coupled system of initial value problem (namely, the reduced system), and two decoupled initial value problems (namely, the layer correction problems), which are easily deduced from the given system of equations. Both the reduced system and the layer correction problems are independent of perturbation parameter, ε. These problems are then solved analytically and/or numerically, and those solutions are combined to give an approximate solution to the problem. Further, error estimates are derived and examples are provided to illustrate the method.

scholarly journals The UKC3 regional coupled environmental prediction system

2018 ◽  
Author(s):  
Huw W. Lewis ◽  
Juan Manuel Castillo Sanchez ◽  
Alex Arnold ◽  
Joachim Fallmann ◽  
Andrew Saulter ◽  
...  
Keyword(s):  
Land Surface ◽  
Coupled System ◽  
Ocean Model ◽  
Surface Drag ◽  
Wave State ◽  
Coupled Modelling ◽  
Ocean Surface Waves ◽  
Regional Prediction ◽  
Prediction Systems ◽  
Environmental Prediction

Abstract. This paper describes an updated configuration of the regional coupled research system, termed UKC3, developed and evaluated under the UK Environmental Prediction collaboration. This represents a further step towards a vision of simulating the numerous interactions and feedbacks between different physical and biogeochemical components of the environment across sky, sea and land using more integrated regional coupled prediction systems at km-scale resolution. The UKC3 coupled system incorporates models of the atmosphere (Met Office Unified Model), land surface with river routing (JULES), shelf-sea ocean (NEMO) and ocean surface waves (WAVEWATCH III), coupled together using OASIS3-MCT libraries. The major update introduced since the UKC2 configuration is an explicit representation of wave processes in the ocean and their feedbacks through wave-to-ocean coupling. Ocean model results demonstrate that wave coupling, in particular representing the wave modified surface drag, has a small but positive improvement on the agreement between simulated sea surface temperatures and in situ observations, relative to simulations without wave feedbacks. Other incremental developments to the coupled modelling capability introduced since the UKC2 configuration are also detailed. Coupled regional prediction systems are of interest for applications across a range of timescales, from hours to decades ahead. The first results of simulations run over extended periods, covering four experiments each of order one month in duration are therefore analysed and discussed in the context of further characterising the potential benefits of coupled prediction on forecast skill, and on the stability of such systems over longer time periods. Results across atmosphere, ocean and wave components are shown to be of at least comparable skill to the equivalent uncoupled control simulations, with notable improvements demonstrated in surface temperature and wave state predictions in some near-coastal regions, and in wind speeds over the sea.

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