scholarly journals Chimera states and the interplay between initial conditions and non-local coupling

2017 ◽  
Vol 27 (3) ◽  
pp. 033110 ◽  
Author(s):  
Peter Kalle ◽  
Jakub Sawicki ◽  
Anna Zakharova ◽  
Eckehard Schöll
Keyword(s):  
Initial Conditions ◽  
Chimera States ◽  
Non Local ◽  
Local Coupling

scholarly journals Asymptotic Stability of Nonlinear Discrete Fractional Pantograph Equations with Non-Local Initial Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 473
Author(s):  
Jehad Alzabut ◽  
A. George Maria Selvam ◽  
Rami Ahmad El-Nabulsi ◽  
D. Vignesh ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorems ◽  
Initial Conditions ◽  
Current Collector ◽  
Stability Of Solutions ◽  
Electric Bus ◽  
Pantograph Equation ◽  
Non Local

Pantograph, the technological successor of trolley poles, is an overhead current collector of electric bus, electric trains, and trams. In this work, we consider the discrete fractional pantograph equation of the form Δ*β[k](t)=wt+β,k(t+β),k(λ(t+β)), with condition k(0)=p[k] for t∈N1−β, 0<β≤1, λ∈(0,1) and investigate the properties of asymptotic stability of solutions. We will prove the main results by the aid of Krasnoselskii’s and generalized Banach fixed point theorems. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

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.

Development and Calculation of a Computer Model and Modern Distributed Algorithms for Dispersed Systems Aggregation

2020 ◽  
Vol 11 (2) ◽  
pp. 56-68
Author(s):  
Nurlybek Zhumatayev ◽  
Zhanat Umarova ◽  
Gani Besbayev ◽  
Almira Zholshiyeva
Keyword(s):  
Distributed Algorithms ◽  
Computer Model ◽  
Initial Conditions ◽  
Relaxation Times ◽  
Calculation Algorithm ◽  
Dispersed Systems ◽  
Perfect Model ◽  
Aggregation Processes ◽  
Non Local ◽  
Non Local Equations

In this work, an attempt has been made to eliminate the contradiction of the Smoluchowski equation, using modern distributed algorithms for creating calculation algorithm and implementation a program for building a more perfect model by changing the type of the kinetic equation of aggregation taking into account the relaxation times. On the basis of the applied Mathcad package, there is a developed computer model for calculating the aggregation of dispersed systems. The obtained system of differential equations of the second order is solved by the Runge-Kutt method. The authors are presetting the initial conditions of the calculation. A subsequent analysis was made of the obtained non-local equations and the study of the behavior of solutions of different orders. Also, this research can be aimed at the generalization of the proposed approach for the analysis of aggregation processes in heterogeneous dispersed systems, involving the creation of aggregation models, taking into account both time and space non-locality.

Burgers' equation by non-local shot noise data

1994 ◽  
Vol 31 (A) ◽  
pp. 351-362 ◽  
Author(s):  
Donatas Surgailis ◽  
Wojbor A. Woyczynski
Keyword(s):  
Shot Noise ◽  
Random Fields ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Scaling Limit ◽  
Linear Partial Differential Equation ◽  
Local Case ◽  
Non Linear ◽  
Noise Data ◽  
Non Local

We study the scaling limit of random fields which are solutions of a non-linear partial differential equation, known as the Burgers equation, under stochastic initial conditions. These are assumed to be of a non-local shot noise type and driven by a Cox process. Previous work by Bulinskii and Molchanov (1991), Surgailis and Woyczynski (1993a), and Funaki et al. (1994) concentrated on the case of local shot noise data which permitted use of techniques from the theory of random fields with finite range dependence. Those are not available for the non-local case being considered in this paper.Burgers' equation is known to describe various physical phenomena such as non-linear and shock waves, distribution of self-gravitating matter in the universe, and other flow satisfying conservation laws (see e.g. Woyczynski (1993)).

scholarly journals Chimera States in Star Networks

2016 ◽  
Vol 26 (09) ◽  
pp. 1630023 ◽  
Author(s):  
Chandrakala Meena ◽  
K. Murali ◽  
Sudeshna Sinha
Keyword(s):  
Analog Circuit ◽  
Initial Conditions ◽  
Mean Field ◽  
Coupled Systems ◽  
Dynamical Equations ◽  
Chimera States ◽  
Diffusive Coupling ◽  
Star Networks ◽  
Random Initial Conditions ◽  
Coupling Strengths

We consider star networks of chaotic oscillators, with all end-nodes connected only to the central hub node, under diffusive coupling, conjugate coupling and mean-field diffusive coupling. We observe the existence of chimeras in the end-nodes, which are identical in terms of the coupling environment and dynamical equations. Namely, the symmetry of the end-nodes is broken and coexisting groups with different synchronization features and attractor geometries emerge. Surprisingly, such chimera states are very wide-spread in this network topology, and large parameter regimes of moderate coupling strengths evolve to chimera states from generic random initial conditions. Further, we verify the robustness of these chimera states in analog circuit experiments. Thus it is evident that star networks provide a promising class of coupled systems, in natural or engineered contexts, where chimeras are prevalent.

Non-Local Coupling and Partial Synchronization in Chaotic Systems

2006 ◽  
Vol 23 (4) ◽  
pp. 786-789 ◽  
Author(s):  
Ao Bin ◽  
Ma Xiao-Juan ◽  
Li Yun-Yun ◽  
Zheng Zhi-Gang
Keyword(s):  
Chaotic Systems ◽  
Partial Synchronization ◽  
Non Local ◽  
Local Coupling

scholarly journals Non-local coupling of two donor-bound electrons

2013 ◽  
Vol 15 (3) ◽  
pp. 033020 ◽  
Author(s):  
J Verduijn ◽  
R R Agundez ◽  
M Blaauboer ◽  
S Rogge
Keyword(s):  
Non Local ◽  
Local Coupling ◽  
Bound Electrons

Effects of different initial conditions on the emergence of chimera states

2018 ◽  
Vol 114 ◽  
pp. 306-311 ◽  
Author(s):  
Zahra Faghani ◽  
Zahra Arab ◽  
Fatemeh Parastesh ◽  
Sajad Jafari ◽  
Matjaž Perc ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Chimera States

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.

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