scholarly journals Dynamic Properties of Coupled Maps

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Chunrui Zhang ◽  
Huifeng Zheng
Keyword(s):  
Computer Simulations ◽  
Collective Behavior ◽  
Periodic Boundary ◽  
Nearest Neighbor ◽  
Dynamic Properties ◽  
Coupled System ◽  
Periodic Boundary Conditions ◽  
Theoretical Predictions ◽  
Coupling Parameters ◽  
Coupled Maps

Dynamic properties are investigated in the coupled system of three maps with symmetric nearest neighbor coupling and periodic boundary conditions. The dynamics of the system is controlled by certain coupling parameters. We show that, for some values of the parameters, the system exhibits nontrivial collective behavior, such as multiple bifurcations, and chaos. We give computer simulations to support the theoretical predictions.

THE DISTRIBUTION OF PERIODIC AND APERIODIC PATTERN EVOLUTIONS IN RINGS OF DIFFUSIVELY COUPLED MAPS

2001 ◽  
Vol 11 (10) ◽  
pp. 2647-2661 ◽  
Author(s):  
PEDRO G. LIND ◽  
JOÃO A. M. CORTE-REAL ◽  
JASON A. C. GALLAS
Keyword(s):  
Boundary Conditions ◽  
Parameter Space ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
One Dimensional ◽  
Quadratic Maps ◽  
Coupled Maps

This paper reports histograms showing the detailed distribution of periodic and aperiodic motions in parameter-space of one-dimensional lattices of diffusively coupled quadratic maps subjected to periodic boundary conditions. Particular emphasis is given to the parameter domains where lattices support traveling patterns.

scholarly journals Efficient MPS Algorithm for Periodic Boundary Conditions and Applications Section: Solid matter Original Author's Text: English Abstract: We present the implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states (MPS) and a similar representation for Hamiltonians and other operators (MPO). It is significantly more efficient for systems of about 100 sites and more than for small quantum systems. We apply the formalism to calculate the ground state and the first excited state of a spin-1 Heisenberg ring and deduce the size of a Haldane gap. The results are compared to previous high-precision DMRG calculations. Furthermore, we study the spin-1 systems with a biquadratic nearest-neighbor interaction and show the first results of an application to a mesoscopic Hubbard ring of spinless fermions, which carries a persistent current. Key words: matrix product representation for quantum states (MPS) and Hamiltonians (MPO), spin-1 Heisenberg ring, density matrix renormalization group (DMRG). List Issues Configure

2013 ◽  
Vol 58 (7) ◽  
pp. 657-665 ◽  
Author(s):  
M. Weyrauch ◽  
◽  
M.V. Rakov ◽  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Nearest Neighbor ◽  
Periodic Boundary Conditions ◽  
Quantum Systems ◽  
Quantum States ◽  
Matrix Product ◽  
Product Representation ◽  
Density Matrix Renormalization ◽  
Small Quantum

scholarly journals Chimeras and Clusters Emerging from Robust-Chaos Dynamics

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
M. G. Cosenza ◽  
O. Alvarez-Llamoza ◽  
A. V. Cano
Keyword(s):  
Collective Behavior ◽  
Coupled System ◽  
Coupled Systems ◽  
Response Dynamics ◽  
Local Dynamics ◽  
Chimera States ◽  
Coupled Maps

We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks of globally coupled robust-chaos oscillators. We describe the collective behavior of a model of globally coupled robust-chaos maps in terms of statistical quantities and characterize clusters, chimera states, synchronization, and incoherence on the space of parameters of the system. We employ the analogy between the local dynamics of a system of globally coupled maps with the response dynamics of a single driven map. We interpret the occurrence of clusters and chimeras in a globally coupled system of robust-chaos maps in terms of windows of periodicity and multistability induced by a drive on the local robust-chaos map. Our results show that robust-chaos dynamics does not limit the formation of cluster and chimera states in networks of coupled systems, as it had been previously conjectured.

NUMERICAL STUDY OF THE t−J MODEL: EXACT GROUND STATE AND FLUX PHASES

1989 ◽  
Vol 03 (12) ◽  
pp. 1853-1863 ◽  
Author(s):  
Y. Hasegawa ◽  
D. Poilblanc
Keyword(s):  
Ground State ◽  
Periodic Boundary ◽  
Nearest Neighbor ◽  
Numerical Study ◽  
Coulomb Repulsion ◽  
Periodic Boundary Conditions ◽  
Strongly Correlated ◽  
Lanczos Algorithm ◽  
Exact Ground State ◽  
Intermediate Value

Strongly correlated 2D electrons described by the t–J model are investigated numerically. Exact ground state for one and two holes in a finite cluster with periodic boundary conditions are obtained by using the Lanczos algorithm. The effects of Coulomb repulsion of the holes on the nearest neighbor sites are taken into account. Commensurate flux phases are investigated for the same size of clusters. They are shown to be a good approximation for the ground state specially in the intermediate value of J/t.

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