Li–Yorke Chaos in Globally Coupled Map Lattice with Delays

2019 ◽  
Vol 29 (13) ◽  
pp. 1950183
Author(s):  
Mayurakshi Nag ◽  
Swarup Poria
Keyword(s):  
Parameter Space ◽  
Coupling Strength ◽  
Coupled Map Lattice ◽  
Matrix Norm ◽  
Ring Network ◽  
Smooth Maps ◽  
Lattice Size ◽  
Global Coupling ◽  
Homogeneous Unit

Delay coupled smooth maps over a ring network with global coupling have been considered. Proof of the existence of chaos in the sense of Li–Yorke in the globally coupled smooth maps with homogeneous unit delay has been given by defining a suitable matrix norm. Conditions for the existence of Li–Yorke chaos depending on the coupling strength, map parameter and lattice size have been derived analytically. Chaotic regions in the parameter space are plotted numerically for delay coupled logistic maps.

scholarly journals Review of accelerator-based searches for Neutral Long-Lived Particles

2019 ◽  
Vol 43 (169) ◽  
pp. 638-645
Author(s):  
Marta Losada
Keyword(s):  
Parameter Space ◽  
Coupling Strength ◽  
Current Status ◽  
Next Generation ◽  
Fixed Target ◽  
Beam Dump ◽  
Basic Formalism ◽  
Neutral Lepton

In this paper we present the current status of searches for neutral long-lived particles. The basic formalism that allows the determination of the number of expected long-lived particles is presented. Heavy neutral leptons can be a type of long-lived particles. The main observational motivations for the existence of heavy neutral lepton is covered as well. A summary of the main results from both collider searches and fixed target/beam dump experiments is presented. The outlook for next generation experiments and their impact on the parameter space of coupling strength and mass of heavy neutral leptons is also discussed.

scholarly journals Robust chaos and the continuity of attractors

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Paul A Glendinning ◽  
David J W Simpson
Keyword(s):  
Normal Form ◽  
Parameter Space ◽  
Hausdorff Metric ◽  
Piecewise Smooth ◽  
Chaotic Attractors ◽  
Unimodal Maps ◽  
Smooth Maps ◽  
Tent Maps ◽  
Piecewise Smooth Maps

Abstract As the parameters of a map are varied an attractor may vary continuously in the Hausdorff metric. The purpose of this paper is to explore the continuation of chaotic attractors. We argue that this is not a helpful concept for smooth unimodal maps for which periodic windows fill parameter space densely, but that for many families of piecewise-smooth maps it provides a way to think about changing structures within parameter regions of robust chaos and form a stronger notion of robustness. We obtain conditions for the continuity of an attractor and demonstrate the results with coupled skew tent maps, the Lozi map and the border-collision normal form.

SELF-SYNCHRONIZATION OF MANY COUPLED OSCILLATORS

1994 ◽  
Vol 04 (06) ◽  
pp. 1563-1577 ◽  
Author(s):  
M. DE SOUSA VIEIRA ◽  
A.J. LICHTENBERG ◽  
M.A. LIEBERMAN
Keyword(s):  
Parameter Space ◽  
Coupled Oscillators ◽  
Phase Locked Loops ◽  
Network Synchronization ◽  
Analytical Expression ◽  
Double Ring ◽  
Digital Phase ◽  
Global Coupling ◽  
Digital Phase Locked Loops

We investigate the synchronization to a common frequency and phase in systems of many coupled digital phase-locked loops. We study cases for which the internal frequencies are identical for all loops and for which they are different. In both cases, we observe that synchronization to a common frequency is possible in a range of the parameter space. We find an analytical expression for the synchronization frequency when the communication between loops is in two directions. Synchronization in phase occurs only when the internal frequencies of the loops are identical. We study the transient convergence to the locked state in the ring, double ring, and global coupling configurations. We also discuss the influence of a multiperiodic or chaotic loop on the dynamics of the system. Our results may have applications to the problem of network synchronization.

scholarly journals COHERENCE AND SYNCHRONIZATION IN DIODE-LASER ARRAYS WITH DELAYED GLOBAL COUPLING

1999 ◽  
Vol 09 (11) ◽  
pp. 2225-2229 ◽  
Author(s):  
JORDI GARCÍA-OJALVO ◽  
JOAN CASADEMONT ◽  
M. C. TORRENT ◽  
CLAUDIO R. MIRASSO ◽  
J. M. SANCHO
Keyword(s):  
Semiconductor Laser ◽  
Diode Laser ◽  
Spontaneous Emission ◽  
Coupling Strength ◽  
Chaos Synchronization ◽  
Laser Array ◽  
Laser Arrays ◽  
Feedback Strength ◽  
Global Coupling ◽  
Phase Solution

The dynamics of a semiconductor-laser array whose individual elements are coupled in a global way through an external mirror is numerically analyzed. A coherent in-phase solution is seen to be preferred by the system at intermediate values of the feedback-coupling strength. At low values of this parameter, a strong amplification of the spontaneous emission noise is observed. A tendency towards chaos synchronization is also observed at large values of the feedback strength.

SYNCHRONIZATION IN COUPLED MAP LATTICES WITH PERIODIC BOUNDARY CONDITION

1999 ◽  
Vol 09 (08) ◽  
pp. 1635-1652 ◽  
Author(s):  
WEN-WEI LIN ◽  
CHEN-CHANG PENG ◽  
CHERN-SHUH WANG
Keyword(s):  
Boundary Condition ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Chaotic Behavior ◽  
Open Interval ◽  
Coupled Map Lattice ◽  
Coupled Map Lattices ◽  
Lattice Size ◽  
Fixed Parameter ◽  
Coupling Strengths

We consider a lattice of coupled logistic maps with periodic boundary condition. We prove that synchronization and almost synchronization occur for the case of 1D lattice with lattice size n=2, 3, 4 provided the coupling strength c is chosen in a suitable open interval contained in [Formula: see text]. For the case of lattice size n≥4, we also show the numerical results of (almost) synchronized chaotic behavior of the coupled map lattice. For each fixed parameter γ∈ [3.57, 4] of the logistic maps, the lattice sizes and the ranges of the coupling strengths c so that the coupled map lattice is synchronized, are given.

scholarly journals Influence of Rashba spin-orbit and Rabi couplings on the spin-mixing and ground state phases of binary Bose-Einstein condensates

2021 ◽  
Author(s):  
Ravisankar Rajamanickam ◽  
Sriraman Thangarasu ◽  
Ramavarmaraja Kishor Kumar ◽  
Muruganandam Paulsamy ◽  
Pankaj Kumar Mishra
Keyword(s):  
Phase Transition ◽  
Plane Wave ◽  
Parameter Space ◽  
Ground State ◽  
Coupling Strength ◽  
Coupling Parameter ◽  
Spin Orbit ◽  
Interspecies Interactions ◽  
Bose Einstein ◽  
Ground State Phases

Abstract We study the miscibility properties and ground state phases of two-component spin-orbit (SO) coupled Bose-Einstein condensates (BECs) in a harmonic trap with strong axial confinement. By numerically solving the coupled Gross-Pitaevskii equations in the two-dimensional setting, we analyze the SO-coupled BECs for two possible permutations of the intra- and interspecies interactions, namely (i) weak intra- and weak interspecies interactions (W-W) and (ii) weak intra- and strong interspecies interactions (W-S). Considering the density overlap integral as a miscibility order parameter, we investigate the miscible-immiscible transition by varying the coupling parameters. We obtain various ground state phases, including plane wave, half quantum vortex, elongated plane wave, and different stripe wave patterns for W-W interactions. For finite Rabi coupling, an increase in SO coupling strength leads to the transition from the fully miscible to the partially miscible state. We also characterize different ground states in the coupling parameter space using the root mean square sizes of the condensate. The spin density vector for the ground state phases exhibits density, quadrupole and dipole like spin polarizations. For the W-S interaction, in addition to that observed in the W-W case, we witness semi vortex, mixed mode, and shell-like immiscible phases. We notice a wide variety of spin polarizations, such as density, dipole, quadrupole, symbiotic, necklace, and stripe-like patterns for the W-S case. A detailed investigation in the coupling parameter space indicates immiscible to miscible state phase transition upon varying the Rabi coupling for a fixed Rashba SO coupling. The critical Rabi coupling for the immiscible-miscible phase transition decreases upon increasing the SO coupling strength.

scholarly journals Взаимная синхронизация наногенераторов, связанных с помощью спиновых волн

2018 ◽  
Vol 44 (7) ◽  
pp. 3
Author(s):  
К.Н. Алешин ◽  
В.В. Матросов ◽  
К.Г. Мишагин
Keyword(s):  
Dynamic Behavior ◽  
Spin Wave ◽  
Parameter Space ◽  
Coupling Strength ◽  
Frequency Mismatch ◽  
Oscillation Suppression

AbstractThe dynamic behavior of a system of two spin-wave-coupled nanooscillators with various values of coupling strength and frequency mismatch has been analyzed. The parameter space of the system has been divided into the regions of existence of synchronous and quasi-synchronous regimes, beats, and the regime of oscillation suppression. The regions of multistable behavior have been identified. The behavior at the boundaries of capture and retention regions has been studied. Dependences of the width of capture and retention bands on the strength of nanooscillator coupling have been obtained.

scholarly journals A Novel Intermittent Jumping Coupled Map Lattice Based on Multiple Chaotic Maps

2021 ◽  
Vol 11 (9) ◽  
pp. 3797
Author(s):  
Rong Huang ◽  
Fang Han ◽  
Xiaojuan Liao ◽  
Zhijie Wang ◽  
Aihua Dong
Keyword(s):  
Parameter Space ◽  
Random Number ◽  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Random Number Generator ◽  
Coupled Map Lattice ◽  
Number Generator ◽  
Multiple Chaotic Maps ◽  
Image Cryptosystem ◽  
Pseudo Random Number Generator

Coupled Map Lattice (CML) usually serves as a pseudo-random number generator for encrypting digital images. Based on our analysis, the existing CML-based systems still suffer from problems like limited parameter space and local chaotic behavior. In this paper, we propose a novel intermittent jumping CML system based on multiple chaotic maps. The intermittent jumping mechanism seeks to incorporate the multi-chaos, and to dynamically switch coupling states and coupling relations, varying with spatiotemporal indices. Extensive numerical simulations and comparative studies demonstrate that, compared with the existing CML-based systems, the proposed system has a larger parameter space, better chaotic behavior, and comparable computational complexity. These results highlight the potential of our proposal for deployment into an image cryptosystem.

Checkerboard Spiral Waves in a 2D Coupled Map Lattice

1997 ◽  
Vol 07 (11) ◽  
pp. 2569-2575 ◽  
Author(s):  
Valery I. Sbitnev
Keyword(s):  
Parameter Space ◽  
Control Parameter ◽  
Nearest Neighbors ◽  
Spatiotemporal Chaos ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
Spatiotemporal Intermittency

An intermittency of spatiotemporal chaos and checkerboard spiral waves is observed in a 2D coupled sigmoid map lattice. A rotating arm of such a spiral consists of sites oscillating in opposite phases with respect to nearest neighbors. A region of the spiral waves exhibited in the control parameter space is presented. The spatiotemporal intermittency stems from a crisis-induced intermittency of chaotic wanderings and zigzag burstings that is shown in this work.

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