On the Influence of the Coupling Strength among Chua’s Circuits on the Structure of Their Hyper-Chaotic Attractors

2016 ◽  
Vol 26 (07) ◽  
pp. 1650115 ◽  
Author(s):  
Sven Freud ◽  
Rainer Plaga ◽  
Ralph Breithaupt
Keyword(s):  
Significant Influence ◽  
Coupling Strength ◽  
Strange Attractor ◽  
Chaotic Dynamics ◽  
Strange Attractors ◽  
Chaotic Attractors ◽  
Physical Unclonable Functions ◽  
Coupling Strengths ◽  
Probability Of Presence ◽  
Random Fluctuations

The hyper-chaotic strange attractor of systems of four Chua’s circuits that are mutually coupled by three strong and three weak couplings is studied, both experimentally and via simulation. A new metric to compare strange attractors is presented. It is found that the strength of the couplings between circuits have a complex and determining influence on the probability for the presence of a trajectory within their attractors. This influence is strictly local, i.e. the probability of the presence of the trajectories is determined by the coupling strength to the directly adjacent circuits and independent of the coupling strengths among other circuits. Fluctuations in the properties of Chua’s circuits due to random fluctuations during the production of its components have a significant influence on the probability of presence of the attractor’s trajectories that could be qualitatively, but not quantitatively, modeled by our simulation. The consequences of these results for the possibility to construct “physical unclonable functions” as networks of Chua’s circuits with a hyper-chaotic dynamics are discussed.

scholarly journals Synchronized Attractors and Phase Entrained with Cavity Loss of the Coupled Laser’s Map

2022 ◽  
Author(s):  
Abdul Abdul ◽  
Altaf Ur Rahman ◽  
Chen Minjing ◽  
Jehan Akbar ◽  
Farhan Saif ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Symmetry Breaking ◽  
Coupling Strength ◽  
Strange Attractors ◽  
Chaotic Attractors ◽  
Cavity Loss ◽  
Numerical Studies ◽  
Coupled Maps ◽  
Basin Boundaries

The laser differential equations are used to transform them into identical coupled maps. Valuable results are deduced during analytical and numerical studies on cavity loss. Phase and spatiotemporal synchronized attractors are observed via quasi-chaos under a certain range of controlling parameters, and symmetry breaking of chaotic attractors due to collision with their basin boundaries, and transpire differently from the previous attractors. During the numerical simulation, it is found that the sequence of repeated strange attractors if the coupling strength further increases, which are orthogonal mirror images (the dynamics of the system is the same at different values of controlling parameters). Moreover, it can help us to predict future problems and their solutions based on current issues, if we develop this model in more general.

EVOLUTION OF ATOM-FIELD PROBABILITY IN A COUPLED CAVITY SYSTEM

2013 ◽  
Vol 22 (03) ◽  
pp. 1350029
Author(s):  
K. V. PRIYESH ◽  
RAMESH BABU THAYYULLATHIL
Keyword(s):  
Coupling Strength ◽  
Probability Amplitude ◽  
Field Coupling ◽  
Level Atom ◽  
Cavity System ◽  
Coupling Strengths ◽  
Field Excitation ◽  
Excitation Probability ◽  
Hopping Strength ◽  
Coupled Cavity

In this paper we have investigated the dynamics of two cavities each with a two-level atom, coupled together with photon hopping. The coupled cavity system is studied in single excitation subspace and the evolution of the atom (field) states probabilities are obtained analytically. The probability amplitude of states executes oscillations with different modes and amplitudes, determined by the coupling strengths. The evolution is examined in detail for different atom field coupling strength, g and field–field hopping strength, A. It is noticed that the exact atomic probability amplitude transfer occurs when g ≪ A with minimal field excitation probability and the period of probability transfer is calculated. In the limit g ≫ A there exists periodic exchange of probability between atom and field inside each cavity and also between cavity 1 and cavity 2. Periodicity of each exchange in this limit also obtained.

Relation between Topological Entropies and Fractal Dimensions of Chaotic Attractors of the Hénon Map

2012 ◽  
Vol 569 ◽  
pp. 447-450
Author(s):  
Xiao Zhou Chen ◽  
Liang Lin Xiong ◽  
Long Li
Keyword(s):  
Linear Relation ◽  
Chaotic Dynamics ◽  
Fractal Dimensions ◽  
Chaotic Attractors ◽  
Two Dimensional ◽  
Hénon Map ◽  
Henon Map ◽  
Efficient Approach ◽  
Integral Relationship

In two-dimensional chaotic dynamics, relationship between fractal dimensions and topological entropies is an important issue to understand the chaotic attractors of Hénon map. we proposed a efficient approach for the estimation of topological entropies through the study on the integral relationship between fractal dimensions and topological entropies. Our result found that there is an approximate linear relation between their topological entropies and fractal dimensions.

scholarly journals Distinguishing f(R) gravity with cosmic voids

2014 ◽  
Vol 11 (S308) ◽  
pp. 589-590 ◽  
Author(s):  
P. Zivick ◽  
P. M. Sutter
Keyword(s):  
Coupling Strength ◽  
Significant Shift ◽  
Initial Estimate ◽  
Galaxy Surveys ◽  
The Public ◽  
Coupling Strengths ◽  
Cosmic Voids

AbstractWe use properties of void populations identified in N-body simulations to forecast the ability of upcoming galaxy surveys to differentiate models of f(R) gravity from \lcdm cosmology. We analyze simulations designed to mimic the densities, volumes, and clustering statistics of upcoming surveys, using the public {\tt VIDE} toolkit. We examine void abundances as a basic probe at redshifts 1.0 and 0.4. We find that stronger f(R) coupling strengths produce voids up to ∼20% larger in radius, leading to a significant shift in the void number function. As an initial estimate of the constraining power of voids, we use this change in the number function to forecast a constraint on the coupling strength of Δ fR0 = 10-5.

Electron-Phonon Coupling Strength of Specific Phonons from First Principles Lapw Calculations

1988 ◽  
Vol 141 ◽  
Author(s):  
H. Krakauer ◽  
R. E. Cohen ◽  
W. E. Pickett
Keyword(s):  
Coupling Strength ◽  
First Principles ◽  
Mode Coupling ◽  
Local Density ◽  
Matrix Elements ◽  
Dual Representation ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling ◽  
Coupling Strengths ◽  
The Difference

AbstractElectron-phonon matrix elements, phonon linewidths and mode coupling strengths are being calculated for La2-xMxCuO4 (M-divalent cation, for paramagnetic x-0.0 and for x-0.15 in a rigid band picture) from first principles local density calculations. The change in potential due to a particular phonon mode is calculated from the difference of self-consistent one-electron potentials, and appropriate Fermi surface averages are carried out for selected modes, allowing us to obtain the phonon linewidth due to the electron-phonon interaction, and the corresponding coupling strength λQ. Here we establish the numerical accuracy within the dual representation of the potential used in the Linearized Augmented Plane Wave (LAPW) method. Evaluations of phonon linewidths and mode coupling strengths are presented for Al and Nb and compared with previous information on these modes. We present preliminary results for the full matrix elements and coupling of the La2CuO4 oxygen planar X-point breathing mode, and compare with a simpler approximation.

scholarly journals Experimentally Accessible Orbits Near a Bykov Cycle

2020 ◽  
Vol 30 (10) ◽  
pp. 2030030
Author(s):  
Roberto Barrio ◽  
Maria Carvalho ◽  
Luísa Castro ◽  
Alexandre A. P. Rodrigues
Keyword(s):  
Chaotic Dynamics ◽  
Vector Fields ◽  
Initial Conditions ◽  
Parabolic Type ◽  
Chaotic Attractors ◽  
Heteroclinic Cycle ◽  
Type Curves ◽  
Local And Global Bifurcations ◽  
Domain Of Parameters ◽  
Two Parameter

This paper reports numerical experiments done on a two-parameter family of vector fields which unfold an attracting heteroclinic cycle linking two saddle-foci. We investigated both local and global bifurcations due to symmetry breaking in order to detect either hyperbolic or chaotic dynamics. Although a complete understanding of the corresponding bifurcation diagram and the mechanisms underlying the dynamical changes is still out of reach, using a combination of theoretical tools and computer simulations we have uncovered some complex patterns. We have selected suitable initial conditions to analyze the bifurcation diagrams, and regarding these solutions we have located: (a) an open domain of parameters with regular dynamics; (b) infinitely many parabolic-type curves associated to homoclinic Shilnikov cycles which act as organizing centers; (c) a crisis region related to the destruction or creation of chaotic attractors; (d) a large Lebesgue measure set of parameters where chaotic regimes are dominant, though sinks and chaotic attractors may coexist, and in whose complement we observe shrimps.

scholarly journals Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons

2007 ◽  
Vol 19 (11) ◽  
pp. 3011-3050 ◽  
Author(s):  
Andreas Kaltenbrunner ◽  
Vicenç Gómez ◽  
Vicente López
Keyword(s):  
Phase Transition ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Stochastic Dynamics ◽  
Upper And Lower Bounds ◽  
Critical Coupling ◽  
Sustained Activity ◽  
Large Ensembles ◽  
Coupling Strengths ◽  
Pulse Coupled Oscillators

An ensemble of stochastic nonleaky integrate-and-fire neurons with global, delayed, and excitatory coupling and a small refractory period is analyzed. Simulations with adiabatic changes of the coupling strength indicate the presence of a phase transition accompanied by a hysteresis around a critical coupling strength. Below the critical coupling production of spikes in the ensemble is governed by the stochastic dynamics, whereas for coupling greater than the critical value, the stochastic dynamics loses its influence and the units organize into several clusters with self-sustained activity. All units within one cluster spike in unison, and the clusters themselves are phase-locked. Theoretical analysis leads to upper and lower bounds for the average interspike interval of the ensemble valid for all possible coupling strengths. The bounds allow calculating the limit behavior for large ensembles and characterize the phase transition analytically. These results may be extensible to pulse-coupled oscillators.

CHAOTIC ATTRACTORS OF THE CONJUGATE LORENZ-TYPE SYSTEM

2007 ◽  
Vol 17 (11) ◽  
pp. 3929-3949 ◽  
Author(s):  
QIGUI YANG ◽  
GUANRONG CHEN ◽  
KUIFEI HUANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Type System ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Chen System ◽  
Numerical Examples ◽  
Special Cases ◽  
Dynamical Properties

A new conjugate Lorenz-type system is introduced in this paper. The system contains as special cases the conjugate Lorenz system, conjugate Chen system and conjugate Lü system. Chaotic dynamics of the system in the parametric space is numerically and thoroughly investigated. Meanwhile, a set of conditions for possible existence of chaos are derived, which provide some useful guidelines for searching chaos in numerical simulations. Furthermore, some basic dynamical properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions and the compound structure of the system are demonstrated with various numerical examples.

SYNCHRONIZING CHAOTIC ATTRACTORS OF CHUA'S CANONICAL CIRCUIT: THE CASE OF UNCERTAINTY IN CHAOS SYNCHRONIZATION

2006 ◽  
Vol 16 (07) ◽  
pp. 1961-1976 ◽  
Author(s):  
I. M. KYPRIANIDIS ◽  
A. N. BOGIATZI ◽  
M. PAPADOPOULOU ◽  
I. N. STOUBOULOS ◽  
G. N. BOGIATZIS ◽  
...  
Keyword(s):  
Coupling Strength ◽  
Chaos Synchronization ◽  
Phase Synchronization ◽  
Initial Conditions ◽  
Chaotic Synchronization ◽  
Chaotic Attractors ◽  
Coexisting Attractors

In this paper, we have studied the dynamics of two identical resistively coupled Chua's canonical circuits and have found that it is strongly affected by initial conditions, coupling strength and the presence of coexisting attractors. Depending on the coupling variable, chaotic synchronization has been observed both numerically and experimentally. Anti-phase synchronization has also been studied numerically clarifying some aspects of uncertainty in chaos synchronization.

Bifurcation Structures in a Bimodal Piecewise Linear Map: Chaotic Dynamics

2015 ◽  
Vol 25 (03) ◽  
pp. 1530006 ◽  
Author(s):  
Anastasiia Panchuk ◽  
Iryna Sushko ◽  
Viktor Avrutin
Keyword(s):  
Parameter Space ◽  
Chaotic Dynamics ◽  
Piecewise Linear ◽  
Chaotic Attractors ◽  
Bifurcation Structure ◽  
Tent Map ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Replacement Technique ◽  
Bifurcation Structures

In this work, we investigate the bifurcation structure of the parameter space of a generic 1D continuous piecewise linear bimodal map focusing on the regions associated with chaotic attractors (cyclic chaotic intervals). The boundaries of these regions corresponding to chaotic attractors with different number of intervals are identified. The results are obtained analytically using the skew tent map and the map replacement technique.

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