scholarly journals ON A DYNAMICAL SYSTEM WITH MULTIPLE CHAOTIC ATTRACTORS

2007 ◽  
Vol 17 (09) ◽  
pp. 3235-3251 ◽  
Author(s):  
XIAODONG LUO ◽  
MICHAEL SMALL ◽  
MARIUS-F. DANCA ◽  
GUANRONG CHEN
Keyword(s):  
Dynamical System ◽  
Monte Carlo ◽  
Chaotic Behavior ◽  
Hypothesis Test ◽  
Surrogate Data ◽  
Chaotic Attractors ◽  
System A ◽  
Numerical Studies

The chaotic behavior of the Rabinovich–Fabrikant system, a model with multiple topologically different chaotic attractors, is analyzed. Because of the complexity of this system, analytical and numerical studies of the system are very difficult tasks. Following the investigation of this system carried out in [Danca & Chen, 2004], this paper verifies the presence of multiple chaotic attractors in the system. Moreover, the Monte Carlo hypothesis test (or, equivalently, surrogate data test) is applied to the system for the detection of chaos.

Simple Chaotic Hyperjerk System

2016 ◽  
Vol 26 (11) ◽  
pp. 1650189 ◽  
Author(s):  
Fatma Yildirim Dalkiran ◽  
J. C. Sprott
Keyword(s):  
Dynamical System ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Nonlinear Function ◽  
Nonlinear Functions ◽  
Third Order ◽  
Experimental Realization ◽  
Numerical Studies ◽  
Hyperjerk System ◽  
Jerk System

In literature many chaotic systems, based on third-order jerk equations with different nonlinear functions, are available. A jerk system is taken to be a part of dynamical systems that can exhibit regular and chaotic behavior. By extension, a hyperjerk system can be described as a dynamical system with [Formula: see text]th-order ordinary differential equations where [Formula: see text] is 4 or up to. Hyperjerk systems have been investigated in literature in the last decade. This paper consists of numerical studies and experimental realization on FPAA for fourth-order hyperjerk system with exponential nonlinear function.

Reversibly Sampling Conformations and Binding Modes Using Molecular Darting

2020 ◽  
Author(s):  
Samuel C. Gill ◽  
David Mobley
Keyword(s):  
Monte Carlo ◽  
Ligand Binding ◽  
Binding Sites ◽  
Degrees Of Freedom ◽  
Dynamics Simulation ◽  
Hiv Integrase ◽  
Binding Modes ◽  
System A ◽  
Multiple Binding ◽  
Internal Degrees Of Freedom

<div>Sampling multiple binding modes of a ligand in a single molecular dynamics simulation is difficult. A given ligand may have many internal degrees of freedom, along with many different ways it might orient itself a binding site or across several binding sites, all of which might be separated by large energy barriers. We have developed a novel Monte Carlo move called Molecular Darting (MolDarting) to reversibly sample between predefined binding modes of a ligand. Here, we couple this with nonequilibrium candidate Monte Carlo (NCMC) to improve acceptance of moves.</div><div>We apply this technique to a simple dipeptide system, a ligand binding to T4 Lysozyme L99A, and ligand binding to HIV integrase in order to test this new method. We observe significant increases in acceptance compared to uniformly sampling the internal, and rotational/translational degrees of freedom in these systems.</div>

UGR CALCULATION BASED ON THE LUMINANCE SPATIAL-ANGULAR DISTRIBUTION

2020 ◽  
Vol 2020 (4) ◽  
pp. 25-32
Author(s):  
Viktor Zheltov ◽  
Viktor Chembaev
Keyword(s):  
Monte Carlo ◽  
Angular Distribution ◽  
Monte Carlo Method ◽  
Visual Task ◽  
New Method ◽  
Lighting System ◽  
Preliminary Assessment ◽  
System A ◽  
The Monte Carlo Method

The article has considered the calculation of the unified glare rating (UGR) based on the luminance spatial-angular distribution (LSAD). The method of local estimations of the Monte Carlo method is proposed as a method for modeling LSAD. On the basis of LSAD, it becomes possible to evaluate the quality of lighting by many criteria, including the generally accepted UGR. UGR allows preliminary assessment of the level of comfort for performing a visual task in a lighting system. A new method of "pixel-by-pixel" calculation of UGR based on LSAD is proposed.

A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR

1989 ◽  
Vol 03 (15) ◽  
pp. 1185-1188 ◽  
Author(s):  
J. SEIMENIS
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Infinite Number ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Hamiltonian Dynamical Systems

We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.

scholarly journals Inverse-square law between time and amplitude for crossing tipping thresholds

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180504 ◽  
Author(s):  
Paul Ritchie ◽  
Özkan Karabacak ◽  
Jan Sieber
Keyword(s):  
Dynamical System ◽  
Feedback Loop ◽  
Tipping Point ◽  
Dimensional System ◽  
Stochastic Forcing ◽  
Inverse Square Law ◽  
System A ◽  
Asymptotic Expressions ◽  
Higher Dimensional ◽  
Random Disturbances

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law between peak of the parameter forcing and the time the parameter spends above a given threshold is also visible in the level curves of equal probability when the system is subject to random disturbances.

scholarly journals Chaotic Itinerancy Observed in Mutually Coupled Gaussian Maps

2018 ◽  
Vol 28 (04) ◽  
pp. 1830011
Author(s):  
Mio Kobayashi ◽  
Tetsuya Yoshinaga
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Chaotic Behavior ◽  
Periodic Points ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Bifurcation Structure ◽  
Unstable Fixed Point ◽  
Gaussian Map ◽  
Gaussian Maps

A one-dimensional Gaussian map defined by a Gaussian function describes a discrete-time dynamical system. Chaotic behavior can be observed in both Gaussian and logistic maps. This study analyzes the bifurcation structure corresponding to the fixed and periodic points of a coupled system comprising two Gaussian maps. The bifurcation structure of a mutually coupled Gaussian map is more complex than that of a mutually coupled logistic map. In a coupled Gaussian map, it was confirmed that after a stable fixed point or stable periodic points became unstable through the bifurcation, the points were able to recover their stability while the system parameters were changing. Moreover, we investigated a parameter region in which symmetric and asymmetric stable fixed points coexisted. Asymmetric unstable fixed point was generated by the [Formula: see text]-type branching of a symmetric stable fixed point. The stability of the unstable fixed point could be recovered through period-doubling and tangent bifurcations. Furthermore, a homoclinic structure related to the occurrence of chaotic behavior and invariant closed curves caused by two-periodic points was observed. The mutually coupled Gaussian map was merely a two-dimensional dynamical system; however, chaotic itinerancy, known to be a characteristic property associated with high-dimensional dynamical systems, was observed. The bifurcation structure of the mutually coupled Gaussian map clearly elucidates the mechanism of chaotic itinerancy generation in the two-dimensional coupled map. We discussed this mechanism by comparing the bifurcation structures of the Gaussian and logistic maps.

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