scholarly journals Complex Dynamical Behaviors of Lorenz-Stenflo Equations

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 513 ◽  
Author(s):  
Fuchen Zhang ◽  
Min Xiao
Keyword(s):  
Gravity Waves ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Acoustic Gravity Waves ◽  
Dynamical Behaviors ◽  
Lyapunov Function Method ◽  
Attractive Sets ◽  
Globally Attractive ◽  
Generalized Lyapunov Function ◽  
Theoretical Results

A mathematical chaos model for the dynamical behaviors of atmospheric acoustic-gravity waves is considered in this paper. Boundedness and globally attractive sets of this chaos model are studied by means of the generalized Lyapunov function method. The innovation of this paper is that it not only proves this system is globally bounded but also provides a series of global attraction sets of this system. The rate of trajectories entering from the exterior of the trapping domain to its interior is also obtained. Finally, the detailed numerical simulations are carried out to justify theoretical results. The results in this study can be used to study chaos control and chaos synchronization of this chaos system.

Dynamical Behaviors of a Modified Lorenz–Stenflo Chaotic System

2017 ◽  
Vol 27 (05) ◽  
pp. 1750074 ◽  
Author(s):  
Fuchen Zhang ◽  
Xingyuan Wang ◽  
Xiaofeng Liao ◽  
Guangyun Zhang ◽  
Chunlai Mu
Keyword(s):  
Chaos Synchronization ◽  
Chaos Control ◽  
Optimization Theory ◽  
Lyapunov Stability Theory ◽  
Theoretical Support ◽  
Dynamical Behaviors ◽  
Special Cases ◽  
Attractive Sets ◽  
Ultimate Bound ◽  
Theoretical Results

In this paper, the ultimate bound and globally exponentially attractive sets of a modified Lorenz–Stenflo system are studied based on the Lyapunov stability theory and optimization theory. Comparing with the best results in the current literature, our new results include the existing results as special cases. Furthermore, the new results offer a theoretical support to studying the Hausdorff dimension of attractor of this modified Lorenz–Stenflo system. These theoretical results are also important and useful for chaos control and chaos synchronization.

GLOBALLY ATTRACTIVE AND POSITIVE INVARIANT SET OF THE LORENZ SYSTEM

2006 ◽  
Vol 16 (03) ◽  
pp. 757-764 ◽  
Author(s):  
PEI YU ◽  
XIAOXIN LIAO
Keyword(s):  
Lyapunov Function ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Lorenz System ◽  
Equilibrium Points ◽  
Invariant Set ◽  
The Lorenz System ◽  
Globally Attractive ◽  
Generalized Lyapunov Function ◽  
Positive Invariant Set

In this paper, based on a generalized Lyapunov function, a simple proof is given to improve the estimation of globally attractive and positive invariant set of the Lorenz system. In particular, a new estimation is derived for the variable x. On the globally attractive set, the Lorenz system satisfies Lipschitz condition, which is very useful in the study of chaos control and chaos synchronization. Applications are presented for globally, exponentially tracking periodic solutions, stabilizing equilibrium points and synchronizing two Lorenz systems.

scholarly journals Analysis of a Generalized Lorenz–Stenflo Equation

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Fuchen Zhang ◽  
Rui Chen ◽  
Xiusu Chen
Keyword(s):  
Gravity Waves ◽  
Finite Amplitude ◽  
Functional Approach ◽  
Engineering Science ◽  
Hyperchaotic System ◽  
Numerical Examples ◽  
Acoustic Gravity Waves ◽  
Attractive Sets ◽  
Globally Attractive ◽  
Hyperchaotic Systems

Although the globally attractive sets of a hyperchaotic system have important applications in the fields of engineering, science, and technology, it is often a difficult task for the researchers to obtain the globally attractive set of the hyperchaotic systems due to the complexity of the hyperchaotic systems. Therefore, we will study the globally attractive set of a generalized hyperchaotic Lorenz–Stenflo system describing the evolution of finite amplitude acoustic gravity waves in a rotating atmosphere in this paper. Based on Lyapunov-like functional approach combining some simple inequalities, we derive the globally attractive set of this system with its parameters. The effectiveness of the proposed methods is illustrated via numerical examples.

scholarly journals Analysis of a Lorenz-Like Chaotic System by Lyapunov Functions

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Fuchen Zhang
Keyword(s):  
Chaotic System ◽  
Chaos Synchronization ◽  
Lorenz System ◽  
Chen System ◽  
Lyapunov Function Method ◽  
Exponential Attractivity ◽  
Positively Invariant Set ◽  
Ultimate Bound ◽  
Special Case ◽  
Theoretical Results

In this paper, we investigate the ultimate bound set and positively invariant set of a 3D Lorenz-like chaotic system, which is different from the well-known Lorenz system, Rössler system, Chen system, Lü system, and even Lorenz system family. Furthermore, we investigate the global exponential attractive set of this system via the Lyapunov function method. The rate of the trajectories going from the exterior of the globally exponential attractive set to the interior of the globally exponential attractive set is also obtained for all the positive parameters values a,b,c. The innovation of this paper is that our approach to construct the ultimate bounded and globally exponential attractivity sets assumes that the corresponding sets depend on some artificial parameters (λ and m); that is, for the fixed parameters of the system, we have a series of sets depending on λ and m. The results contain the known result as a special case for the fixed λ and m. The efficiency of the scheme is shown numerically. The theoretical results may find wide applications in chaos control and chaos synchronization.

On the dynamics of a modified Lorenz–Stenflo system

2020 ◽  
Vol 31 (07) ◽  
pp. 2050104
Author(s):  
Paulo C. Rech
Keyword(s):  
Dynamical System ◽  
Gravity Waves ◽  
Cross Sections ◽  
Continuous Time ◽  
Periodic Structures ◽  
Finite Amplitude ◽  
Variable Formula ◽  
Acoustic Gravity Waves ◽  
Dynamical Behaviors ◽  
New System

The Lorenz–Stenflo system is a four-parameter four-dimensional autonomous nonlinear continuous-time dynamical system, derived to model the time evolution of finite amplitude acoustic gravity waves in a rotating atmosphere. In this paper, we propose a modified Lorenz–Stenflo system, where the variable [Formula: see text] in the fourth equation of the original Lorenz–Stenflo system was replaced by [Formula: see text]. We investigate cross-sections of the parameter-space of this new system, characterizing regions of different dynamical behaviors. We show that the aforementioned replacement may promote the emergence of organized periodic structures in places of these cross-sections, where they did not exist before modification.

Acoustic-Gravity Waves in Whirling Polar Thermosphere

2015 ◽  
Vol 47 (9) ◽  
pp. 10-22 ◽  
Author(s):  
Yuriy P. Ladikov-Roev ◽  
Oleg K. Cheremnykh ◽  
Alla K. Fedorenko ◽  
Vladimir E. Nabivach
Keyword(s):  
Gravity Waves ◽  
Acoustic Gravity Waves

scholarly journals Acoustic–gravity waves from multi-fault rupture

2021 ◽  
Vol 915 ◽  
Author(s):  
Byron Williams ◽  
Usama Kadri ◽  
Ali Abdolali
Keyword(s):  
Gravity Waves ◽  
Fault Rupture ◽  
Acoustic Gravity Waves

Abstract

scholarly journals Extinction and persistence of a stochastic SIRV epidemic model with nonlinear incidence rate

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramziya Rifhat ◽  
Zhidong Teng ◽  
Chunxia Wang
Keyword(s):  
Epidemic Model ◽  
Control Strategies ◽  
Random Perturbations ◽  
Disease Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Analysis Theory ◽  
Lyapunov Function Method ◽  
Random Fluctuations ◽  
Theoretical Results

AbstractIn this paper, a stochastic SIRV epidemic model with general nonlinear incidence and vaccination is investigated. The value of our study lies in two aspects. Mathematically, with the help of Lyapunov function method and stochastic analysis theory, we obtain a stochastic threshold of the model that completely determines the extinction and persistence of the epidemic. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics. In other words, neglecting random perturbations overestimates the ability of the disease to spread. The numerical simulations are given to illustrate the main theoretical results.

Investigation of acoustic gravity waves in the upper atmosphere by the artificial periodic inhomogeneities method at Nizhny Novgorod

1996 ◽  
Vol 39 (3) ◽  
pp. 224-228
Author(s):  
N. V. Bakhmet'eva ◽  
V. V. Belikovich ◽  
E. A. Benediktov ◽  
V. N. Bubukina ◽  
N. P. Goncharov ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Upper Atmosphere ◽  
Acoustic Gravity Waves ◽  
Periodic Inhomogeneities
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