The dynamic and thermodynamic origin of dissipative chaos: chemical Lorenz system

2020 ◽  
Vol 22 (47) ◽  
pp. 27896-27902
Author(s):  
Feng Zhang ◽  
Liufang Xu ◽  
Jin Wang
Keyword(s):  
Chaotic Dynamics ◽  
Lorenz System ◽  
Flux Flow ◽  
System P ◽  
Potential Landscape ◽  
Probability Flux

Dissipative chaotic dynamics and its onset/offset are determined by the intrinsic potential landscape and nonequilibrium probability flux flow.

Chaos in the Periodically Parametrically Excited Lorenz System

2021 ◽  
Vol 31 (08) ◽  
pp. 2130024
Author(s):  
Weisheng Huang ◽  
Xiao-Song Yang
Keyword(s):  
Chaotic Dynamics ◽  
Lorenz System ◽  
Stable Equilibrium ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Parametrically Excited ◽  
The Lorenz System

We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different attractor basins due to the periodic variations of the attractor basins of the time-varying stable equilibrium points when a parameter of the Lorenz system is varying periodically.

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.

scholarly journals Dynamical characteristics of magnetospheric energetic ion time series: evidence for low dimensional chaos

2003 ◽  
Vol 21 (9) ◽  
pp. 1995-2010 ◽  
Author(s):  
M. A. Athanasiu ◽  
G. P. Pavlos ◽  
D. V. Sarafopoulos ◽  
E. T. Sarris
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Prediction Models ◽  
Surrogate Data ◽  
Nonlinear Phenomena ◽  
Energetic Ions ◽  
Dynamical Characteristics ◽  
Noise Perturbation ◽  
Low Dimensional

Abstract. This paper is a companion to the first work (Pavlos et al., 2003), which contains significant results concerning the dynamical characteristics of the magnetospheric energetic ions’ time series. The low dimensional and nonlinear deterministic characteristics of the same time series were described in Pavlos et al. (2003). In this second work we present significant results concerning the Lyapunov spectrum, the mutual information and prediction models. The dynamical characteristics of the magnetospheric ions’ signals are compared with corresponding characteristics obtained for the stochastic Lorenz system when a coloured noise perturbation is present. In addition, the null hypothesis is tested for the dynamical characteristics of the magnetospheric ions’ signal by using nonlinear surrogate data. The results of the above comparisons provide significant evidence for the existence of low dimensional chaotic dynamics underlying the energetic ions’ time series.Key words. Magnetospheric physics (energetic particles) – Radio sciences (nonlinear phenomena)

Message Embedded Chaotic Masking Synchronization Scheme Based on the Generalized Lorenz System and Its Security Analysis

2016 ◽  
Vol 26 (08) ◽  
pp. 1650140 ◽  
Author(s):  
Sergej Čelikovský ◽  
Volodymyr Lynnyk
Keyword(s):  
Numerical Experiments ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Bounded Function ◽  
Security Analysis ◽  
Encryption Scheme ◽  
The Novel ◽  
Generalized Lorenz System ◽  
Synchronization Signal ◽  
Synchronization Scheme

This paper focuses on the design of the novel chaotic masking scheme via message embedded synchronization. A general class of the systems allowing the message embedded synchronization is presented here, moreover, it is shown that the generalized Lorenz system belongs to this class. Furthermore, the secure encryption scheme based on the message embedded synchronization is proposed. This scheme injects the embedded message into the dynamics of the transmitter as well, ensuring thereby synchronization with theoretically zero synchronization error. To ensure the security, the embedded message is a sum of the message and arbitrary bounded function of the internal transmitter states that is independent of the scalar synchronization signal. The hexadecimal alphabet will be used to form a ciphertext making chaotic dynamics of the transmitter even more complicated in comparison with the transmitter influenced just by the binary step-like function. All mentioned results and their security are tested and demonstrated by numerical experiments.

scholarly journals Dynamics of the Modified n-Degree Lorenz System

2019 ◽  
Vol 4 (2) ◽  
pp. 315-330 ◽  
Author(s):  
Sk. Sarif Hassan ◽  
Moole Parameswar Reddy ◽  
Ranjeet Kumar Rout
Keyword(s):  
Dynamical Systems ◽  
Fixed Points ◽  
Lyapunov Exponents ◽  
Limit Cycle ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Lorenz Model ◽  
Periodic Behavior ◽  
Chaotic Model

AbstractThe Lorenz model is one of the most studied dynamical systems. Chaotic dynamics of several modified models of the classical Lorenz system are studied. In this article, a new chaotic model is introduced and studied computationally. By finding the fixed points, the eigenvalues of the Jacobian, and the Lyapunov exponents. Transition from convergence behavior to the periodic behavior (limit cycle) are observed by varying the degree of the system. Also transiting from periodic behavior to the chaotic behavior are seen by changing the degree of the system.

CONTROLLING CHAOTIC DYNAMICS USING BACKSTEPPING DESIGN WITH APPLICATION TO THE LORENZ SYSTEM AND CHUA'S CIRCUIT

1999 ◽  
Vol 09 (07) ◽  
pp. 1425-1434 ◽  
Author(s):  
SAVERIO MASCOLO ◽  
GIUSEPPE GRASSI
Keyword(s):  
Steady State ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Backstepping Design ◽  
Chua’S Circuit ◽  
General Applicability ◽  
Recursive Procedure ◽  
Chua's Circuit ◽  
The Lorenz System

In this Letter backstepping design is proposed for controlling chaotic systems. The tool consists in a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. The advantages of the method are the following: (i) it represents a systematic procedure for controlling chaotic or hyperchaotic dynamics; (ii) it can be applied to several circuits and systems reported in literature; (iii) stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory can be achieved. In order to illustrate the general applicability of backstepping design, the tool is utilized for controlling the chaotic dynamics of the Lorenz system and Chua's circuit. Finally, numerical simulations are carried out to show the effectiveness of the technique.

Chaotic Dynamics of the Fractional Lorenz System

2003 ◽  
Vol 91 (3) ◽  
Author(s):  
Ilia Grigorenko ◽  
Elena Grigorenko
Keyword(s):  
Chaotic Dynamics ◽  
Lorenz System

QUANTIFYING SMOOTH AND NONSMOOTH REGULAR AND CHAOTIC DYNAMICS

2005 ◽  
Vol 15 (06) ◽  
pp. 2041-2055 ◽  
Author(s):  
J. AWREJCEWICZ ◽  
L. DZYUBAK
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Numerical Method ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Duffing Oscillator ◽  
Stick Slip ◽  
Excited System ◽  
Two Degree Of Freedom

This paper addresses two main paths of investigations. First, a new numerical method to trace regular and chaotic domains of any nonlinear system governed by ordinary differential equations is proposed. Second, the introduced approach is first testified using the well-known chaotic behavior of a Duffing oscillator and Lorenz system, and is then applied to analysis of discontinuous two-degree-of-freedom self-excited system with friction. Stick-slip and slip-slip chaos is reported, among others.

scholarly journals Realization of a Novel Chaotic System Using Coupling Dual Chaotic System

2021 ◽  
Author(s):  
Salam K. Mousa ◽  
Raied K. Jamal
Keyword(s):  
Time Series ◽  
Chaotic System ◽  
Optical Communications ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Fourier Transforms ◽  
Optical Coupling ◽  
Before And After ◽  
The Lorenz System

Abstract This paper establishes coupling between two various chaotic systems for Lorenz and Rössler circuits. The x-dynamics of Lorenz circuit was coupled numerically with the x dynamics of Rössler circuit. As a result of the optical coupling between these two chaotic systems, it has been observed an exceptional variation in the time series and attractors, which exhibits a novel behavior, leading to a promises method for controlling the chaotic systems. However, performing fast Fourier transforms (FFT) of chaotic dynamics before and after coupling showed an increase in the bandwidth of the Rössler system after its coupling with the Lorenz system, which, in turn increases the possibility of using this system for secure and confidential optical communications.

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