A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2009 ◽  
Vol 19 (06) ◽  
pp. 1931-1949 ◽  
Author(s):  
QIGUI YANG ◽  
KANGMING ZHANG ◽  
GUANRONG CHEN
Keyword(s):  
Special Form ◽  
Topological Structure ◽  
Complex Dynamics ◽  
Type System ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Compound Structure ◽  
Two Parameters ◽  
First Time ◽  
New System

In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.

A UNIFIED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2006 ◽  
Vol 16 (10) ◽  
pp. 2855-2871 ◽  
Author(s):  
QIGUI YANG ◽  
GUANGRONG CHEN ◽  
TIANSHOU ZHOU
Keyword(s):  
Canonical Form ◽  
Special Form ◽  
Lorenz System ◽  
Type System ◽  
Chaotic Attractors ◽  
Lorenz Attractor ◽  
System A ◽  
Generalized Lorenz System ◽  
Two Parameters ◽  
First Time

Based on the generalized Lorenz system, a conjugate Lorenz-type system is introduced, and a new unified Lorenz-type system containing these two classes of systems is naturally constructed in the paper. Such a unified system is state-equivalent to a simple special form, which is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, three new chaotic attractors, called conjugate attractors, are found for the first time, which are conjugate to the Lorenz attractor, the Chen attractor, and the Lü attractor, respectively.

scholarly journals A Novel 2D – Grid of Scroll Chaotic Attractor Generated by CNN

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 99 ◽  
Author(s):  
Ahmed M. Ali ◽  
Saif M. Ramadhan ◽  
Fadhil R. Tahir
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Attractor ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Electronic Circuits ◽  
Nonlinear Networks ◽  
Design And Implementation ◽  
Simulation Results ◽  
New System

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and chaos in symmetry pattern. A novel grid of scroll chaotic attractor, based on a new system, shows symmetry scrolls about the origin. Also, the equilibrium points are located in a manner such that the symmetry about the line x=y has been achieved. The complex dynamics of system can be generated using CNNs, which in turn are derived from a CNN array (1×3) cells. The paper concerns on the design and implementation of 2×2 and 3×3 2D-grid of scroll via the CNN model. Theoretical analysis and numerical simulations of the derived model are included. The simulation results reveal that the grid of scroll attractors can be successfully reproduced using PSpice.

A Novel Simple Hyperchaotic System with Two Coexisting Attractors

2019 ◽  
Vol 29 (14) ◽  
pp. 1950203 ◽  
Author(s):  
Jiaopeng Yang ◽  
Zhengrong Liu
Keyword(s):  
Complex Dynamics ◽  
Chaotic Dynamic ◽  
Cross Product ◽  
Hyperchaotic System ◽  
Compound Structure ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Periodic Attractors ◽  
New Hyperchaotic System ◽  
New System

This article introduces a new hyperchaotic system of four-dimensional autonomous ordinary differential equations, with only cubic cross-product nonlinearities, which can respectively display two hyperchaotic attractors with only nonhyperbolic equilibria line. Several issues such as basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new hyperchaotic and chaotic system are investigated, either theoretically or numerically. Of particular interest is the fact that the two coexisting attractors of the new hyperchaotic system are symmetrical, and this hyperchaotic system can generate plenty of complex dynamics including two coexisting chaotic or periodic attractors. Moreover, some chaotic features of the attractor are justified numerically. Finally, 0-1 test is used to analyze and describe the complex chaotic dynamic behavior of the new system.

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.

CONSTRUCTING MULTIWING HYPERCHAOTIC ATTRACTORS

2010 ◽  
Vol 20 (03) ◽  
pp. 727-734 ◽  
Author(s):  
BO YU ◽  
GUOSI HU
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Topological Structure ◽  
Construction Method ◽  
Chaotic Attractors ◽  
Hyperchaotic System ◽  
Simple Construction ◽  
System A ◽  
New Hyperchaotic System ◽  
New System

Few reports have introduced chaotic attractors with both multiwing topological structure and hyperchaotic dynamics. A simple construction method, for designing chaotic system with multiwing attractors, is presented in this paper. The number of wings in the attractor was doubled on applying this method to an arbitrary smooth chaotic system. Moreover, the hyperchaotic property is preserved in the new system. A new hyperchaotic system with 16-wing attractors is constructed; the result system is not only verified via numerical simulation but also confirmed by a DSP-based experiment.

scholarly journals Further Discussions of the Complex Dynamics of a 2D Logistic Map: Basins of Attraction and Fractal Dimensions

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2001
Author(s):  
Sameh S. Askar ◽  
Abdulrahman Al-Khedhairi
Keyword(s):  
Phase Plane ◽  
Complex Dynamics ◽  
Logistic Map ◽  
Fractal Dimensions ◽  
Basins Of Attraction ◽  
Chaotic Attractors ◽  
Complex Dynamic ◽  
2D Logistic Map ◽  
Two Parameters ◽  
Periodic Cycles

In this paper, we study the complex dynamic characteristics of a simple nonlinear logistic map. The map contains two parameters that have complex influences on the map’s dynamics. Assuming different values for those parameters gives rise to strange attractors with fractal dimensions. Furthermore, some of these chaotic attractors have heteroclinic cycles due to saddle-fixed points. The basins of attraction for some periodic cycles in the phase plane are divided into three regions of rank-1 preimages. We analyze those regions and show that the map is noninvertible and includes Z0,Z2 and Z4 regions.

scholarly journals Symmetries in Hidden Bifurcation Routes to Multiscroll Chaotic Attractors Generated by Saturated Function Series

2019 ◽  
Vol 3 (4) ◽  
pp. 511 ◽  
Author(s):  
Faiza Zaamoune ◽  
Tidjani Menacer ◽  
René Lozi ◽  
Guanrong Chen
Keyword(s):  
Open Access ◽  
Original Work ◽  
Range Extension ◽  
Chaotic Attractors ◽  
Function Series ◽  
Creative Commons ◽  
Basic Cell ◽  
Two Parameters ◽  
First Time ◽  
Open Access Article

In this paper, hidden bifurcation routes to multiscroll chaotic attractors generated by saturated function series are explored. The method to nd such hidden bifurcation routes (HBR) depending upon two parameters is similar to the method introduced by Menacer, et al. (2016) for Chua multiscroll attractors. These HBR are characterized by the maximal range extension (MARE) of their attractors and coding the appearance order of the scrolls under the control of the two parameters. Moreover, these HDR have interesting symmetries with respect to the two parameters. The novelty that this article introduces, is firstly the paradigm of MARE and the formula giving their approximate value depending upon parameters p and q, which is linked to the size of the scrolls; secondly the coding of the HBR which is dened for the first time including the basic cell; and thirdly unearthing the symmetries of these routes, allowing to obtain their coding without any numerical computation.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Iridium-Catalyzed Silylation of C-H bonds in Unactivated Arenes: A Sterically-Encumbered Phenanthroline Ligand Accelerates Catalysis Enabling New Reactivity

2019 ◽  
Author(s):  
Caleb Karmel ◽  
Zhewei Chen ◽  
John Hartwig
Keyword(s):  
High Activity ◽  
Functional Group ◽  
Activity Analysis ◽  
High Reactivity ◽  
High Yield ◽  
Phen Ligand ◽  
Mechanistic Studies ◽  
Phenanthroline Ligand ◽  
First Time ◽  
New System

We report a new system for the silylation of aryl C-H bonds. The combination of [Ir(cod)(OMe)]<sub>2</sub> and 2,9-Me<sub>2</sub>-phenanthroline (2,9-Me<sub>2</sub>phen) catalyzes the silylation of arenes at lower temperatures and with faster rates than those reported previously, when the hydrogen byproduct is removed, and with high functional group tolerance and regioselectivity. Inhibition of reactions by the H<sub>2</sub> byproduct is shown to limit the silylation of aryl C-H bonds in the presence of the most active catalysts, thereby masking their high activity. Analysis of initial rates uncovered the high reactivity of the catalyst containing the sterically hindered 2,9-Me<sub>2</sub>phen ligand but accompanying rapid inhibition by hydrogen. With this catalyst, under a flow of nitrogen to remove hydrogen, electron-rich arenes, including those containing sensitive functional groups, undergo silylation in high yield for the first time, and arenes that underwent silylation with prior catalysts react over much shorter times with lower catalyst loadings. The synthetic value of this methodology is demonstrated by the preparation of key intermediates in the synthesis of medicinally important compounds in concise sequences comprising silylation and functionalization. Mechanistic studies demonstrate that the cleavage of the aryl C-H bond is reversible and that the higher rates observed with the 2,9-Me<sub>2</sub>phen ligand is due to a more thermodynamically favorable oxidative addition of aryl C-H bonds.

scholarly journals Sicily Before the Greeks. The Interaction with Aegean and the Levant in the Pre-colonial Era

2020 ◽  
Vol 6 (1) ◽  
pp. 172-205
Author(s):  
Davide Tanasi
Keyword(s):  
Material Culture ◽  
Complex Dynamics ◽  
Eastern Mediterranean ◽  
Colonial Era ◽  
Local Material ◽  
Gradual Process ◽  
Multiple Variables ◽  
New Perspective ◽  
First Time ◽  
The Relationship

AbstractThe relationship between Sicily and the eastern Mediterranean – namely Aegean, Cyprus and the Levant – represents one of the most intriguing facets of the prehistory of the island. The frequent and periodical contact with foreign cultures were a trigger for a gradual process of socio-political evolution of the indigenous community. Such relationship, already in inception during the Neolithic and the Copper Age, grew into a cultural phenomenon ruled by complex dynamics and multiple variables that ranged from the Mid-3rd to the end of the 2nd millennium BCE. In over 1,500 years, a very large quantity of Aegean and Levantine type materials have been identified in Sicily alongside with example of unusual local material culture traditionally interpreted as resulting from external influence. To summarize all the evidence during such long period and critically address it in order to attempt historical reconstructions is a Herculean labor.Twenty years after Sebastiano Tusa embraced this challenge for the first time, this paper takes stock on two decades of new discoveries and research reassessing a vast amount of literature, mostly published in Italian and in regional journals, while also address the outcomes of new archaeometric studies. The in-depth survey offers a new perspective of general trends in this East-West relationship which conditioned the subsequent events of the Greek and Phoenician colonization of Sicily.

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