scholarly journals A new chaotic attractor from 2D discrete mapping via border-collision period-doubling scenario

2005 ◽  
Vol 2005 (3) ◽  
pp. 235-238 ◽  
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Chaotic Attractor ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
The Other ◽  
Chaotic Attractors ◽  
Classical Period ◽  
New Chaotic Attractor

The following map is studied:(x,y)→(1+a(|x|−y2)+y,bx). It is proved numerically that this model can display two different chaotic attractors, one is new and the other is a Lozi-type attractor. The new chaotic attractor is allowed via a border-collision period-doubling scenario, which is different from the classical period-doubling bifurcation.

DYNAMICS AND MODULATED CHAOS FOR TWO COUPLED OSCILLATORS

2004 ◽  
Vol 14 (01) ◽  
pp. 337-346 ◽  
Author(s):  
QINSHENG BI
Keyword(s):  
Coupled Oscillators ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
The Other ◽  
Van Der Pol ◽  
Parametrically Excited ◽  
Van Der Pol Oscillators ◽  
Period Doubling Bifurcations

The dynamical behavior of two coupled parametrically excited van der Pol oscillators is investigated in this paper. A special road to chaos is explored in detail. Period-doubling bifurcation associated with one of the frequencies of the system may be observed, the other frequency of the coupled oscillators plays a role in the evolution. It is found that one of the frequencies of the system contributes to the cascade of period-doubling bifurcations associated with the other frequency, which leads to a generalized modulated chaos.

scholarly journals Sequence of Routes to Chaos in a Lorenz-Type System

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Fangyan Yang ◽  
Yongming Cao ◽  
Lijuan Chen ◽  
Qingdu Li
Keyword(s):  
Limit Cycles ◽  
Chaotic Attractor ◽  
Type System ◽  
Period Doubling ◽  
Pitchfork Bifurcation ◽  
Basins Of Attraction ◽  
Chaotic Attractors ◽  
Main Route ◽  
Route To Chaos ◽  
Period Doubling Bifurcations

This paper reports a new bifurcation pattern observed in a Lorenz-type system. The pattern is composed of a main bifurcation route to chaos (n=1) and a sequence of sub-bifurcation routes with n=3,4,5,…,14 isolated sub-branches to chaos. When n is odd, the n isolated sub-branches are from a period-n limit cycle, followed by twin period-n limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis. When n is even, the n isolated sub-branches are from twin period-n/2 limit cycles, which become twin chaotic attractors via period-doubling bifurcations. The paper also shows that the main route and the sub-routes can coexist peacefully by studying basins of attraction.

A NEW CHAOTIC ATTRACTOR COINED

2002 ◽  
Vol 12 (03) ◽  
pp. 659-661 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic Attractor ◽  
Autonomous System ◽  
Three Dimensional ◽  
The Other ◽  
Lorenz Attractor ◽  
New Chaotic Attractor

This letter reports the finding of a new chaotic attractor in a simple three-dimensional autonomous system, which connects the Lorenz attractor and Chen's attractor and represents the transition from one to the other.

scholarly journals A new 2-D multi-stable chaotic attractor and its MultiSim electronic circuit design

2021 ◽  
Vol 22 (2) ◽  
pp. 699
Author(s):  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Mohamad Afendee Mohamed ◽  
Mustafa Mamat ◽  
W. S. Mada Sanjaya ◽  
...  
Keyword(s):  
Circuit Design ◽  
Chaotic Attractor ◽  
Electronic Circuit ◽  
Stable System ◽  
Chaotic Attractors ◽  
Sliding Control ◽  
Practical Engineering ◽  
New Chaotic Attractor ◽  
Electronic Circuit Design

<span>A new multi-stable system with a double-scroll chaotic attractor is developed in this paper. Signal plots are simulated using MATLAB and multi-stability is established by showing two different coexisting double-scroll chaotic attractors for different states and same set of parameters. Using integral sliding control, synchronized chaotic attractors are achieved between drive-response chaotic attractors. A MultiSim circuit is designed for the new chaotic attractor, which is useful for practical engineering realizations.</span>

A novel 4D chaotic system with multistability: Dynamical analysis, circuit implementation, control design

2019 ◽  
Vol 33 (21) ◽  
pp. 1950240 ◽  
Author(s):  
Jian-Jun He ◽  
Bang-Cheng Lai
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Electronic Circuit ◽  
Period Doubling ◽  
Control Design ◽  
Critical Value ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
The Novel

The purpose of this work is to introduce a novel 4D chaotic system and investigate its multistability. The novel system has an unstable origin and two stable symmetrical hyperbolic equilibria. When the parameter increases across a critical value, the equilibria lose their stability and double Hopf bifurcations occur with the appearance of limit cycles. A pair of point, periodic, chaotic attractors are observed in the system from different initial values for given parameters. The chaos of the system is yielded via period-doubling bifurcation. A double-scroll chaotic attractor is numerically observed as well. By using the electronic circuit, the chaotic attractor of the system is realized. The control problem of the system is reported. An effective controller is designed to stabilize the system.

CHAOTIC FEATURE OF MARTIN PROCESS IMPOSED ON THE COSINE FUNCTION

Fractals ◽  
2009 ◽  
Vol 17 (02) ◽  
pp. 191-195
Author(s):  
CHUANHOU GAO ◽  
ZHIMIN ZHOU ◽  
JIUSUN ZENG ◽  
JIMING CHEN
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Bifurcation Diagram ◽  
Chaotic Attractor ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Cosine Function ◽  
Maximum Lyapunov Exponent ◽  
System Parameters ◽  
Stable Focus

By analyzing the phase diagram of Martin process on the cosine function, it is shown that with the change of system parameters the system will eventually converge to a chaotic attractor. The process is repeated and stable focus, period doubling bifurcation occurs during this process. Further computation gives the maximum Lyapunov exponent of the system and meanwhile, the bifurcation diagram is drawn. Thus it is proved from theory that the system exhibits strong chaotic properties.

scholarly journals The Effect of Convection in Nonlinear One-Zone Stellar Models

1993 ◽  
Vol 134 ◽  
pp. 355-358
Author(s):  
M. Saitou
Keyword(s):  
Limit Cycle ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Variable Stars ◽  
Period Doubling Bifurcation ◽  
The Other ◽  
Other Hand ◽  
Pulsating Variable Stars ◽  
Stellar Models

AbstractWe study the convective nonlinear one-zone models of the pulsating variable stars. In the small convective case, the solution shows chaotic behavior through the period doubling bifurcation as the temperature is lower although the temperature at which the chaos appears is lower than in the case of no convection. On the other hand, in the strong convective case, the solution only shows period-one limit cycle.

scholarly journals The Orderliness of Music from the Perspective of Complex Information Systems

Proceedings ◽  
2020 ◽  
Vol 47 (1) ◽  
pp. 55
Author(s):  
Shan Zhang
Keyword(s):  
Information Systems ◽  
20Th Century ◽  
Natural Science ◽  
The Other ◽  
Western Music ◽  
Classical Period ◽  
20Th Century Music ◽  
Complex Information ◽  
History Of ◽  
The One

By applying the concept of natural science to the study of music, on the one hand, we can understand the structure of music macroscopically, on the other, we can reflect on the history of music to a certain extent. Throughout the history of western music, from the classical period to the 20th century, music seems to have gone from order to disorder, but it is still orderly if analyzed carefully. Using the concept of complex information systems can give a good answer in the essence.

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