Chaos Entanglement: Leading Unstable Linear Systems to Chaos

2014 ◽  
Vol 24 (04) ◽  
pp. 1450047
Author(s):  
Hongtao Zhang ◽  
Xinzhi Liu ◽  
Xianguo Li
Keyword(s):  
Linear Systems ◽  
Equilibrium Points ◽  
Saddle Points ◽  
Dynamical Analysis ◽  
New Approach ◽  
Powerful Approach ◽  
Linear Subsystem ◽  
Special Approach ◽  
Multiple Linear Systems ◽  
Stable Linear

Chaos entanglement is a new approach to connect linear systems to chaos. The basic principle is to entangle two or multiple linear systems by nonlinear coupling functions to form an artificial chaotic system/network such that each of them evolves in a chaotic manner. However, it is only applicable for stable linear systems, not for unstable ones because of the divergence property. In this study, a bound function is introduced to bound the unstable linear systems and then chaos entanglement is realized in this scenario. Firstly, a new 6-scroll attractor, entangling three identical unstable linear systems by sine function, is presented as an example. The dynamical analysis shows that all entangled subsystems are bounded and their equilibrium points are unstable saddle points when chaos entanglement is achieved. Also, numerical computation exhibits that this new attractor possesses one positive Lyapunov exponent, which implies chaos. Furthermore, a 4 × 4 × 4-grid attractor is generalized by introducing a more complex bound function. Hybrid entanglement is obtained when entangling a two-dimensional stable linear subsystem and a one-dimensional unstable linear subsystem. Specifically, it is verified that it is possible to produce chaos by entangling unstable linear subsystems through linear coupling functions — a special approach referred to as linear entanglement. A pair of 2-scroll chaotic attractors are established by linear entanglement. Our results indicate that chaos entanglement is a powerful approach to generate chaotic dynamics and could be utilized as a guideline to effectively create desired chaotic systems for engineering applications.

scholarly journals CHAOS ENTANGLEMENT: A NEW APPROACH TO GENERATE CHAOS

2013 ◽  
Vol 23 (05) ◽  
pp. 1330014 ◽  
Author(s):  
HONGTAO ZHANG ◽  
XINZHI LIU ◽  
XUEMIN SHEN ◽  
JUN LIU
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Complex Dynamics ◽  
Saddle Points ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
New Approach ◽  
One Dimensional ◽  
Linear Subsystem ◽  
Stable Linear

A new approach to generate chaotic phenomenon, called chaos entanglement, is proposed in this paper. The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner. Firstly, a new attractor, entangling a two-dimensional linear subsystem and a one-dimensional one by sine function, is presented as an example. Dynamical analysis shows that both entangled subsystems are bounded and all equilibra are unstable saddle points when chaos entanglement is achieved. Also, numerical computation shows that this system has one positive Lyapunov exponent, which implies chaos. Furthermore, two conditions are given to achieve chaos entanglement. Along this way, by different linear subsystems and different entanglement functions, a variety of novel chaotic attractors have been created and abundant complex dynamics are exhibited. Our discovery indicates that it is not difficult any more to construct new artificial chaotic systems/networks for engineering applications such as chaos-based secure communication. Finally, a possible circuit is given to realize these new chaotic attractors.

Coprime Factorizations in Stable Linear Systems

1988 ◽  
Author(s):  
Charles A. Desoer ◽  
A. Nazli Gundes ◽  
M. Guntekin Kabuli
Keyword(s):  
Linear Systems ◽  
Coprime Factorizations ◽  
Stable Linear

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

scholarly journals A new approach to constrained state estimation for discrete-time linear systems with unknown inputs

2017 ◽  
Vol 28 (1) ◽  
pp. 326-341 ◽  
Author(s):  
Jose Fernando Garcia Tirado ◽  
Alejandro Marquez-Ruiz ◽  
Hector Botero Castro ◽  
Fabiola Angulo
Keyword(s):  
State Estimation ◽  
Linear Systems ◽  
Discrete Time ◽  
New Approach ◽  
Unknown Inputs ◽  
Time Linear

scholarly journals A New Approach to Assess the Quality of Small High-Speed Centrifugal Fans Using Noise Measurement

1999 ◽  
Vol 5 (2) ◽  
pp. 147-153 ◽  
Author(s):  
Dingjun Cui ◽  
Ian A. Craighead
Keyword(s):  
Signal Processing ◽  
Quality Assessment ◽  
Condition Monitoring ◽  
High Speed ◽  
Noise Levels ◽  
New Approach ◽  
Commercial Market ◽  
Centrifugal Fans ◽  
Special Approach

The requirements for a special approach for the quality assessment of small high-speed centrifugal fans are outlined and a new parameter designating the noise levels from the product in comprehensive form will be discussed and described as a criterion for such quality assessment.By applying techniques of signal processing and condition monitoring, the sources of the vibration and noise in different sections of the product can be identified, then the noise from each source from different components can be determined. Using this criterion, more aspects of the quality of the products can be assessed and suggestions to improve the quality of the products can be made. Finally, the assessment of a number ofvacuum cleaner motor/fan units available in the commercial market will be presented and compared with conventional specifications. It will be shown that the new parameter provides a more useful indication of appliance quality.

scholarly journals Memory Dynamics in Attractor Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Guoqi Li ◽  
Kiruthika Ramanathan ◽  
Ning Ning ◽  
Luping Shi ◽  
Changyun Wen
Keyword(s):  
Energy Function ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Saddle Points ◽  
Memory Systems ◽  
Initial Stimulus ◽  
Attractor Network ◽  
Local Maxima ◽  
Attractor Networks ◽  
New Energy

As can be represented by neurons and their synaptic connections, attractor networks are widely believed to underlie biological memory systems and have been used extensively in recent years to model the storage and retrieval process of memory. In this paper, we propose a new energy function, which is nonnegative and attains zero values only at the desired memory patterns. An attractor network is designed based on the proposed energy function. It is shown that the desired memory patterns are stored as the stable equilibrium points of the attractor network. To retrieve a memory pattern, an initial stimulus input is presented to the network, and its states converge to one of stable equilibrium points. Consequently, the existence of the spurious points, that is, local maxima, saddle points, or other local minima which are undesired memory patterns, can be avoided. The simulation results show the effectiveness of the proposed method.

Quantized control of stochastic stable linear systems

1999 ◽  
Vol 32 (2) ◽  
pp. 4971-4976
Author(s):  
K.-S. Lee ◽  
A.H. Haddad
Keyword(s):  
Linear Systems ◽  
Quantized Control ◽  
Stable Linear
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