Synchronization of chaos and hyperchaos using linear and nonlinear feedback functions

Ali, M. K.; Jin-Qing, Fang

doi:10.1103/physreve.55.5285

Cited by 52 publications

(26 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To prove the stability of the output feedback case, the following stability concept and lemma are employed. In view of the results of the previous section, the observer-based synchronization between two subsystems boils down to designing an observer-based stabilizing output feedback control for the error dynamics defined in (2). In case the full state is measurable, it is shown that the state feedback law 12 u is a globally asymptotically stabilizing control for the error dynamics.…”

Section: Observer-based Synchronizationmentioning

confidence: 99%

“…There can be other possibilities to distribute 12 u to 1 u and 2 u . Other distribution methods are also possible as long as the resultant coupling functions …”

Section: Remarkmentioning

confidence: 99%

“…Firstly, the resulting feedback laws for synchronization are in the form of linear feedback or linear feedback with variable gain ( [2], [4], [14], [17], [23], [25], [41], [43]). Secondly, feedback interaction is unidirectional ( [39], [40]) in the sense that a reference model without input is employed for synchronization.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Nonlinear Synchronization Scheme for Hindmarsh-Rose Models

Kim¹,

Allgöwer²

2010

Journal of Electrical Engineering and Technology

View full text Add to dashboard Cite

-Multiple subsystems are required to behave synchronously or cooperatively in many areas. For example, synchronous behaviors are common in networks of (electro-) mechanical systems, cell biology, coupled neurons, and cooperating robots. This paper presents a feedback scheme for synchronization between Hindmarsh-Rose models which have polynomial vector fields. We show that the problem is equivalent to finding an asymptotically stabilizing control for error dynamics which is also a polynomial system. Then, an extension to a nonlinear observer-based scheme is presented, which reduces the amount of information exchange between models.

show abstract

Section: Observer-based Synchronizationmentioning

confidence: 99%

“…There can be other possibilities to distribute 12 u to 1 u and 2 u . Other distribution methods are also possible as long as the resultant coupling functions …”

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

A Nonlinear Synchronization Scheme for Hindmarsh-Rose Models

Kim¹,

Allgöwer²

2010

Journal of Electrical Engineering and Technology

View full text Add to dashboard Cite

show abstract

“…The starting state vectors X0=[X0(1),X0 (2) [3] for synchronizing chaotic and hyperchaotic systems. We now derive our main result.…”

mentioning

confidence: 99%

New feedback functions for synchronizing chaotic maps

Ali

1998

Discrete Dynamics in Nature and Society

Self Cite

View full text Add to dashboard Cite

Synchronization of chaotic maps is studied using the method of variable feedback. A general method is presented for generating feedback functions for maps. These feedback functions are found very efficient. Our study shows that when the driver and the response systems are fed by common noise, the noise does not affect synchronization. With different but weak noise added to the driver and response systems, approximate synchronization persists. [7] observed that two initially different trajectories of a chaotic attractor fed by common noise coalesce when calculations are carried out with finite precision. Lech et al.[8] and Pikovsky [9] have shown that if the calculations are done with higher precision the coalescence time -(for maps -=no. of iterations) increases exponentially and the procedure soon becomes practically impossible to implement. Clearly, the application of common noise for synchronization of chaotic attractors has inherent difficulties. In this work we will see that synchronization of chaotic attractors in the presence of common noise poses no additional difficulty [2].

show abstract

“…Especially, the problem of synchronization of coupled chaotic oscillators has been intensively studied mainly in view of potential application to secure communication [16], [17]- [21]. The idea of synchronization has also been implemented to higher dimensional systems exhibiting hyperchaotic behavior [22]- [24]. This seems to be very impressive as multidimensional systems improve the degree of security in communication.…”

mentioning

confidence: 99%

Two-time synchronism and induced synchronization in a Kerr coupler

Szlachetka

Misiak

Grygiel

2003

The European Physical Journal D - Atomic, Molecular and Optical

View full text Add to dashboard Cite

A pair (A, B) of interacting oscillators treated as a master system sending signals to its slave copy (a, b) through two communication channels A ⇒ a and B ⇒ b is considered. The effect of non-simultaneous (two-time) synchronization of the pairs (a, A) and (b, B) is demonstrated with the help of coupled Kerr oscillators producing hyperchaos. An individual pair, for example, (b, B) can also be synchronized when its communication channel B ⇒ b is turned off, provided that the second channel for the pair(a, A) is turned on. The resulted synchronization is termed induced. The efficiencies of the presented synchronization precesses are studied.. . This seems to be very impressive as multidimensional systems improve the degree of security in communication. Quite recently, a scheme of dual chaos synchronization has been proposed [25]. In the dual synchronization, signals from two noninteracting master oscillators through a single communication channel are sent to a system containing two corresponding slave oscillators. In this short paper we discuss the possibility of applying a chaos controlling method to achieve synchronization of two different pairs of oscillators. The general set up to be considered is presented in Fig. 1 The master system consists of two coupled oscillators (A, B) which interact with each other ( the symbol α denotes a parameter of interaction between A and B). If α = 0 the master system consists of two independent oscillators. The slave system (a, b) is a copy of the master system. The signals from the two master subsystems (A, B) are transmitted to the their counterparts (a, b) in the slave system by linear feedback functions. The control parameters are * Electronic address: przems@main.amu.edu.pl † Electronic address: grygielk@main.amu.edu.pl ‡ Electronic address: misiak@zon10.physd.amu.edu.pl The synchronization state is achieved if Xa(t) = XA(t) and X b (t ′ ) = XB(t ′ ). The question is whether and when t = t ′ .denoted by S 1 and S 2 , respectively. The slave and masters systems are assumed to start from different initial conditions. As a master system (A, B) let us consider two coupled Kerr oscillators governed by the following equations [26]:

show abstract

Synchronization of chaos and hyperchaos using linear and nonlinear feedback functions

Cited by 52 publications

References 21 publications

A Nonlinear Synchronization Scheme for Hindmarsh-Rose Models

A Nonlinear Synchronization Scheme for Hindmarsh-Rose Models

New feedback functions for synchronizing chaotic maps

Two-time synchronism and induced synchronization in a Kerr coupler

Contact Info

Product

Resources

About