Top PDF Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems

Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems

Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems

Abstract. In this paper, we present new schemes to synchronize different dimensional chaotic and hyperchaotic systems. Based on coexistence of generalized synchronization (GS) and inverse generalized synchronization (IGS), a new type of hybrid chaos synchronization is constructed. Using Lyapunov stability theory and stability theory of linear continuous-time systems, some sufficient conditions are derived to prove the coexistence of generalized synchronization and inverse generalized synchronization between 3D master chaotic system and 4D slave hyperchaotic system. Finally, two numerical examples are illustrated with the aim to show the effectiveness of the approaches developed herein.
Show more

16 Read more

Function based hybrid synchronization types and their coexistence in non identical fractional order chaotic systems

Function based hybrid synchronization types and their coexistence in non identical fractional order chaotic systems

In recent years, fractional calculus has been noticed for having superior characteris- tics over conventional calculus in the modeling dynamics of natural phenomena [7–13]. The recent development in fractional calculus has been focused on dynamical systems in fractional sense, for example the nonlinear fractional-order systems with disturbances [14]. These systems are characterized by the fact that the order of the derivative is a non- integer number. In particular, it has been shown that may also have complex dynamics such as chaos and bifurcation [15–17]. Some efforts have been recently made devoted to the synchronization of fractional-order chaotic system [18, 19]. It is worth noting that, dif- ferently from integer-order systems, most of the approaches for fractional-order systems are related to the synchronization of identical systems rather than non-identical systems [20]. On the other hand, referring to function-based hybrid synchronization schemes, only few schemes have been proposed to date; see [21–23]. Similar considerations hold for the coexistence of different synchronization types in fractional-order systems, given that very few attempts have been made. For example, in [24] the coexistence of some synchroniza- tion types has been illustrated, including the inverse generalized synchronization and the Q-S synchronization. However, no function-based hybrid synchronization schemes have been analyzed in [25].
Show more

12 Read more

Modified generalized projective synchronization of fractional order chaotic Lü systems

Modified generalized projective synchronization of fractional order chaotic Lü systems

More recently, many investigations were devoted to the chaotic behavior, chaotic con- trol, and synchronization of fractional-order dynamical systems. For example, it has been shown that Chua’s circuit with an order as low as . can produce a chaotic attractor []. In [], it was shown that nonautonomous Duffing systems with an order less than . can still behave in a chaotic manner. In [], chaotic behavior of the fractional-order ‘jerk’ model, in which chaotic attractors can be obtained with a system of the order as low as ., was stud- ied. Bifurcations and chaos in the fractional-order simplified Lorenz system [], chaotic behavior and its control in the fractional-order Chen system [] were reported. In [], chaotic and hyperchaotic behaviors in fractional-order Rössler equations were studied. Chaotic dynamics and synchronization of fractional-order Arneodo systems [], the Lü system [], and a unified system [], synchronization of fractional-order hyperchaotic modified systems [] were also reported.
Show more

13 Read more

Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional order chaotic systems

Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional order chaotic systems

In this paper, we have presented a new approach to rigorously study the coexistence of some synchronization types between fractional-order chaotic systems characterized by different dimensions and different orders. The paper has shown that identical synchro- nization (IS), antiphase synchronization (AS), and inverse full state hybrid projective syn- chronization (IFSHPS) coexist when synchronizing a three-dimensional master system with a fourth-dimensional slave system. It has been shown that the approach presents the remarkable feature of being both rigorous and applicable to a wide class of commensu- rate and incommensurate systems of different dimensions and orders. All the numerical examples reported through the paper have clearly highlighted the capability of the pro- posed approach in successfully achieving the co-existence of IS, AS, and IFSHPS between chaotic and hyperchaotic systems of different dimensions for both commensurate and in- commensurate fractional-order systems. These examples of coexistence have included the chaotic commensurate three-dimensional Rössler system of order 2.7, the hyperchaotic commensurate four-dimensional Chen system of order 3.84, the chaotic incommensurate three-dimensional Lü system of order 2.955, and the hyperchaotic incommensurate four- dimensional Lorenz system of order 3.86. Finally, we would stress that the topic related to the coexistence of synchronization types in fractional-order systems is almost unex- plored in the literature. We feel that the additional features introduced by the conceived approach, related to both the number of coexisting synchronization types and the capa- bility to synchronize chaotic dynamics with hyperchaotic ones, provides a deeper insight into the synchronization phenomena between systems described by fractional differential equations.
Show more

16 Read more

Synchronization between two non identical fractional order hyperchaotic systems

Synchronization between two non identical fractional order hyperchaotic systems

Recently, the study of dynamics of fractional-order chaotic systems has received interest of many researchers. Yu and Li in [20] used Laplace transformation theory and variational itera- tion method to study R¨ossler system, Wu, Lu and Shen discussed the synchronization of a new fractional- order hyperchaotic system via active control [21], Wang, Yu and Diao in [22] stud- ied the hybrid projective synchronization between fractional-order chaotic systems of different dimensions, Sahab and Ziabari [23] analyzed the chaos between two different hyperchaotic systems by generalized backstepping method, S.T. Mohammad and H. Mohammad in [24] pro- posed a controller based on active sliding mode theory to synchronize the chaotic fractional order systems, Zhang and Lu introduced a new type of hybrid synchronization called full state hybrid lag projective synchronization and applied it to the R¨ossler system and the hyperchaotic Lorenz system to verify their results numerically [25]. A. Ouannas in [26] studied the Q-S syn- chronization of chaotic dynamical systems in continuous-time, Boutefnouchet, Taghvafard and Erjaee in their paper [27] discussed the phase synchronization in coupled chaotic systems.
Show more

13 Read more

Generalized combination complex synchronization of new hyperchaotic complex Lü like systems

Generalized combination complex synchronization of new hyperchaotic complex Lü like systems

On the other hand, with the development of complex systems, synchronization of chaotic complex systems has gained a great deal of attentions. Some synchronization schemes of chaotic real systems were extended to the complex space, such as complete synchronization [], anti-synchronization [, ], projective synchronization [], etc. Recently, many authors have studied some new kinds of synchronization for complex dy- namical systems, for example, complex complete synchronization [], complex projective synchronization [], complex modified projective synchronization [, ], and so forth.
Show more

17 Read more

Hybrid Adaptive Synchronization of Hyperchaotic Systems with Fully Unknown Parameters

Hybrid Adaptive Synchronization of Hyperchaotic Systems with Fully Unknown Parameters

Chaos is an omnipresent phenomenon. Scientists who understand its existence have been struggling to control chaos to our benefit. There is a great need to control the chaotic systems as chaos theory plays an important role in industrial applications particularly in chemical reac- tions, biological systems, information processing and secure communications [1-3]. Many scientists who are interested in this field have struggled to achieve the syn- chronization or anti-synchronization of different hyper- chaotic systems. Therefore due to its complexity and applications, a wide variety of approaches have been proposed for the synchronization or anti-synchronization of hyperchaotic systems. The types of synchronization used so far include generalized active control [4-8], non- linear control [9,10], and adaptive control [11-19].
Show more

8 Read more

On the impulsive synchronization control for a class of chaotic systems

On the impulsive synchronization control for a class of chaotic systems

Recently impulsive control theory and its application in chaos synchronization have become a research hotspot. For instance, based on impulsive control strategies, the reduced- order observer for the synchronization of generalized Lorenz chaotic systems is built in [16], the adaptive modified function projective synchronization of multiple time-delayed chaotic Rossler systems is discussed in [17], the hybrid synchronization of L¨u hyperchaotic system with disturbances is investigated in [18], and the robust synchronization of perturbed Chen’s fractional-order chaotic systems is studied in [19]. However, these results are just about one kind of chaotic systems, which limits their applied scope. Hence how to design the impulsive strategy to realize the synchronization suitable for more chaotic systems activates our research.
Show more

6 Read more

Generalized Synchronization of Different Dimensional Spatial Chaotic Dynamical Systems

Generalized Synchronization of Different Dimensional Spatial Chaotic Dynamical Systems

Based on Lyapunov stability theory, constructive schemes are presented in this paper to research the generalized syn- chronization and the inverse generalized synchronization be- tween different dimensional spatial chaotic dynamical sys- tems. Besides, the new synchronization criterions are estab- lished in the form of simple algebraic conditions which are very convenient to be verified.

5 Read more

Generalized and inverse generalized synchronization of fractional order discrete time chaotic systems with non identical dimensions

Generalized and inverse generalized synchronization of fractional order discrete time chaotic systems with non identical dimensions

Chaos refers to the high sensitivity of a dynamical system to small changes in the ini- tial condition. Discrete chaotic systems have been around for a while. Perhaps the most commonly studied and applied discrete chaotic system is the Hénon map, which was intro- duced in 1976 [9] as a discretization of the Poincaré section of the famous continuous-time Lorenz system. Soon after, numerous other maps were proposed and became of interest to researchers in the fields of communications and control including the Lozi system [10] and the 2-component flow model [11]. Generalizations of these 2-component systems to higher dimensions were proposed at a later stage including, for instance, the generalized Hénon map [12] and the Stefanski system [13]. This type of chaotic systems has found applications in many fields including engineering and science [14–17].
Show more

14 Read more

Explosive Synchronization in Complex Dynamical Networks Coupled with Chaotic Systems

Explosive Synchronization in Complex Dynamical Networks Coupled with Chaotic Systems

Explosive synchronization (ES), as one kind of abrupt dynamical transitions in nonlinearly coupled systems, has become a hot spot of modern complex networks. At present, many results of ES are based on the networked Kura- moto oscillators and little attention has been paid to the influence of chaotic dynamics on synchronization transitions. Here, the unified chaotic systems (Lorenz, Lü and Chen) and Rössler systems are studied to report evidence of an explosive synchronization of chaotic systems with different topological network structures. The results show that ES is clearly observed in coupled Lorenz systems. However, the continuous transitions take place in the coupled Chen and Lü systems, even though a big shock exits during the syn- chronization process. In addition, the coupled Rössler systems will keep syn- chronous once the entire network is completely synchronized, although the coupling strength is reduced. Finally, we give some explanations from the dynamical features of the unified chaotic systems and the periodic orbit of the Rössler systems.
Show more

14 Read more

Synchronization and control of a network of coupled Reaction-Diffusion systems of
            generalized FitzHugh-Nagumo type*

Synchronization and control of a network of coupled Reaction-Diffusion systems of generalized FitzHugh-Nagumo type*

and where ǫ, δ > 0, are small parameters. In this case, the underlying (ODE) part of system (1) induces an asymptotic evolution to a unique limit cycle for the trajectories diferent from (0, 0). We showed some results on asymptotic behaviour and synchronization for the network. Here, we will generalize some of these results. Let us consider a network of coupled reaction diffusion systems of the following generalized FHN type,

10 Read more

SYNCHRONIZATION T-CHAOTIC SYSTEM

SYNCHRONIZATION T-CHAOTIC SYSTEM

Chaos is an important phenomenon, happens vastly in both natural and man-made systems. Lorenz [1] faced to the first chaotic attractor in 1963. In continue, a lot of researches were achieved on chaotic systems [2-11]. A new 3D chaotic system (T-system) from the Lorenz system was derived in [12,13]. Over the last two decades, chaos control and synchronization have been absorbed increasingly attentions due to their wide applications in many fields [14–25]. Active control [28], backstepping [28] and adaptive control [28] are three different methods for synchronization of T system. Active control [28] and backstepping [28] methods are selected when system parameters are known, and adaptive control [28] method is applied when system parameters are unknown. GBM [26,27], a new method to optimize backstepping method, controls chaos in nonlinear systems better than backstepping design.
Show more

5 Read more

Master slave synchronization of chaotic systems with a modified impulsive controller

Master slave synchronization of chaotic systems with a modified impulsive controller

Synchronization of chaotic systems has become an active research area because of its po- tential applications in different industrial areas [–]. Communication security scheme is one of the hottest fields based on chaos synchronization. In this secure communication scheme, the message signals are injected to a chaotic carrier in the transmitter and then are masked or encrypted. The resulting masked signals are transmitted across a public channel to the receiver. To recover the message in the receiver, the synchronization be- tween the chaotic systems at the transmitter and receiver ends is required. Since Pecora and Carroll [] originally proposed the synchronization of the drive and response systems with different initial states in , many synchronization techniques such as coupling control [], adaptive control [], feedback control [], fuzzy control [], observer-based control [], etc. have been developed in the literature.
Show more

12 Read more

Feedback Chaotic Synchronization with Disturbances

Feedback Chaotic Synchronization with Disturbances

presented the adaptive synchronization of fractional Lorenz systems using a re- duced number of control signals and parameters [13]. Kajbaf et al. used sliding mode controller to obtain chaotic systems [14]. Wang et al. proposed a new feedback synchronization criterion based on the largest Lyapunov exponent [15]. However, most synchronization criterions were obtained under ideal cir- cumstances. If parameters perturbation and external disturbance exist, this kind of criterions will take no effect. According to this practical problem, some solu- tions have been presented. For examples, Jiang et al. proposed a LMI criterion [16] for chaotic feedback synchronization. Although the simulations showed that it is robust to a random noise with zero mean, but no rigorous mathematical proof was provided and we can’t determine if their method is effective for other kinds of noise. In Ref. [17], parameters perturbation was involved in their scheme. The theoretical proof and numerical simulations were given in their work, but external disturbance didn’t receive attention, which made their method unila- teral.
Show more

11 Read more

Adaptive Isochronal Synchronization in Mutually Coupled Chaotic Systems

Adaptive Isochronal Synchronization in Mutually Coupled Chaotic Systems

[11] [14]-[16]. In this case, somewhat counter intuitively, chaotic units synchronize without any relative time delay, although the transmitted signal is received with a large time lag. In most of the rigorous results based on the Lyapunov-Krasovskii stability or Lyapunov-Razumikhin stability, the proposed scheme is very specific, but also the added controller is sometimes too big to be physically practical. One practical scheme is the linear feed- back. However, in such a technique it is very difficult to find the suitable feedback constant, and thus numerical calculation has to be used, e.g., the calculation of the conditional Lyapunov exponents. Due to numerical calcu- lation, such a scheme is not regular since it can be applied only to particular models. More unfortunately, it has been reported that the negativity of the conditional Lyapunov exponents is not a sufficient condition for com- plete chaos synchronization, see [17]. Therefore, the synchronization based on these numerical schemes cannot be strict (i.e., high-qualitative), and is generally not robust against the effect of noise. Especially, in these schemes a very weak noise or a small parameter mismatch can trigger the desynchronization problem due to a sequence of bifurcations [18].
Show more

8 Read more

Fuzzy synchronization of the 3D chaotic systems using belbic

Fuzzy synchronization of the 3D chaotic systems using belbic

chaotic systems (Sara Dadras and Hamid Reza Momeni, 2009). Simulation results depicts that this proposed controller can synchronize these chaotic systems. The rest of the paper is organized as follows. In Section 2, the Brain Emotional Learning Based Intelligent Controller (BELBIC) is described. In Section 3, the T–S fuzzy models will be presented for a new 3D chaotic system (Sara Dadras and Hamid Reza Momeni, 2009). In Section 4, synchronization between two new fuzzy chaotic system is achieved by BELBIC is described. Finally, Section 5 provides, conclusion of this work.
Show more

5 Read more

ADAPTIVE SYNCHRONIZATION OF UNCERTAIN LI AND T CHAOTIC SYSTEMS

ADAPTIVE SYNCHRONIZATION OF UNCERTAIN LI AND T CHAOTIC SYSTEMS

In this paper, we use adaptive control method to derive new results for the global chaos synchronization of identical uncertain Li systems (2009), identical uncertain T systems (2008) and non-identical Li and uncertain T systems. In adaptive synchronization of identical chaotic systems, the parameters of the master and slave systems are unknown and we devise feedback control laws using estimates of the system parameters. In adaptive synchronization of non-identical chaotic systems, the parameters of the master system are known, but the parameters of the slave systems are unknown and we devise feedback control laws using the estimates of the parameters of the slave system. Our adaptive synchronization results derived in this paper for uncertain Li and T systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical Li and T chaotic systems. Numerical simulations are given to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the global chaos synchronization of the uncertain chaotic systems addressed in this paper.
Show more

12 Read more

Reduced order multi switching hybrid synchronization of chaotic systems

Reduced order multi switching hybrid synchronization of chaotic systems

In the phenomenon of hybrid synchronization of chaotic systems, coexistence of complete synchronization and anti-synchronization occurs. Sometimes because of this coexistence this type of synchronization is also referred to as mixed synchronization [33]. Complete synchro- nization implies that the differences of state variables of synchronized systems with different initial values converge to zero. Anti-synchronization is a phenomenon in which the state vari- ables of synchronized systems with different initial values have the same absolute values but of opposite signs. Consequently, the sum of two signals is expected to converge to zero when anti-synchronization occurs. The coexistence of complete and anti-synchronization turns out to be very useful in applications of secure communication. Many successful studies have been reported on hybrid synchronization of chaotic systems [34–36].
Show more

16 Read more

ANTI-SYNCHRONIZATION OF PAN AND LIU CHAOTIC SYSTEMS BY ACTIVE NONLINEAR CONTROL

ANTI-SYNCHRONIZATION OF PAN AND LIU CHAOTIC SYSTEMS BY ACTIVE NONLINEAR CONTROL

In this paper, we derive new results for the anti-synchronization of identical Pan chaotic systems (2010), identical Liu chaotic systems (2004) and non-identical Pan and Liu chaotic systems by active nonlinear control. The stability results for the anti-synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active nonlinear control method is effective and convenient to achieve anti-synchronization of the chaotic systems addressed in this paper. Numerical simulations are shown to illustrate the effectiveness of the anti-synchronization results derived in this paper for identical and non-identical Pan and Liu chaotic systems.
Show more

9 Read more

Show all 10000 documents...

Related subjects