Figure - available from: Journal of Nonlinear Dynamics
This content is subject to copyright. Terms and conditions apply.
Source publication
An active backstepping technique is proposed for the realization of multiswitching synchronization of periodically forced hyperchaotic Van der Pol-Duffing oscillators. The active backstepping technique is a systematic design approach with recursive procedures that skillfully optimizes the choice of Lyapunov functions and active control technique. U...
Citations
... In 2008, Ucar [2] achieved synchronization for two identical chaotic systems in an unconventional way by switching the state variables, and inspired by Ucar's work so many researchers extended this phenomenon combining with dual synchronization schemes and multi-drive and response systems synchronization schemes. Among all the switched synchronization schemes that have been accomplished for one master and one slave systems, [3][4][5] are especially noticeable. ...
A new switched anti-synchronization scheme involving twelve hyperchaotic dynamical systems is proposed in this paper. In this scheme, anti-synchronization has been achieved for six pairs of hyperchaotic systems where first five pairs are taken as pairs of drive systems and the last pair is taken as pair of response systems. This synchronization scheme is constructed by using dual synchronization and compound–compound synchronization in a switched manner. In the existing dual compound–compound synchronization scheme, synchronization has been achieved for six pairs of chaotic systems without any switching effect while in this novel scheme, dual compound–compound anti-synchronization is accomplished with multi-switching (switched) phenomenon for twelve hyperchaotic dynamical systems. Many existing synchronization schemes are particular cases of the proposed scheme. The nonlinear control method and Lyapunov stability criteria have been used to achieve asymptotically stable synchronization states. An example of six pairs of hyperchaotic systems is considered to verify the scheme where hyperchaotic Pang-Liu system is the first system and hyperchaotic Chen system is the second system in each pair. Numerical results and mathematical analysis are in good agreement.
... Utilizing the adaptive control method, this work [21] is further studied in [24] with uncertain parameters. The MSS scheme is further improved for two nonidentical hyperchaotic systems in [3,11]. ...
... However, the aforementioned asymptotic multi-switching synchronization (AMSS) stability analysis [3,11,21,24] is investigated by the feedback linearization (FBL). The FBL-based algorithms are in general highly sensitive to the external disturbance signals. ...
... This attribute gives rise to inefficient use of the energy [10]. Moreover, these investigations [3,11,21,24] focus on the AMSS. In the AMSS, the tracking error converges to the origin as t → ∞. ...
Quick recovery of the information signals in secure communications restricts the hacking duration. The
short synchronization convergence time is a crucial parameter for faster recovery. This paper develops a
novel nonlinear finite-time synchronization control algorithm. This controller accomplishes the global
finite-time multi-switching synchronization between two externally perturbed chaotic systems in the drive–
response system synchronization scheme. The proposed controller assures the global convergence of the
error dynamics in finite-time based on the Lyapunov theory. This implicitly guarantees the global stability
of the closed loop. This paper considers L
p
(0 < p < 1) norm inequality for the construction of the
Lyapunov function. This method provides a means to determine the parameters of the proposed finite-time
controller. This paper also studies the significance of structural components of the proposed controller that
are responsible for the finite-time synchronization convergence. Computer simulation results of ‘two
identical chaotic Lorenz systems’ and ‘chaotic Lorenz and Chen systems’ validate the theoretical findings.
The paper discusses the simulation results and compares them with peer works as well
... Multi-switching synchronization has also been achieved by Ajayi et al. [23] for identical chaotic systems. Recently, Vincent et al. [24] has defined a new type of multi-switching synchronization which provides more degree of freedom to state variables to create error vector in different manner. ...
... For third switch, p 1 = p 2 = p 3 = 1, q 1 = q 2 = q 3 = 3, r 1 = r 2 = r 3 = 1, s 1 = s 2 = s 3 = 2 are taken. Thus, initial conditions for error dynamical system are (23,23,14). Synchronization between the state variables w 1 , 3x 2 (y 1 + 2z 3 ) and w 2 , 3x 3 (y 1 + 2z 3 ) are shown Fig. 5a, b. ...
... For third switch, p 1 = p 2 = p 3 = 1, q 1 = q 2 = q 3 = 3, r 1 = r 2 = r 3 = 1, s 1 = s 2 = s 3 = 2 are taken. Thus, initial conditions for error dynamical system are (23,23,14). Synchronization between the state variables w 1 , 3x 2 (y 1 + 2z 3 ) and w 2 , 3x 3 (y 1 + 2z 3 ) are shown Fig. 5a, b. ...
This manuscript presents a theoretical and numerical analysis to achieve compound synchronization of four non-identical chaotic systems for different multi-switching states. Multi-switching compound synchronization is achieved for three drive systems and one response system via active backstepping technique. By using Lyapunov stability theory, asymptotically stable synchronization states are established. To elaborate the considered scheme an example of Pehlivan system, Liu system, Qi system and Lu system is discussed. The conclusions drawn from computational and analytical approaches are in excellent agreement.
... Ucar et al. achieved multi-switching synchronization for chaotic systems by active control method. Later, multi-switching synchronization for different chaotic systems by adaptive control [26], multi-switching synchronization for identical systems [27] and multi switching combination synchronization by backstepping method [28] have also been achieved. Wang and Sun [26] considered the problem of complete multi-switching synchronization for fully unknown parameters, while the multi-switching problem considered by Ajayi et al. [27] was limited to the case of complete synchronization of identical systems. ...
... Later, multi-switching synchronization for different chaotic systems by adaptive control [26], multi-switching synchronization for identical systems [27] and multi switching combination synchronization by backstepping method [28] have also been achieved. Wang and Sun [26] considered the problem of complete multi-switching synchronization for fully unknown parameters, while the multi-switching problem considered by Ajayi et al. [27] was limited to the case of complete synchronization of identical systems. This paper generalizes the synchronization achieved by Wang and Sun [26] and Ajayi et al. [27]. ...
... Wang and Sun [26] considered the problem of complete multi-switching synchronization for fully unknown parameters, while the multi-switching problem considered by Ajayi et al. [27] was limited to the case of complete synchronization of identical systems. This paper generalizes the synchronization achieved by Wang and Sun [26] and Ajayi et al. [27]. ...
In this paper, multi-switching synchronization between two chaotic systems with fully unknown parameters has been studied. The proposed scheme presents a generalized way to achieve different synchronizations for different switching states of two chaotic systems. Investigations are accomplished by using adaptive control method and Lyapunov stability theory. To analyze the proposed methodology, example of chaotic T system and Liu system have been considered. Theoretical results are validated by numerical simulations.
... Due to the unpredictability of the switched states this synchronization scheme provides an additional security in secure communication. Inspite of its clear importance to secure communication and chaotic encryption schemes, only a few studies of this kind of synchronization have been reported [29][30][31][32]. To the best of our knowledge there have been no previous studies on reduced-order multi-switching synchronization. ...
In this article, a new synchronization scheme is presented by combining the concept of reduced-order synchronization with multi-switching synchronization schemes. The presented scheme, reduced-order multi-switching hybrid synchronization, is notable addition to the earlier multi-switching schemes providing enhanced security in applications of secure communication. Based on the Lyapunov stability theory, the active control method is used to design the controllers and derive sufficient condition for achieving reduced-order multi-switching hybrid synchronization between a new hyperchaotic system taken as drive system and Qi chaotic system serving as response system. Numerical simulations are performed in MATLAB using the Runge-Kutta method to verify the effectiveness of the proposed method. The results show the utility and suitability of the active control method for achieving the reduced-order multi-switching hybrid synchronization among dynamical chaotic systems.
... Later, complete synchronization between different switches of Lorenz and Chen systems was achieved by Wang and Sun [35] for the unknown parameters. Ajayi et al. [1] also achieved multi-switching synchronization for identical systems. Recently, Vincent et al. [29] achieved combination synchronization among three different chaotic systems. ...
The paper addresses a combination synchronization scheme achieved for different switches of three master and one slave hyperchaotic systems. An asymptotically stable synchronized state is derived for different switches of master systems and slave system by using nonlinear control method and Lyapunov stability criteria. To elaborate the presented scheme Pang–Liu hyperchaotic system, Zheng hyperchaotic system and Chen hyperchaotic system are considered as master systems and Newton–Leipnik hyperchaotic system is considered as slave system. Theoretical and graphical results converge to the same conclusion which proves the efficiency of the applied approach.
... One of the main advantages is its multi-switching property, which increased the complexity and diversity of chaos synchronization in a preset multi-switching manner. Afterwards, some important results have been reported including complete synchronization [12,13] , switched function synchronization [14,15] , reduced order hybrid synchronization [16] etc. However, all mentioned works still belong to the scope of two chaotic or hyberchaotic systems. ...
By considering network transmission mode, this paper addresses the finite-time multi-switching synchronization problem for two kinds of multiple chaotic systems. For multiple same-order chaotic systems, we construct the general switching rules and analyze the existence of switching cases. The presented schemes guarantee the states of each derive system to be finite-timely synchronized with the desired states of every respond system in the different transmission paths and switching sequences. For multiple different order chaotic systems, we analyze a special multi-switching hybrid synchronization behavior, where part of the states are completely synchronized and the others belong to combination synchronization. Moveover, the easily verifiable criterion is derived for such synchronization. Finally, numerical examples are given to show the effectiveness of the presented theoretical results.
... It has evolved to include synchronization between different systems, increased and reduced order systems, compound synchronization, combinationÀcombination synchronization and many other forms (Vincent et al., 2015;Ojo et al., 2013bOjo et al., , 2014a. Switching synchronization of chaotic systems is one in which the different states of the response system are synchronized with the desired state of the drive system (Uar et al., 2008;Zheng, 2016;Ajayi et al., 2014). Vincent et al. (2015) opined that the synchronization of different states of the slave system synchronizing with desired states of the master in the masterÀslave configuration will improve security of information transmission through synchronization. ...
... Since multi-switching synchronization (MSS) was firstly proposed in [1], a larger number of research contributions on this issues have been given to show the potential advantages of anti-attack ability and complexity on secure communication and other fields, such as, MSS between two hyperchaotic circuits was studied in [2]. MSS for two 4D hyperchaotic systems was analyzed in [3]. ...
... In 2006, Ahmet Ucar [24] proposed the multi-switching synchronization of coupled chaotic systems via active controls. In recent years, a few studies of this kind of synchronization have been reported [25,26]. However, multi-synchronization via the adaptive control method has rarely been mentioned. ...
... Second, for synchronization problem, the results have been obtained for various kinds of systems, such as [30], 31, and [32]. Furthermore, for multi-switching synchronization problem, the works have investigated in [24][25][26][27]. However, the above obtained results are all for the integer-order systems. ...
In this work, we combine the active and adaptive control theories, and propose a novel synchronization scheme for a class of fractional-order chaotic systems with different structure and different order. Based on the new version of fractional-order Lyapunov stability theory, we design the adaptive controllers and updating laws of different switching. We use the fractional-order Lorenz chaotic system and the fractional-order Chen chaotic system as examples to analyze the multi-switching synchronization process for fractional-order chaotic systems with different structures and different orders. Finally, numerical simulations are also given to illustrate the effectiveness and validation of the proposed method, and the model uncertainties and external disturbances are added to the considered systems to verify the robustness of the proposed controllers.
