Synchronization of different fractional order chaotic systems using active control

Bhalekar, Sachin; Daftardar-Gejji, Varsha

doi:10.1016/j.cnsns.2009.12.016

Cited by 216 publications

(106 citation statements)

References 62 publications

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“…However, analytical and closed solutions of these types of fractional equations cannot generally be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behavior of such fractional equations and exploring their applications (see, e.g., [14][15][16] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Salmonella Infection

Rihan¹

2017

Current Topics in Salmonella and Salmonellosis

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In this chapter, we propose a mathematical epidemic model, with integer and fractional order to describe the dynamics of Salmonella infection in animal herds. We investigate the qualitative behaviors of such model and find the conditions that guarantee the asymptotic stability of disease-free and endemic steady states. To assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control, we estimate basic reproduction number R 0 . This threshold parameter specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. We also provide an unconditionally stable implicit scheme for the fractional-order epidemic model. The theoretical and computational results give insight into the modelers and infectious disease specialists.

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Section: Introductionmentioning

confidence: 99%

Dynamics of Salmonella Infection

Rihan¹

2017

Current Topics in Salmonella and Salmonellosis

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“…Studies on chaos synchronization for the fractional order systems are just beginning to attract some attention due to its potential applications in secure communication and control processing. There are many different methods and strategies of fractional order continuous and discrete chaos synchronization have been developed such as activation feedback method, linear and nonlinear feedback synchronization [3,4,8,13,20,25,29], sliding mode control [12,16,22,23,30,34], adaptive control [1,2,5,9,14,21,33], and projective synchronization [10,17,24]. To the best of our knowledge, most of research efforts mentioned above have concentrated on studying the synchronization of fractional order chaotic systems whose models are identical, different.…”

Section: Introductionmentioning

confidence: 99%

Projective reduce order synchronization of fractional order chaotic systems with unknown parameters

Al-Sawalha¹

2017

J. Nonlinear Sci. Appl.

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This paper, mainly concerns the adaptive projective reduce order synchronization behavior of uncertain chaotic system. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of two chaotic and hyperchaotic systems asymptotically synchronized up to a desired identical and different scaling matrix. Numerical simulation results show that the proposed method is effective, convenient, and also faster for projective dual synchronization of chaotic and hyperchaotic systems.

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“…Chaos synchronization of complex Chen and Lu chaotic systems are addressed in citeMahmoud, with designing an active control method. Furthermore, in [36] synchronization of two different fractional order chaotic system is studied. Consequently, the modified projective synchronization of two chaotic systems with known system parameters by acitve control method are rarely investigated by the researchers.…”

Section: Introductionmentioning

confidence: 99%

“…Chaos synchronization of complex Chen and Lu chaotic systems are addressed in citeMahmoud, with designing an active control method. Furthermore, in [36] active …”

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confidence: 99%

Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

Tirandaz

Ahmadnia

Tavakoli

2017

IJECE

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The synchronization problem of chaotic systems using active modified projective nonlinear control method is rarely addressed. Thus the concentration of this study is to derive a modified projective controller to synchronize the two chaotic systems. Since, the parameter of the master and follower systems are considered known, so active methods are employed instead of adaptive methods. The validity of the proposed controller is studied by means of the Lyapunov stability theorem. Furthermore, some numerical simulations are shown to verify the validity of the theoretical discussions. The results demonstrate the effectiveness of the proposed method in both speed and accuracy points of views.Copyright c 2017 Institute of Advanced Engineering and Science.All rights reserved. Corresponding Author:Hamed Tirandaz Hakim Sabzevari University Electrical and Computer Engineering Faculty, Hakim Sabzevari University, Sabzevar, Iran. Phone +98051-4401288 Email: tirandaz@hsu.ac.ir INTRODUCTIONMaster-slave synchronization of chaotic systems is strikely nonlinear, since the aperiodic and nonregular behavior of chaotic systems and their sensitivity to the initial conditions. Chaotic behavior may appear in many physical systems. So, chaos synchronization subject has received a great deal of attention in the last to decades, due to its potential applications in physics, chemistry, electrical engineering, secure communication and so on [1]. Up to now, many types of controling methods are revealed and investigated for control and synchronization of chaotic systems. Active method [2,3,4,5,6], adaptive method [7,8,9] [22,23,24] are some of the introduced methods by the researchers. Among these methods, synchronization with some types of projective methods are extensively investigated in the last decades, since the faster synchronization due to its synchronization scaling factors, which master and slave chaotic systems would be synchronized up to a proportional rate. Projective lag method [25], modified projective synchronization (MPS) [26,27,28], function projective synchronization (FPS) [29], modified function projective synchronization [30,28], generalized function projective synchronization [31,32] and modified projective lag synchronization [33,34] are some generalized schemes of projective method, which utilize some type of scaling factors.When the parameters of a chaotic system are known beforehand, active related methods are preferably chosen than adaptive methods. Active synchronization problem of two chaotic systems with known parameters are vastly investigated by the researchers. For example, in [5,3,35], the active controlling method is studied for synchronization of two typical chaotic systems. And also, in [2], an active method for controling the behavior of a unified chaotic system is presented. Chaos synchronization of complex Chen and Lu chaotic systems are addressed in citeMahmoud, with designing an active control method. Furthermore, in [36] active

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Synchronization of different fractional order chaotic systems using active control

Cited by 216 publications

References 62 publications

Dynamics of Salmonella Infection

Dynamics of Salmonella Infection

Projective reduce order synchronization of fractional order chaotic systems with unknown parameters

Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

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