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 چکیده
1 مقدمه
2 تدوین مسئله و مقدمات
3 معیار سنکرونیزاسیون
4 شبیه سازی

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 بسیاری از سیستم های تاخیری در زمینه های پژوهشی مختلف از جمله زیست شناسی، شیمی، اپتیک غیر خطی، اقتصاد، و اپیدمیولوژی، نامنظم یافت شده اند.
برای مثال، در پیاده سازی سخت افزاری، تاخیرهای زمانی به دلیل سرعت های کلیدزنی محدود ارتباطات رخ می دهد.
تاخیر زمانی ممکن است که منجر به برخی از رفتارهای دینامیکی پیچیده مانند آشوب (بی نظمی)، نوسان، دیورژانس، و بی ثباتی شود.
تعداد کمی گزارش در سنکرونیزاسیون برای سیستم های نامنظم با تاخیرهای متغیر با زمان وجود دارد. در [12]، Lu et.al.، یک طرح تطبیقی برای ثبات و سنکرونیزاسیون سیستم های نامنظم Lure با تاخیرهای متغیر با زمان با استفاده از اصل ثابت معادلات دیفرانسیل کاربردی پیشنهاد کرده است. در حالی که در [22]، Zhen et.al. ، پیشنهاد داده که از مدل کنترل لغزش برای دستیابی به سنکرونیزاسیون سیستم های نامنظم متغیر با زمان استفاده شود. مدل کنترل لغزش سنکرونیزاسیون برای ایجاد بردار اختلال خارجی با حد بالای ناشناخته طراحی شده است. در این مقاله، ما برخی از معیارهای سنکرونیزاسیون سیستم های کوپلینگ با تاخیر متغیر با زمان با استفاده از روش کنترل فیدبک به دست می آوریم. شرایط مشتق شده برای سنکرونیزاسیون به راحتی می تواند تأیید شود.

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Introduction. In this paper, we address the complete synchronization of a class of time-varying delayed chaotic systems. Chaos synchronization is a basic focus in nonlinear science due to its extensive applications in secure communications, biological science, neural networks, automatic control, etc. Since the 1990s, chaos control and synchronization have sparked increasing interest of many researchers, and many schemes have been developed. The readers are referred to the review monographs [1],[6], where the authors presented the main ideas involved in the field of chaos synchronization as well as many potential applications. So far, a lot of research on this subject has been done, and many fundamental results have been reported on synchronization and control of chaotic systems by scholars from physics, engineering, biology, and mathematics, etc. Various control schemes have been developed to synchronize chaotic systems such as drive-response, coupling control, adaptive control, feedback control, observer-based control, impulsive control, intermittent control, to name some typical ones. Many delayed systems in various research fields including biology, chemistry, nonlinear optics, economics, and epidemiology, have been found to be chaotic. For instance, in hardware implementation, time delays occur due to finite switching speeds of communications. Time delay may lead to some complex dynamic behaviors such as chaos, oscillation, divergence, and instability. There are rather few reports on the synchronization for chaotic systems with time-varying delays. In [12], Lu et al. proposed an adaptive scheme for stabilization and synchronization of chaotic Lure systems with time-varying delays using the invariant principle of functional differential equations. While in [22], Zhen et al. proposed to use sliding model control to achieve synchronization for time-varying chaotic systems. The sliding model synchronization controller is designed to satisfy the external disturbance vector with an unknown upper bound. In this paper, we obtain some criteria for synchronization of systems with coupling time-varying delays using feedback control. The derived conditions for the synchronization can be easily verified.

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چکیده
1 معرفی
2 مدل راکتور شیمیایی نامنظم
3سنکرونیزاسیون بوسیله کنترل حالت لغزش
4 شبیه سازی عددی
5 نتیجه گیری

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در این مقاله، ما دینامیک های  یک سیستم راکتور شیمیایی نامنظم رامورد مطالعه قرار می دهیم. خواص اساسی مدل راکتور شیمیایی مانند توان لیاپانوف، جذب کننده بی نظمی، تعادل و ثبات آن ها شرح داده شده است. برای سنکرونیزاسیون، ما از طرح کنترل حالت لغزش استفاده می کنیم. قوانین کنترل به دست آمده توسط Lemma Barbalate برآورده می شوند. شبیه سازی عددی برای نشان دادن کارایی روش پیشنهادی مورد مطالعه، ارائه شده است.

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INTRODUCTION Chaos, is an interesting phenomenon in nonlinear dynamical systems, has been studied over the last four decades [2, 16, 20, 23, 24, 31, 32]. Chaotic and hyperchaotic systems are nonlinear deterministic systems that displays complex and unpredictable behavior. Also these systems are sensitive respect to initial conditions. The chaotic and hyperchaotic systems have many important fields in applied nonlinear sciences, such as laser physics, secure communications, nonlinear circuits, control, neural networks, and active wave propagation [3, 4, 7, 13, 16, 17, 22, 25, 29]. The synchronization of chaotic systems has been investigated since its introduction in the paper by Pecora and Carrol in 1990 [24] and has been widely investigated in many fields, such as physics, chemistry, ecological science and secure communications [5, 14, 31]. Various techniques and methods have been proposed to achieve chaos synchronization and anti-synchronization such as adaptive control [9, 19, 30], adaptive sliding mode control [26], sliding mode control [33], active control [10] and nonlinear control [1]. Fortunately, 82 KHEIRI AND NADERI some existing methods of synchronizing can be generalized to anti-synchronization chaotic systems. Recently synchronization of chaotic complex systems studied in [21]. Dynamics of chemical reactors model has been studied in [11, 12]. The chaotic behavior of chemical reactor model has been studied in [15] by means of computer assisted proof. Synchronization of two identical chemical reactors model has been obtained via linear feedback controller in [28]. We study dynamical qualitative behavior of chemical reactor model. For this purpose, we verify the stability of fixed points and characteristic of chaos for proposed model. We apply sliding mode to synchronization of the model. This paper is organized as follows: In section 2, the dynamical properties of chemical reactor model including Lyapunov exponents, bifurcations and stability of equilibria, will be discussed. We using sliding mode control method for chaos synchronization of two identical chemical reactors model in section 3. By using the Barbalate’s lemma, proved that the error system is asymptotically stable in origin. In section 4, numerical simulations are computed to check the analytical expressions. Our concluding remarks are presented in section 5. 2. CHAOTIC CHEMICAL REACTOR MODEL Chemical dynamics in a well-stirred reactor provides one of the most clear-cut examples of complex non-equilibrium behavior, since it can generate deterministic chaos from the intrinsic nonlinearities of the dynamics. Since this form of chaos is amenable to a small number of macro variables, one may reasonably expect that it constitutes an ideal case study for understanding the passage from microscopic to macroscopic behavior [12]. Chaotic dynamics is characterized by its sensitivity to initial conditions and is sensitive to external disturbances. Questions such as chaotic dynamics amplify internal noises and destroy the macroscopic description, and what the deterministic chemical chaos would become in the picture of a microscopic description beyond the phenomenological kinetics, are of much interest.

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چکیده
1 معرفی
2 سیستم Genesio
2 1 کنترل و تبدیل سیستم Genesio نامنظم به یک سیستم تناوبی
2 2 شبیه سازی عددی
3 سیستم ژنراتور چرخش هسته ای (NSG)
3 1 هماهنگ سازی دو سیستم نامنظم
3 2شبیه سازی عددی
4 جذب کننده Four-Scroll
4 1 هماهنگ سازی دو سیستم نامنظم
4 2شبیه سازی عددی
5 نتیجه گیری

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ما همگام سازی (سنکرونیزاسیون) سیستم Genesio به یک سیستم تناوبی با استفاده از روش کنترل فعال را شرح دادیم. این استراتژی می تواند برای سنکرونیزاسیون هر سیستم نامنظم به سیستم تناوبی با دوره مورد نظر، مورد استفاده قرار گیرد. این روش ممکن است برای کنترل نوسانات نامنظم در سیستم های الکترونیکی، سلول های بیولوژیکی و غیره مفید باشد. ما همچنین سنکرونیزاسیون بین دو سیستم نامنظم متفاوت Genesio و سیستم های NSG و همچنین دو سیستم جذب کننده همسان از طریق  روش کنترل فعال را شرح دادیم. ما معتقدیم که این طرح سنکرونیزاسیون ممکن است برای ارسال پیام مفید باشد. ما نشان دادیم که یک سیستم نامنظم را می توان به سیستم تناوبی و یا هر سیستم دیگرهمگام (سنکرون ) کنیم.

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Introduction Chaos synchronization is an important topic in the non-linear science. In 1990, Pecorra and Carroll [1] introduced the idea of chaos synchronization. Two or more coupled chaotic systems are called synchronized if their behaviors are closely related. Chaos synchronization has received much attention due to its applications in many area such secure communication, information processing, biological systems and chemical reactions. Usually two dynamical systems are called synchronized if the distance between their corresponding states converges to zero as time goes to infinity. This type of synchronization is called identical synchronization. A generalization, of this concept for unidirectionally coupled dynamical systems was proposed by Rulkov et.al.(1995) [2] where two coupled systems are called synchronized if a static functional relationship exists between the states of the systems. This kind of synchronization is called generalized synchronization(GS). In 2009 synchronization in unidirectionally coupled Rossler system was proposed by Khan and Mandal [3] and also synchronization in bidirectionally coupled systems reported by Tarai et.al. [4,5]. In 2011 Khan et.al. [6] have discussed various type of control for controlling chaos in a unified chaotic system and recently in 2012 generalized anti-synchronization of different chaotic systems was proposed by Khan et.al. [7]. In 1996, Kocarev and Parlitz [8] formulated a condition for the occurrence of GS for the master and slave system. Using technique from active control theory, ER-Weibai and Karl.E.Lonngren(1997) [9] demonstrate that a coupled Lorenz systems can synchronize. Further ER-Weibai and Karl.E.Lonngren [10] have investigated sequential synchronization of two Lorenz system using active control. In 2001, synchronization of Rossler and Chen chaotical dynamical syatems using active control was studied by Agiza and Yassen [11]. In 2002 Ming-Chuang Ho, Yao-Chen Hung [12] generalized the technique of active control theory and applied them to synchronize two different systems. Sinha et.al. [13] proposed a general approach in the design of active controllers for non-linear systems exhibiting chaos in 2003. Synchronization of two chaotic four-dimensional systems using active control technique was proposed by Youming and Wenxian in 2007 [14]. In 2009 Sudheer and Sabir [15] was investigated hybrid synchronization of hyperchaotic Lu system via active control. Recently in 2012 Shahzad [16] was investigated chaos synchronization of an ellipsoidal satellite via active control. Synchronization scheme for many coupled chaotic systems are not explored till now. Synchronization strategy for coupled chaotic Genesio system is very important from the theoretical point of view and this strategy is reported by us in this paper. The synchronization strategy between two identical coupled chaotic systems as well as two different chaotic systems are also very important from the application point of view. This motivates us to study the synchronization between Genesio system and Nuclear spin generator systems and synchronization between Four-scroll attractor systems in this paper.

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