Sharif Digital Repository

This Letter tries to find the area in parameter space of a non-salient Permanent-Magnet Synchronous Machine (PMSM) in which chaos can occur. This area is briefly named as chaotic area. The predicted chaotic area is obtained by checking some conditions which are necessary for existence of chaos in a dynamical system. In this Letter, it is assumed that this machine is in the generator mode, and its model is based on direct and quadrature axis of stator voltages and currents. The information of the predicted area is used in non-chaotic maximum power control of torque in the machine  

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Our simulation results show that the (Abelian) BTW sandpile model, the (non-Abelian) Zhang model, and the ("Abelian") Manna model possesses different "weak chaos" exponents, so they may belong to different universality classes. Finally, we show that getting off the critical point destroys this behavior in these models  

This paper deals with a new fractional calculus based method to stabilize fixed points of single-input 3D systems. In the proposed method, the control signal is determined by fractional order integration of a linear combination of the system linearized model states. The tuning rule for this method is based on the stability theorems in the incommensurate fractional order systems. The introduced technique can be used in suppression of chaotic oscillations. To evaluate the performance of the proposed technique in practical applications, it has been experimentally applied to control chaos in two chaotic circuits  

It has been pointed out that the numerical simulation results presented in the above paper are not consistent with reality. The reason for this inconsistency has analytically been clarified in this note. © 2009 IEEE  

This paper illustrates the control of chaos using a fuzzy estimating system based on batch training and recursive least square methods for a continuous time dynamic system. The fuzzy estimator system is trained on both Ott-Geobogi-Yorke (OGY) control algorithm and Pyragas's delayed feedback control algorithm. The system, considered for this study, is a Bonhoeffer-van der Pol (BVP) oscillator. It is found that the implemented fuzzy control system constructed on OGY algorithm results in smaller control transient response than that of the OGY control algorithm itself. The transient response of Pyragas fuzzy control does not show a significant improvement in compare to the Pyragas control... 

Mixing processes are widely used in industries and are being studied by a number of scientists; even though, a fundamental insight of the subject is still lacking. In this paper, some basic thoughts are set on the analogy between fluid mixing phenomena and fractal geometry/ properties/ processes. To this end, an unstable horseshoe pattern, which leads to a continuous extending boundary with maximum stretching and folding, is created and repeated. As a result, self-similarity property along with instability is imposed throughout the region, enhancing the fluid mixing. The procedures are verified computationally using the techniques of capacity and information dimensions, which are measured as... 

In this paper via a novel method of discretized continuous-time Kalman filter, the problem of synchronization and cryptography in fractional-order systems has been investigated in presence of noisy environment for process and output signals. The fractional-order Kalman filter equation, applicable for linear systems, and its extension called the extended Kalman filter, which can be used for nonlinear systems, are derived. The result is utilized for chaos synchronization with the aim of cryptography while the transmitter system is fractional-order, and both the transmitter and transmission channel are noisy. The fractional-order stochastic chaotic Chen system is then presented to apply the... 

In this note some points to paper [L. Pan, W. Zhou, J. Fang, D. Li, Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control, Commun Nonlinear Sci Numer Simulat 2010;15:3754-3762] are presented. Hereby, we illustrate that the way that authors in [1] treat with fractional version of Lyapunov stability theorem suffers lack of a correct justification  

In this paper, control of a non-isothermal continuous stirred tank reactor in which two parallel autocatalytic reactions take place has been addressed. The reactor shows chaotic behavior for a certain set of reactor parameters. In order to control the product concentration, an optimal state feedback controller has been designed. Since concentrations of reactor species are not measured, an observer has been designed for implementation of the proposed control scheme. The local asymptotic stability of the closed-loop system including observer dynamics has been shown via the Lyapunov stability theorem. effectiveness of the proposed controller in load rejection and set point tracking has been... 

A modification to the control law presented in [Y. Lei, W. Xu, H. Zheng, Synchronization of two chaotic nonlinear gyros using active control, Phys. Lett. A 343 (2005) 153] is proposed. © 2007 Elsevier B.V. All rights reserved  

In this paper chaotic behavior of nonlinear viscoelastic panels in a supersonic flow is investigated. The governing equations, based on von Kàrmàn's large deflection theory of isotropic flat plates, are considered with viscoelastic structural damping of Kelvin's model included. Quasi-steady aerodynamic panel loadings are determined using piston theory. The effect of constant axial loading in the panel middle surface and static pressure differential have also been included in the governing equation. The panel nonlinear partial differential equation is transformed into a set of nonlinear ordinary differential equations through a Galerkin approach. The resulting system of equations is solved... 

This paper will consider the mathematical definition of chaos (in sense of Devaney) in order to select appropriate chaos tests. The tests chosen according to investigate the properties mentioned in the definition. In fact, these are prerequisites of chaoticity. Either it will be represented that "sensitivity dependence on initial conditions" is not equivalent to chaos, although some researchers considering it. Hence, it is implied that checking all of the properties mentioned in the definition are required to establish chaos. As our case study, some sample stocks were selected from Tehran Stock Exchange (TSE) and the chosen tests implemented on their returns time series. Incoming results... 

This paper presents two different stabilization methods based on the fractional-calculus theory. The first method is proposed via using the fractional differentiator, and the other is constructed based on using the fractional integrator. It has been shown that the proposed techniques can be used to suppress chaotic oscillations in 3-D chaotic systems. To show the practical capability of the methods, some experimental results on the control of chaos in chaotic circuits are presented. © 2008 IEEE  

In this paper the problem of controlling unstable fixed points (in discrete systems) and periodic orbits (in continuous system) is investigated via a new scheme involving fractional derivatives. This method is based on applying feedback of measured states and using the period of fixed points and periodic orbits. In this method there is no need of information for fixed point and periodic orbits, just the period is enough. The effectiveness of this method is investigated via some demonstrative example  

Finding the oscillatory region in the order space is one of the most challenging problems in nonlinear fractional-order systems. This paper proposes a method to find the possible oscillatory region in the order space for a nonlinear fractional-order system. The effectiveness of the proposed method in finding the oscillatory region and special order sets placed in its boundary is confirmed by presenting some examples  

In this paper the problem of controlling unstable fixed points (in discrete systems) and periodic orbits (in continuous system) is investigated via a new scheme involving fractional derivatives. This method is based on applying feedback of measured states and using the period of fixed points and periodic orbits. In this method there is no need of information for fixed point and periodic orbits, just the period is enough. The effectiveness of this method is investigated via some demonstrative example  

In this note, it is shown that some of the results reported in the above titled paper on the behavior analysis of a fractional order system are not consistent with reality. To support this claim, theoretical justifications and numerical results are presented. Also, it is analytically explained that why such inconsistencies have been occurred in the aforementioned paper  

Abstract In this paper, a word based chaotic image encryption scheme for gray images is proposed that can be used in both synchronous and self-synchronous modes. The encryption scheme operates in a finite field where we have also analyzed its performance according to numerical precision used in implementation. We show that the scheme not only passes a variety of security tests, but also it is verified that the proposed scheme operates faster than other existing schemes of the same type even when using lightweight short key sizes