Sharif Digital Repository

The taping mode Atomic Force Microscopic (T-AFM) can be assumed as a cantilever beam which its base is excited by a sinusoidal force and nonlinear potential interaction with sample. Thus the cantilever may cause chaotic behavior which decreases the performance of the sample topography. In order to modeling, using the galerkin method, the PDE equation is reduced to a single ODE equation which properly describing the continuous beam. In this paper a nonlinear delayed feedback control.is proposed to control.chaos in T-AFM system. Assuming model parameters uncertainties, the first order Unstable Periodic Orbits (UPOs) of the system is stabilized using the sliding nonlinear delayed feedback... 

This paper deals with the existence of chaos in the fractional order unified system. In an earlier published work, based on the numerical simulation results it is claimed that the lowest effective dimension in the fractional order unified system in order to present chaotic behaviors is 2.76. In this paper, it is analytically shown that the fractional order unified system can be chaotic for effective dimensions lower than the claimed lowest effective dimension. Also, the lowest effective dimension for existence of chaos in such a system is analytically determined. Computer simulation results, obtained based on a reliable numerical method, are brought to back up the presented analytical work... 

The taping mode Atomic Force Microscopic (T-AFM) can be assumed as a cantilever beam which its base is excited by a sinusoidal force and nonlinear potential interaction with sample. Thus the cantilever may cause chaotic behavior which decreases the performance of the sample topography. In order to modeling, using the galerkin method, the PDE equation is reduced to a single ODE equation which properly describing the continuous beam. In this paper a nonlinear delayed feedback control is proposed to control chaos in T-AFM system. Assuming model parameters uncertainties, the first order Unstable Periodic Orbits (UPOs) of the system is stabilized using the sliding nonlinear delayed feedback... 

The cavity quantum electrodynamics of various complex systems is here analyzed using a general versatile code developed in this research. Such quantum multi-partite systems normally consist of an arbitrary number of quantum dots in interaction with an arbitrary number of cavity modes. As an example, a nine-partition system is simulated under different coupling regimes, consisting of eight emitters interacting with one cavity mode. Two-level emitters (e.g. quantum dots) are assumed to have an arrangement in the form of a linear chain, defining the mutual dipole-dipole interactions. It was observed that plotting the system trajectory in the phase space reveals a chaotic behavior in the... 

The chaotic behavior of the secondary asteroid in a system of binary asteroids due to the asphericity and orbital eccentricity is investigated analytically and numerically. The binary asteroids are modeled with a sphere–ellipsoid model, in which the secondary asteroid is ellipsoid. The first-order resonance is studied for different values of asphericity and eccentricity of the secondary asteroid. The results of the Chirikov method are verified by Poincare section which show good agreement between analytical and numerical methods. It is also shown that asphericity and eccentricity affect the size of resonance regions such that beyond the threshold value, the resonance overlapping occurs and... 

This paper introduces a system with switching multi-model structure which can generate chaos. Sub-models in this structure are fractional-order linear systems with any desired commensurate order less than 1. It shows that this system is capable of demonstrating chaotic behavior if its parameters and switching rule are suitably chosen. The structure of the proposed system is defined in a general form; consequently various chaotic attractors can be created by this system with different choices of order, parameters and switching rule. Numerical simulations illustrate behavior of the introduced system in some different situations  

Present study is devoted to investigate the size effect on chaotic behavior of a micro-electro-mechanical resonator under external electrostatic excitation. Using Galerkin's decomposition method, approximating the actuation force with a new effective lumped model, and neglecting higher order terms in the Taylor-series expansion, a simplified model of the main system is developed. By utilizing the Melnikov's method and based on the new form of the electrostatic force, an expression in terms of the system parameters is developed which can be used to rapidly estimate the chaotic region of the simplified system. Based on the analysis of the simple proposed model, it is shown that the effect of... 

This paper presents an attempt to control the chaotic behavior of Rayleigh-Bénard convection system in weakly elastic fluids. In this article, a nonlinear model is presented which fundamentally refers to a model introduced by Khayat. The nonlinear model has chaotic behavior which is controlled by using sliding mode method. In the presence of uncertainty for some parameters of the model, a controller is designed to stabilize the dynamic of the system on the desired trajectory. Different simulation results are presented to demonstrate the effectiveness of the designed controller in tracking different desired trajectories. ©2009 IEEE  

In this paper, we address global non-fragile control and synchronization of a new fractional order chaotic system. First we inspect the chaotic behavior of the fractional order system under study and also find the lowest order (2.49) for the introduced dynamics to remain chaotic. Then, a necessary and sufficient condition which can be easily extended to other fractional-order systems is proposed in terms of Linear Matrix Inequality (LMI) to check whether the candidate state feedback controller with parameter uncertainty can guarantee zero convergence of error or not. In addition, the proposed method provides a global zero attraction of error that guarantees stability around all existing... 

This paper presents an algorithm for synchronizing two different chaotic systems by using a combination of Unscented Kalman-Bucy Filter (UKBF) and sliding mode controller. It is assumed that the drive chaotic system is perturbed by white noise and shows stochastic chaotic behavior. In addition the output of the system does not contain the whole state variables of the system, and it is also affected by some independent white noise. By combining the UKBF and the sliding mode control, a synchronizing control law is proposed. Simulation results show the ability of the proposed method in synchronizing chaotic systems in presence of noise  

In this paper, we analytically study the influences of using frequency domain approximation in numerical simulations of fractional order systems. The number and location of equilibria, and also the stability of these points, are compared between the original system and its frequency based approximated counterpart. It is shown that the original system and its approximation are not necessarily equivalent according to the number, location and stability of the fixed points. This problem can cause erroneous results in special cases. For instance, to prove the existence of chaos in fractional order systems, numerical simulations have been largely based on frequency domain approximations, but in... 

Synchronization of two coupled Chen systems through one of their variables is experimentally studied in this paper. We explore the chaotic behavior of the rescaled Chen system by the bifurcation analysis and computing its Lyapunov exponents which these results are also verified by circuitry realization of the system. Also, using 0-1 test, the chaotic manner of the circuit signals is validated. Finally, we synchronize two Chen circuits using unidirectional continues coupling with only one state variable and show despite the presence of the noise and the fact that two implemented circuits are not completely identical; the circuits achieve complete synchronization. © ICROS  

The taping mode Atomic Force Microscopic (T-AFM) can be assumed as a cantilever beam which its base is excited by a sinusoidal force and nonlinear potential interaction with sample. Thus the cantilever may cause chaotic behavior which decreases the performance of the sample topography. In order to modeling, using the galerkin method, the PDE equation is reduced to a single ODE equation which properly describing the continuous beam. In this paper a nonlinear delayed feedback control is proposed to control chaos in T-AFM system. Assuming model parameters uncertainties, the first order Unstable Periodic Orbits (UPOs) of the system is stabilized using the sliding nonlinear delayed feedback... 

Minimum entropy control technique, an approach for controlling chaos without using the dynamical model of the system, can be improved by being combined with a nature-based optimization technique. In this paper, an ACO-based optimization algorithm is employed to minimize the entropy function of the chaotic system. The feedback gain of a delayed feedback controller is adjusted in the ACO algorithm. The effectiveness of the idea is investigated on suppressing chaos in the tapping-mode atomic force microscope equations. Results show a good performance. The PSO-based version of the minimum entropy control technique is also used to control the chaotic behavior of the AFM, and corresponding results... 

The minimum entropy (ME) control is a chaos control technique which causes chaotic behavior to vanish by stabilizing unstable periodic orbits of the system without using mathematical model of the system. In this technique some controller type, normally delayed feedback controller, with an adjustable parameter such as feedback gain is used. The adjustable parameter is determined such that the entropy of the system is minimized. Proposed in this paper is the PSO-based multi-variable ME control. In this technique two or more control parameters are adjusted concurrently either in a single or in multiple control inputs. Thus it is possible to use two or more feedback terms in the delayed feedback... 

The minimum entropy (ME) control is a chaos control technique which causes chaotic behavior to vanish by stabilizing unstable periodic orbits of the system without using mathematical model of the system. In this technique some controller type, normally delayed feedback controller, with an adjustable parameter such as feedback gain is used. The adjustable parameter is determined such that the entropy of the system is minimized. Proposed in this paper is the PSO-based multi-variable ME control. In this technique two or more control parameters are adjusted concurrently either in a single or in multiple control inputs. Thus it is possible to use two or more feedback terms in the delayed feedback... 

In this paper a linear delayed feedback control is proposed and experimentally applied to eliminate chaos in a nonlinear electrical circuit which is known as Sprott circuit. The chaotic behavior of the system is suppressed by stabilizing one of its first order Unstable Periodic Orbits (UPOs) by a controller designed based on so-called Pyragas method. The effectiveness of this method, firstly, is numerically investigated by stabilizing the unstable first order periodic orbit and then verified experimentally by a laboratory setup. ©2007 IEEE