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Topological Indices in Discreat Dynamical Systems and Application
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
In order to generalize the Morse Index for fixed points of a flow, Conley introduced an invariant for isolated invariant sets under a flow which is known as Conley Index.However a similar generalization in discrete dynamical systems is more difficult. Category theory, shape theory and algebraic topology have been used in the generalization. In this thesis we propose a construction of Conley index for discrete dynamical systems, which goes along Conley lines as long as it was possible, but certain modifications has been done for convenience. After introducing the index, we will consider some applications: the generalized Morse inequalities and the Morse decomposition. At the end we will...
Widespread chaos in rotation of the secondary asteroid in a binary system
, Article Nonlinear Dynamics ; Volume 81, Issue 4 , September , 2015 , Pages 2031-2042 ; 0924090X (ISSN) ; Assadian, N ; Sharif University of Technology
Kluwer Academic Publishers
2015
Abstract
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...
Control of chaos in atomic force microscopes using delayed feedback based on entropy minimization
, Article Communications in Nonlinear Science and Numerical Simulation ; Volume 14, Issue 3 , 2009 , Pages 637-644 ; 10075704 (ISSN) ; Alasty, A ; Sharif University of Technology
2009
Abstract
Active chaos control of a tapping mode atomic force microscope (AFM) model via delayed feedback method is presented. The feedback gain is obtained and adapted according to a minimum entropy (ME) algorithm. In this method, stabilizing an unstable fixed point of the system Poincare map is achieved by minimizing the entropy of points distribution on the Poincare section. Simulation results show the feasibility of the proposed method in applying the delayed feedback technique for chaos control of an AFM system. © 2007 Elsevier B.V. All rights reserved