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    Existence of limit cycles for predator-prey systems with a class of functional responses

    , Article Ecological Modelling ; Volume 142, Issue 1-2 , 2001 , Pages 1-9 ; 03043800 (ISSN) Hesaaraki, M ; Moghadas, S. M ; Sharif University of Technology
    2001
    Abstract
    In this paper we study the problem of the existence of limit cycles for a predator-prey system with a functional response. From the ecological point of view, the existence of a limit cycle shows the oscillatory behaviour of the populations. A necessary and sufficient condition for the existence of limit cycles when the derivative of the functional response is positive, decreasing, and concave upward is given. Global stability of the system can be established by our results. In addition it is shown that the local stability and global stability of the critical point of the system are equivalent. The results cover most of the models which have been proposed in the ecological literature for... 

    Study of limit cycles and stability analysis of fractional arneodo oscillator

    , Article Journal of Optimization Theory and Applications ; Volume 156, Issue 1 , 2013 , Pages 68-78 ; 00223239 (ISSN) Rostami, M ; Haeri, M ; Sharif University of Technology
    2013
    Abstract
    This paper deals with the existence and the characteristics of the limit cycles in the fractional-order Arneodo system. The analysis is done using the describing function method. Our focus is on a special case where two limit cycles exist. The parametric range for the case of interest is derived, and the frequency and the amplitude of the oscillation are predicted. Numerical simulation results are presented to further demonstrate the reliability of the analysis  

    Nonexistence of limit cycles in two classes of predator-prey systems

    , Article Applied Mathematics and Computation ; Volume 175, Issue 1 , 2006 , Pages 356-365 ; 00963003 (ISSN) Aghajani, A ; Moradifam, A ; Sharif University of Technology
    2006
    Abstract
    This paper deals with the question of nonexistence of limit cycles in two famous classes of predator-prey systems. We present some sufficient conditions for the nonexistence of limit cycles in these systems. Our results extend and improve the results presented by Moghadas. © 2005 Elsevier Inc. All rights reserved  

    Dynamic stability and control of a novel handspringing robot

    , Article Mechanism and Machine Theory ; Volume 137 , 2019 , Pages 154-171 ; 0094114X (ISSN) Zabihi, M ; Alasty, A ; Sharif University of Technology
    Elsevier Ltd  2019
    Abstract
    In the field of mobile robotics, legged locomotion plays an essential role in transporting robots over various terrain types. A significant portion of research on legged robots has been focused on one-legged robots. In contrast with different types of locomotion of multi-legged robots, one-legged robots have only one type of motion, called hopping. Hopping motion, as a type of hybrid behavior, is generally comprised of flight and stance phases. Dynamic stabilizing of hopping motion provides a challenging control problem because of its nonlinear and hybrid behavior. The majority of one-legged hopping robots investigated so far are only capable of hopping with one side of their leg. In this... 

    Combustion Instability in a Silo Type Gas Turbine Combustor

    , M.Sc. Thesis Sharif University of Technology Nosrati Shoar, Somayeh (Author) ; Farshchi, Mohammad (Supervisor) ; Hejranfar, Kazem (Supervisor)
    Abstract
    Nowadays, one of the most important desires of the human being is to reduce his living environmental pollution. Using the diluted combustion systems in new gas turbines in order to produce the minimum amount of has been done to satisfy this desire. It should be noted that reducing this amount and using the lower flame temperature will result in some consequences. The most important problem occurred in industrial and aerial gas turbines are the instability of the combustion due to dilution of the fuel to air mixture which it results in heat release fluctuations. If the heat release fluctuations and acoustic pressure are in the same phases, the amplitude of the fluctuations will increase which... 

    A different switching surface stabilizing an existing unstable periodic gait: an analysis based on perturbation theory

    , Article Nonlinear Dynamics ; Volume 81, Issue 4 , 2015 , Pages 2127-2140 ; 0924090X (ISSN) Safa, A. T ; Alasty, A ; Naraghi, M ; Sharif University of Technology
    Kluwer Academic Publishers  2015
    Abstract
    Limit cycle walkers are known as a class of walking robots capable of presenting periodic repetitive gaits without having local controllability at all times during motion. A well-known subclass of these robots is McGeer’s passive dynamic walkers solely activated by the gravity field. The mathematics governing this style of walking is hybrid and described by a set of nonlinear differential equations along with impulses. In this paper, by applying perturbation method to a simple model of these machines, we analytically prove that for this type of nonlinear impulsive system, there exist different switching surfaces, leading to the same equilibrium points (periodic solutions) with different... 

    Spatial limit cycles around the moon in the TBP

    , Article Acta Astronautica ; Volume 67, Issue 1-2 , 2010 , Pages 46-52 ; 00945765 (ISSN) Aram, A ; Zohoor, H ; Sohrabpour, S ; Sharif University of Technology
    2010
    Abstract
    Stable and unstable limit cycles are important orbits in chaotic systems. So many works are done to find and to quench chaos by stabilizing them. In this paper a new family of limit cycle orbits around the Moon is introduced as a result of restricted three-body problem. The family is completely spatial and can be used as an out-of-plane velocity magnifier. Lyapunov exponent in the Floquet theory has also been checked and stability of the orbits has been measured  

    Stability improvement of a dynamic walking system via reversible switching surfaces

    , Article Multibody System Dynamics ; Volume 43, Issue 4 , 2018 , Pages 349-367 ; 13845640 (ISSN) Tehrani Safa, A ; Mohammadi, S ; Naraghi, M ; Alasty, A ; Sharif University of Technology
    Abstract
    Inspired by the effects of a switching surface on the stability of passive dynamic walking (Safa and Naraghi in Robotica 33(01):195–207, 2015; Safa et al. in Nonlinear Dyn. 81(4):2127–2140, 2015), this paper suggests a new control strategy for stabilization of dynamic bipedal locomotion. It verifies that the stability improvement of a dynamic walking system is feasible while preserving the speed, step-length, period, natural dynamics, and the energy effectiveness of the gait. The proposed control policy goes behind the three primary principles: (i) The system’s switching surface has to be replaced by a new one if an external disturbance is induced. (ii) The new switching surface has to be... 

    Regular oscillations or chaos in a fractional order system with any effective dimension

    , Article Nonlinear Dynamics ; Volume 54, Issue 3 , 2008 , Pages 213-222 ; 0924090X (ISSN) Tavazoei, M. S ; Haeri, M ; Sharif University of Technology
    2008
    Abstract
    This paper introduces a fractional order system which can generate regular oscillations or create chaos. It shows that this system is capable to create regular or nonregular oscillations under suitable conditions. These necessary conditions are achieved by violation of the no-chaos criteria. The effective dimension of the proposed system can be chosen any order less than three. Therefore, this system is a good example for limit cycle or chaos generation via fractional-order systems with low orders. Numerical simulations illustrate behavior of the proposed system in different situations. © 2008 Springer Science+Business Media B.V  

    Ivestigation of Some Properties of Lienard Equations

    , M.Sc. Thesis Sharif University of Technology kanigolzari, Anvar (Author) ; Hesaaraki, Mahmoud (Supervisor)
    Abstract
    In this thesis , we consider the generalized lienard system (dx/dt=1/(a(x)) [h(y)-F(x)])¦(dy/dt=-a(x)g(x) )and under suitable assumptions on a , F , g , h we obtain sufficient and necessary conditions for the intersection of all orbits with the vertical isocline y=F(x) . using these conditions we give some sufficient condition for the oscillation of solutions . then existence and uniqueness of periodic solutions for a kind of lienard equation with a deviating argument are studied . finally we study existence and uniqueness of limit cycles for the generalized lienard system(x ̇=ϕ(y)-F(x))¦(y ̇=-g(x))
     

    Approximation behavior of Van der Pol equation: Large and small nonlinearity parameter

    , Article IMECS 2011 - International MultiConference of Engineers and Computer Scientists 2011, 16 March 2011 through 18 March 2011 ; Volume 2 , March , 2011 , Pages 1539-1544 ; 9789881925121 (ISBN) Azarkhalili, B ; Moghadas, P ; Rasouli, M ; Sharif University of Technology
    2011
    Abstract
    The labels mathematician, engineer, and physicist have all been used in reference to Balthazar van der Pol. The van der Pol oscillator, which we study in this paper, is a model developed by him to describe the behavior of nonlinear vacuum tube circuits in the relatively early days of the development of electronics technology. Our study in this paper will be based entirely on numerical solutions. The rigorous foundations for the analysis (e.g., the proof that the equation has a limit cycle solution which is a global attractor) date back to the work of Lienard in 1928, with later more general analysis by Levinson and others  

    A proof for non existence of periodic solutions in time invariant fractional order systems

    , Article Automatica ; Volume 45, Issue 8 , 2009 , Pages 1886-1890 ; 00051098 (ISSN) Tavazoei, M. S ; Haeri, M ; Sharif University of Technology
    2009
    Abstract
    The aim of this note is to highlight one of the basic differences between fractional order and integer order systems. It is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals. As a result, a limit cycle cannot be expected in the solution of these systems. Our investigation is based on Caputo's definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems. © 2009 Elsevier Ltd. All rights reserved  

    Multivariable control of the bifurcation and harmonic perturbations to improve the performance of air-handling units

    , Article ISA Transactions ; Volume 60 , 2016 , Pages 119-127 ; 00190578 (ISSN) Moradi, H ; Vossoughi, G ; Sharif University of Technology
    ISA - Instrumentation, Systems, and Automation Society  2016
    Abstract
    In this research, nonlinear dynamics of an air-ehandling unit (AHU) is studied for tracking objectives, in the presence of harmonic perturbations. Three arbitrary realistic set-paths are considered for the indoor temperature and relative humidity. Two controllers based on feedback linearization (FBL) and pole placement approaches are designed to preserve the dynamic system around the desired tracking paths. It is shown that FBL controller works efficiently in bifurcation control and transforms the quasi-periodic limit cycles into the periodic ones (and consequently comfortable indoor conditions). In addition, FBL controller guarantees suppression of larger periodic limit cycles into the... 

    Obstacle Avoidance Control Algorithm for Multi Agent Autonomous Underwater Vehicle

    , M.Sc. Thesis Sharif University of Technology Ghasemi, Iman (Author) ; Sayyaadi, Hassan (Supervisor)
    Abstract
    According to the importance of obstacle and collision avoidance for multiple Autonomous underwater vehicle (AUV) that are synchronized for starting the path following, in this study the coordination path following controller for a group of underactuated underwater vehicle with considering of obstacle and collision avoidance presented. The proposed control method is based on graph theory and back stepping with modeling of obstacle using limit cycle. At first, for controller design the back stepping method for path following of one AUV is used. Then the designed controller using of principles of graph theory, has been extended for multiple AUV and as the result multiple AUV is synchronized and... 

    Modeling and Control of One-legged Somersaulting Robot

    , M.Sc. Thesis Sharif University of Technology Zabihi, Mehdi (Author) ; Alasty, Aria (Supervisor)
    Abstract
    Inspired by the agility of animal and human locomotion, the number of researchers studying and developing legged robots has been increasing at a rapid rate over the last few decades. In comparison to multi-legged robots, single-legged robots only have one type of locomotion gait, i.e., hopping, which represents a highly nonlinear dynamical behavior consisting of alternating flight and stance phases. Hopping motion should be dynamically stabilized and therefore, presents challenging control problems. A large fraction of studies on legged robots have focused on modeling and control of single-legged hopping machines. In this research, somersaulting is introduced as a kind of hopping motion for... 

    Mathematical Frameworks for the Study of Oscillatory Networks in Neuroscience

    , M.Sc. Thesis Sharif University of Technology Kazemi, Seakineh (Author) ; Fotouhi Firouzabad, Morteza (Supervisor)
    Abstract
    In this thesis, we first introduce the required biological preparations and popular models for modeling single neuron, synapse and cable. Then by introduction of limit cycle oscillators and the necessary prerequisites, investigations are limited to systems involving weakly coupled oscillators. As two examples of such models, famous Kuramoto and Wilson- Cowan models are described. In the following, we introduce some methods for reduction dimension of weakly coupled oscillators and finally we apply one of the expressed methods on the dynamics of cortical network  

    A homotopy analysis method for limit cycle of the van der Pol oscillator with delayed amplitude limiting

    , Article Applied Mathematics and Computation ; Volume 217, Issue 22 , July , 2011 , Pages 9404-9411 ; 00963003 (ISSN) Eigoli, A. K ; Khodabakhsh, M ; Sharif University of Technology
    2011
    Abstract
    In this work, a powerful analytical method, called Liao's homotopy analysis method is used to study the limit cycle of a two-dimensional nonlinear dynamical system, namely the van der Pol oscillator with delayed amplitude limiting. It is shown that the solutions are valid for a wide range of variation of the system parameters. Comparison of the obtained solutions with those achieved by numerical solutions and by other perturbation techniques shows that the utilized method is effective and convenient to solve this type of problems with the desired order of approximation  

    Stability improvement of a dynamic walking system via reversible switching surfaces

    , Article Multibody System Dynamics ; 2017 , Pages 1-19 ; 13845640 (ISSN) Tehrani Safa, A ; Mohammadi, S ; Naraghi, M ; Alasty, A ; Sharif University of Technology
    Abstract
    Inspired by the effects of a switching surface on the stability of passive dynamic walking (Safa and Naraghi in Robotica 33(01):195–207, 2015; Safa et al. in Nonlinear Dyn. 81(4):2127–2140, 2015), this paper suggests a new control strategy for stabilization of dynamic bipedal locomotion. It verifies that the stability improvement of a dynamic walking system is feasible while preserving the speed, step-length, period, natural dynamics, and the energy effectiveness of the gait. The proposed control policy goes behind the three primary principles: (i) The system’s switching surface has to be replaced by a new one if an external disturbance is induced. (ii) The new switching surface has to be... 

    Nonlinear oscillations of a fluttering functionally graded plate

    , Article Composite Structures ; Volume 79, Issue 2 , 2007 , Pages 242-250 ; 02638223 (ISSN) Haddadpour, H ; Navazi, H. M ; Shadmehri, F ; Sharif University of Technology
    2007
    Abstract
    In this paper, the nonlinear aeroelastic behavior of functionally graded plates is studied in supersonic flow. For this purpose, the von Karman strains and piston theory have been employed to model structural nonlinearity and quasi-steady aerodynamic panel loading, respectively. The material properties of the plate are assumed to be graded continuously in the direction of thickness. The variation of the properties follows a simple power-law distribution in terms of the volume fractions of constituents. The Hamilton's principle is used to construct the coupled nonlinear partial differential equations of motion. The derived equations are transformed into a set of coupled ordinary differential... 

    Bifurcation structure of two coupled FHN neurons with delay

    , Article Mathematical Biosciences ; Volume 270 , 2015 , Pages 41-56 ; 00255564 (ISSN) Farajzadeh Tehrani, N ; Razvan, M ; Sharif University of Technology
    Elsevier Inc  2015
    Abstract
    This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing the pitchfork bifurcation of non-trivial rest point. The asymptotic stability and possible Hopf bifurcations of the trivial rest point are studied by analyzing the corresponding characteristic equation. Homoclinic, fold, and pitchfork bifurcations of limit cycles are found. The delay-dependent stability...