Sharif Digital Repository

In this thesis, behavior of a single neuron and a collection of neurons, has modeled by using ordinary differential equation techniques. In modeling of a single neuron, cell’s potential and parameters related to ion’s are variables of differential equation. Often some of this variables change very faster than the others. That causes using small perturbation methods in modeling. The Hodgkin-hoxley equations identified as main model and its reduced models used in thesis. In modeling of a network of neurons, there are also synaptic and neuron variables and also they change in different speeds, too. That again leads us to small perturbation theory. Synapses are hyperpolarizing and depolarizing.... 

Nonlinear nature of polymerization reactors has always attracted great attentions in various scientific areas such as modeling, simulation, dynamical behavior investigation and control engineering as well. Free radical polymerization in continuous reactors, whether in terms of design and startup or in terms of economical concerns, has numerous fans in industrial aspects. In the following thesis, the dynamical behavior of continuous stirred tank reactor of Vinyl Acetate free radical polymerization is examined in an industrial scale. A control system with optimum performance is designed for this CSTR as well. According to the common behavior of this type of reactor, it may demonstrate... 

In this thesis, implementing parametric resonance for the purpose of improvement in sensitivity of MEMS gyroscopes is studied. Based on a parametric study on effect of each factor on the sensor’s performance, the desired values for each parameter is determined. Stability of periodic orbits is studied using Floquet Theory. In addition, three expositions are defined and proved in order to make Floquet Theory applicable for stability analysis of origin. Based on this analysis, the relation between stabilities in the system and occurrence of parametric resonance is illustrated. Due to the complexity of dynamics of a parametrically excited MEMS gyroscope, bifurcations are observed in performance... 

Optical memories are key elements in integrated photonics circuits. Semiconductor micro-ring lasers are good candidates in designing and constructing optical memories. Designing of these memories are usually inactive and are based on nonlinear optics such as Kerr effect or saturation absorption. Bifurcation analyses show that semiconductor micro-ring lasers coupled with waveguide, in the presence of external feedback, have two stable modes. At the coupling point, clockwise and counter clockwise states for one mode have zero and for another mode have π phase differences. In this project, by using boundary conditions, we obtain resonance frequency of a system of two semiconductor lasers in the... 

Optical ¬memories are one of the most important elements in photonic integrated circuits (PCI). Usually these memories have been designed in type of inactive and were based on nonlinear optic effects such as saturation absorption and Kerr effect in Micro¬ ring resonator. Semiconductor Micro¬ ring laser is appropriate candidate for designing and constructing of optical memories. Bifurcation analysis indicates that semiconductor Micro ring laser coupled with waveguide in the presence of external optical feedback from end face of waveguide has two stable modes. Phase differences of clockwise and counter clockwise fields of these modes in the coupling point for one of them is zero (in phase... 

Resonantly actuated microstructures known as microresoantors, are the basic parts of many of MEMS devices such as highly sensitive pressure sensors, mass sensors, biosensors, RF filters, AFMs , ... . Vibration analysis of microresonators specially that of the coupled in-plane and out-f-plane motions has draught many attentions, during recent years. The purpose of the present thesis was to analyze the vibration and dynamics of an FGM microresonator consisted of a clamped-clamped beam with a relative massive pedal attached to the middle of the beam. By modeling the system initially, linear natural in-plane and out-of-plane frequencies and associated mode shapes are obtained. Results are... 

In this thesis, an extended nonlinear model of peripheral milling process (2D) is presented. For the first time, cutting forces are described through a complete third order polynomial function of the axial depth of cut. Also, cubic nonlinearity is considered for the structural stiffness as a function of tool tip displacement. To complete the model, process damping and tool wear effects are also considered. A set of experiments including modal tests to determine natural frequencies and structural damping ratios; and also cutting force measurements at different feed rates to determine nonlinear cutting force coefficients, are carried out. Also, measurement of critical axial depth of cut at... 

The dynamics of a reaction–diffusion predator–prey system with strong Allee effect in the prey population is considered. Nonexistence of non constant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and non homogeneous periodic solutions as well as non constant steady state solutions are studied.
These results show that the impact of the Allee effect essentially increases the system spatiotemporal complexity  

In this thesis, we study diffusive heterogeneous predator-prey system with Holling type-II functional response in the presence of harvesting in prey equation i.e.8>>>>><>>>>>: Δu = u a(x)u2 buv1 + mu ch(x) inΩ;Δv = v v2 +duv1 + muinΩ;@u = @v = 0 on @Ω,where Ω is a smooth bounded region in RN and a(x) is a nonnegative continuous function on Ω, with Ω0 a region such that Ω0 Ω and a(x) > 0on ΩnΩ0. We show that in the case of weak prey growth rate, i.e. less than the first eigenvalue of Δ in Ω0 with Dirichlet boundary condition,the system has a positive solution for the values of in a bounded interval and c > 0 sufficiently small. We also investigate the multiplicity of positive solutions... 

This thesis presents an investigation of the dynamics of two coupled non-identical FitzHugh–Nagumo neurons. It is known that signal transmission in coupled neurons is not instantaneous in general, and time delay is inevitable in signal transmission for real neurons. Therefore we consider the system of two coupled 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 and we will study the excitability of the neurons. By bifurcation study of the system the coupling strength and delay-dependent stability regions are illustrated in the parameter plane, to describe typical... 

Aiming to improve the extraction performance of wind energy has led to the noticeable increase of the structural dimensions in the modern wind turbines. The larger blade with more flexibility experiences large structural deformation even under nominal operational loading, so the nonlinear modeling and analysis of these structures have become as important subject of the recent wind turbine researches. In this dissertation, the geometrical exact model of the rotating wind turbine blade under the effects of the tower tip's motion, and also the operational loading comprising the aerodynamic and gravitational loadings is presented. In this way, the geometrical exact beam formulation is developed... 

Self-excitation vibration or chatter in the milling process is one of the most critical factors in reducing the tool life and surface smoothness. With the change of tool speed or depth of cut, bifurcation phenomena occur at some points (bifurcation points) such that the system behaviour becomes unstable and the chatter is observed. In this study, using nonlinear modelling for cutting forces, two main methods for active control of this process are proposed. The first is an intelligent control based on emotional learning, which is a model-free strategy. In this method, the critic generates a signal (stress signal) using error and its derivative. The purpose of this controller is to reduce the... 

In this research, the effect of the changes of the factors affecting the stability and vibrations of the rotating shaft with the middle universal joint has been investigated. Using the energy method, the rotor motion equations for two five-degree-of-freedom Jefkat rotors have been obtained. By considering the effect of system vibrations on the angle between the rotors and using the existing constraint relations at the connection point of the rotors and inserting them into the equations, finally the equation of motion of the investigated system has been obtained as seven degrees of freedom. Due to the variable speed of the output shaft, the coefficients of the degrees of freedom are dependent...