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Global stability of a deterministic model for HIV infection in vivo
, Article Chaos, Solitons and Fractals ; Volume 34, Issue 4 , 2007 , Pages 1225-1238 ; 09600779 (ISSN) ; Nasri, M ; Razvan, M. R ; Sharif University of Technology
2007
Abstract
A deterministic model for human immunodeficiency virus (denoted HIV) infection in the presence of combination therapy is considered. Global asymptotic stability of the disease-free equilibrium is discussed and the endemic equilibrium is also investigated. © 2006 Elsevier Ltd. All rights reserved
On the existence of canards in a nonlinear fluid system manifesting oscillatory behaviour
, Article International Journal of Non-Linear Mechanics ; Volume 98 , 2018 , Pages 58-63 ; 00207462 (ISSN) ; Lundberg, P ; Razvan, M. R ; Sharif University of Technology
Elsevier Ltd
2018
Abstract
In an earlier study dealing with a nonlinear fluid oscillator governed by two autonomous ODEs, the solutions were found to display some aberrant characteristics adjacent to the boundaries of the oscillatory regime in parameter space. It was argued that this behaviour indicated the presence of canards. In the present study it is formally proved that this indeed is the case, and some numerical examples illustrating the phenomenon as well as its effects are presented. © 2017 Elsevier Ltd
Symmetric bursting behaviors in the generalized FitzHugh-Nagumo model
, Article Biological Cybernetics ; Volume 107, Issue 4 , 2013 , Pages 465-476 ; 03401200 (ISSN) ; Fallah, H ; Razvan, M. R ; Sharif University of Technology
2013
Abstract
In the current paper, we have investigated the generalized FitzHugh-Nagumo model. We have shown that symmetric bursting behaviors of different types could be observed in this model with an appropriate recovery term. A modified version of this system is used to construct bursting activities. Furthermore, we have shown some numerical examples of delayed Hopf bifurcation and canard phenomenon in the symmetric bursting of super-Hopf/homoclinic type near its super-Hopf and homoclinic bifurcations, respectively
Real-time trajectory generation for mobile robots
, Article 10th Congress of the Italian Association for Artificial Intelligence, AI IA 2007, Rome, 10 September 2007 through 13 September 2007 ; Volume 4733 LNAI , 2007 , Pages 459-470 ; 03029743 (ISSN); 9783540747819 (ISBN) ; Manzuri, M. T ; Razvan, M. R ; Tajfard, M ; Khoshbakht, S ; Sharif University of Technology
Springer Verlag
2007
Abstract
This paper presents a computationally effective trajectory generation algorithm for omni-directional mobile robots. This method uses the Voronoi diagram to find a sketchy path that keeps away from obstacles and then smooths this path with a novel use of Bezier curves. This method determines velocity magnitude of a robot along the curved path to meet optimality conditions and dynamic constrains using Newton method. The proposed algorithm has been implemented on real robots, and experimental results in different environments are presented. © Springer-Verlag Berlin Heidelberg 2007
Biological and two-sex life table parameters of the carob moth, apomyelois (=ectomyelois) ceratoniae (zeller, 1839) (lep.: pyralidae) at various constant temperatures
, Article Journal of Agricultural Science and Technology ; Volume 25, Issue 5 , 2023 , Pages 1101-1114 ; 16807073 (ISSN) ; Ravan, S ; Soufbaf, M ; Razvan, M. R ; Khani, A ; Sharif University of Technology
Tarbiat Modares University
2023
Abstract
Biological parameters and life tables are the most appropriate criteria for measuring a population’s adaptation to environmental and dietary circumstances. The effects of temperatures 10, 14, 20, 25, 27, 30, 33, and 35℃ on biological and life table parameters of the carob moth Ectomyelois ceratoniae (Zeller) [a 10:14 hour (D: L cycle) and 65±5% RH] were experimentally studied. Based on the age-stage, two-sex life table theory, data were analyzed at different temperatures. The findings indicated that by increasing temperature, the mean incubation period of eggs, larvae, pupae, total immature development time, and adult longevity change significantly. The Adult Pre-Oviposition Periods (APOP)...
On the Poincaré index of isolated invariant sets
, Article Scientia Iranica ; Volume 15, Issue 6 , 2008 , Pages 574-577 ; 10263098 (ISSN) ; Fotouhi, M ; Sharif University of Technology
Sharif University of Technology
2008
Abstract
In this paper, the Conley index theory is used to examine the Poincaré index of an isolated invariant set. Some limiting conditions on a critical point of a planar vector field are obtained to be an isolated invariant set. As a result, the existence of infinitely many homoclinic orbits for a critical point with the Poincaré index greater than one is shown. © Sharif University of Technology
Hopf bifurcation of an age-structured virus infection model
, Article Discrete and Continuous Dynamical Systems - Series B ; Volume 23, Issue 2 , March , 2018 , Pages 861-885 ; 15313492 (ISSN) ; Aminataei, A ; Browne, C. J ; Razvan, M. R ; Sharif University of Technology
American Institute of Mathematical Sciences
2018
Abstract
In this paper, we introduce and analyze a mathematical model of a viral infection with explicit age-since infection structure for infected cells. We extend previous age-structured within-host virus models by including logistic growth of target cells and allowing for absorption of multiple virus particles by infected cells. The persistence of the virus is shown to depend on the basic reproduction number R0. In particular, when R0 ≤ 1, the infection free equilibrium is globally asymptotically stable, and conversely if R0 > 1, then the infection free equilibrium is unstable, the system is uniformly persistent and there exists a unique positive equilibrium. We show that our system undergoes a...
Global analysis of an SAIS model
, Article Journal of Biological Dynamics ; Volume 6, Issue 2 , 2012 , Pages 457-474 ; 17513758 (ISSN) ; Yasaman, S ; Sharif University of Technology
2012
Abstract
This paper is concerned with global analysis of an SAIS epidemiological model in a population of varying size introduced by Busenberg and van den Driessche. In this model the population is divided into three subgroups of susceptible, asymptomatic and infective individuals. It has been shown that this system has no periodic solutions and all its trajectories tend to the equilibria of the system. We use the Poincaré Index theorem to determine the number of the equilibria and their stability properties. We have shown that bistability occurs for suitable values of parameters and found a set of examples of all possible dynamics of the system
Global dynamics of a differential susceptibility model
, Article International Journal of Biomathematics ; Volume 5, Issue 5 , September , 2012 ; 17935245 (ISSN) ; Yasaman, S ; Sharif University of Technology
2012
Abstract
An SIS epidemiological model in a population of varying size with two dissimilar groups of susceptible individuals has been analyzed. We prove that all the solutions tend to the equilibria of the system. Then we use the Poincaré Index theorem to determine the number of the rest points and their stability properties. It has been shown that bistability occurs for suitable values of the involved parameters. We use the perturbations of the pitchfork bifurcation points to give examples of all possible dynamics of the system. Some numerical examples of bistability and hysteresis behavior of the system has been also provided
Global analysis of a model of differential susceptibility induced by genetics
, Article Nonlinear Analysis: Real World Applications ; Volume 12, Issue 4 , 2011 , Pages 2183-2197 ; 14681218 (ISSN) ; Yasaman, S ; Sharif University of Technology
2011
Abstract
This paper is concerned with global analysis of an SIS epidemiological model in a population of varying size with two dissimilar groups of susceptible individuals. We prove that this system has no periodic solutions and use the Poincar index theorem to determine the number of rest points and their stability properties. It has been shown that multiple equilibria (bistability) occurs for suitable values of parameters. We also give some numerical examples of all possible bifurcations of this system
Emergence of bursting in two coupled neurons of different types of excitability
, Article Chaos, Solitons and Fractals ; Volume 132 , 2020 ; Yasaman, S ; Sharif University of Technology
Elsevier Ltd
2020
Abstract
In this manuscript, a spiking neuron of type I excitability and a silent neuron of type II excitability are coupled through a gap junction with unequal coupling strengths, and none of the coupled neurons can burst intrinsically. By applying the theory of dynamical systems (e.g. bifurcation theory), we investigate how the coupling strength affects the dynamics of the neurons, when one of the coupling strengths is fixed and the other varies. We report four different regimes of oscillations as the coupling strength increases. (1) Spike–Spike Phase–Locking, where both neurons are in tonic spiking mode but with different frequencies; (2) Spike–Burst mode, where the type II neuron bursts while the...
Combinatorial Knot Floer Homology and Double Branched Cover
, Ph.D. Dissertation Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
Using a Heegaard diagram for the pullback of a knot K ⊂ S3 in its cyclic double branched cover Σ2(K), we give a combinatorial proof for the invariance of the associated knot Floer homology over Z
Multigrid for Reservoir Simulation
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
Reservoir simulation, recognition of the past and present reservoir behavior and prediction of its behavior in the future, which forms one of the most important parts of the management of a reservoir. In fact, the reservoir is like a living creature and increasing the accuracy in predicting its behavior requires a precise model. Reservoirs have high physical dimensions that are associated with high physical changes. As a result, a large number of computational cells are needed to simulate the reservoirs, which results in a very large linear equation system. The numerical solution of these systems is very time consuming. Many observed examples indicate that 80 \% of the runtime is included....
Dynamics of Two Coupled Neurons of Different Types of Excitability
, Ph.D. Dissertation Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
Excitability is one of the most important characteristics of a neuron. In 1948, Hodgkin identified three different types of excitability of neurons. Excitability an all of its types can be observed in Hodgkin-Huxley model of neuronal dynamics (H-H model) as a four-dimensional system of differential equations and in at least two dimensional reductions of H-H type models. By applying the theory of dynamical systems (e.g. bifurcation theory), one can give a mathematical definition of excitability.Excitability of the neuron is equivalent to that the neuronal model is near a bifurcation through which the state of the system approaches to a stable limit cycle. In this thesis, a two-dimensional...
Canards in Complex Oscillatory Systems
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
Canard, first observed in Van der Pol oscillations, is a typical phenomenon in oscillatory systems. Canard is also observed in many oscillatory systems such as electrical circuits and neurons. In many fields of science and engineering there are complex oscillations that exhibit canard for certain values of parameters. These three dimensional systems exhibit complex oscillatory behavior never observed in two dimensional dynamics. Some of these systems are chaotic for certain parameter values. It seems than in oscillatory systems canards can make complex behavior. Several methods such as the singular perturbation theory have been used to study this complexity. In this project, we study canard...
Numerical Solution for Governing Equations of Borehole Shale Structure Stability
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
In this thesis we employ finite elements and conjugate gradient methods to exibit a numerical solution for governing equations of borehole stability
Oscillations in Neuronal Dynamical Systems
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
Periodic orbits are one of the basic objects of interest in Dynamical systems. And methods for detecting, counting and determining the periods of periodic orbits are of great interest. In spite of this interest, periodic orbits remain difficult to detect. The most celebrated existence result is the Poincare-Bendixson theorem. Unfortunately, this theorem is false in general for higher dimensional systems. The success of fixed point theory inspired the hope that similar topological techniques could be of use in proving the existence of periodic orbits. In this Thesis we have analyzed some topological and geometrical theories which could be of use in proving the existence of periodic orbits....
Scattering Theory on Locally symmetric Spaces
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
Scattering theory on locally symmetric space first was studied by Peter Lax and Ralph Phillips. They studied the and develop scattering theory on it. Without the Fourier analysis tools this theory was completed with a lot of computations. In this thesis first we try to construct Fourier analysis by definition Fourier transform then by means of new tools we prove very short version of scattering theory on locally symmetric space . In general case for studying scattering theory we need firs spectral decomposition of Hilbert space of square integrable functions locally symmetric spaces of rational rank one is achieved by quotient of symmetric space where G is Lie group and K is maximal...
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...
Numerical Methods for Approximation and Visualization of Invariant Manifolds in Dynamical Systems
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
Invariant manifolds are important objects in the theory of dynamical systems. The stable manifold theorem is a very important theorem about this concept which proves the existence of stable and unstable manifolds in a wide range of dynamical systems. The importance of invariant manifolds encourages us to view their pictures. It helps us to understand their bahavior. For this purpose, at first we need to approximate the invariant manifold we want to visualize. There are several algorithms designed to approximate invariant manifolds. Those algorithms approximate a set of points on an invariant manifold and then provide an approximation of the manifold by the calculated points. Visualizing an...