Sharif Digital Repository

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  

In this paper, bifurcation analysis is performed for the nonlinear milling process under sub-harmonic resonance and regenerative chatter, with tool wear and process damping effects. Multiple-scales approach is used to construct analytical approximate solutions for non-autonomous parametrically excited equations of the system with time delay terms. The new bifurcation parameters are the detuning parameter (deviation of the tooth passing frequency from three times of the chatter frequency), damping ratio (affected by process damping) and tool wear width. Jump phenomenon and multi-values responses are observed in the first order solution under sub-harmonic resonance condition. Periodic,... 

The dynamics driven interaction between the bubbles in a cavitation cluster is known to be a complex phenomenon indicative of a highly active nonlinear as well as chaotic behavior in ultrasonic fields. By considering the cluster of encapsulated microbubble with a thin elastic shell in ultrasonic fields, in this paper, the dynamics of microbubbles has been studied via applying the methods of chaos physics. Bifurcation, Lyapunov exponent, and time series are plotted with respect to variables such as amplitude, initial bubble radius, frequency and viscosity. The findings of the study indicate that a bubble cluster undergoes a chaotic unstable region as the amplitude and frequency of ultrasonic... 

To generalize simple bead-linker model of swimmers to higher dimensions and to demonstrate the chemotaxis ability of such swimmers, here we introduce a low-Reynolds predator, using a two-dimensional triangular bead-spring model. Two-state linkers as mechanochemical enzymes expand as a result of interaction with particular activator substances in the environment, causing the whole body to translate and rotate. The concentration of the chemical stimulator controls expansion versus the contraction rate of each arm and so affects the ability of the body for diffusive movements; also the variation of activator substance's concentration in the environment breaks the symmetry of linkers' preferred... 

Herein, the fracture toughness of ternary epoxy systems containing nanosilica and hollow glass microspheres (HGMS) is investigated. The experimental measurements reveal synergistic fracture toughness in some hybrid compositions: The incorporation of 10 phr of HGMS and nanosilica alone modify the fracture toughness of epoxy by 39% and 91%, respectively. However, use of 10 phr hybrid modifier can enhance the fracture toughness of the resin up to 120%. Observations reveal different toughening mechanisms for the blends i.e., plastic deformation for silica nanoparticles and crack bifurcation for HGMS. Both of these toughening mechanisms additively contribute to the synergism in ternary epoxies  

In this paper, we show that an amplitude phase frequency model (APFM) which is used as a nonlinear adaptive filter in signal processing can exhibit chaotic behavior. It is illustrated that both frequency and amplitude of the input components have effect on the filter characteristics which can lead the filter to behave chaotically for some values of these parameters. We have exploited different measures such as the Lyapunov exponents, bifurcation diagram, sensitivity to initial condition, and 0-1 test on time series to confirm our claim. Existence of the chaotic behavior in APFM does not conform to the prior conjectures about this filter. © 2008 Elsevier B.V. All rights reserved  

In some diseases there is a focal pattern of velocity in regions of bifurcation, and thus the dynamics of bifurcation has been investigated in this work. A computational model of blood flow through branching geometries has been used to investigate the influence of bifurcation on blood flow distribution. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier-Stokes equations for Newtonian fluids. The governing equations of mass and momentum conservation were solved to calculate the pressure and velocity fields. Movement of blood flow from an arteriole to a venule via a capillary has been simulated using the volume of fluid (VOF) method. The proposed simulation... 

A new generation of sustainable development research uses mathematical models. This article proposes a heuristic approach to analyze sustainability in a society utilizing a mathematical model. First, an alternative definition of sustainable development has been proposed. Second, the interactions between transport and the other major components of a society have been simulated by a system of differential equations in the form of Lotka-Volterra type predator-prey model. Some of the model parameters have been considered as control parameters in order to reflect the impact of strategies of reducing transport and economic levels of activities in favour of the environment on the one hand, and... 

Elastic stability of shell structures under certain loading conditions is characterized by a dramatically unstable postbuckling behavior. The presence of simultaneous 'competing' buckling modes (corresponding to the same critical buckling load) is understood to be largely responsible for such behavior. In this paper, within the framework of linear bifurcation eigenvalue analysis and Donnell shallow shell theory, the presence of simultaneous buckling modes in axially compressed isotropic cones is determined using the semi-analytical method of Galerkin. The results are presented in the plane of the dimensionless reciprocal meridional and circumferential buckling half wavelengths, and are... 

This study presents a cellular-based mapping for a special class of dynamical systems for embedding neuron models, by exploiting an efficient memristor crossbar-based circuit for its implementation. The resultant reconfigurable memristive dynamical circuit exhibits various bifurcation phenomena, and responses that are characteristic of dynamical systems. High programmability of the circuit enables it to be applied to real-time applications, learning systems, and analytically indescribable dynamical systems. Moreover, its efficient implementation platform makes it an appropriate choice for on-chip applications and prostheses. We apply this method to the Izhikevich, and FitzHugh-Nagumo neuron... 

With the successes in numerous applications from signal filtering to chemical and mass sensing, micro- and nano-electro-mechanical resonators continue to be one of the most widely studied topics of the micro-electro-mechanical systems community. Nonlinearities arising out of different sources such as mid-plane stretching and electrostatic force lead to a rich nonlinear dynamics in the time response of these systems which should be investigated for appropriate design and fabrication of them. Motivated by this need, present study is devoted to analyzing the nonlinear dynamics and chaotic behavior of nano resonators with electrostatic forces on both sides. Based on the potential function and... 

Cardiovascular diseases are one of the major causes of death in the world; atherosclerosis being one aspect. Carotid bifurcation is one of the sites that are vulnerable to this disease. Wall Shear Stress (WSS) is known to be responsible for the process of atherogenesis. In this study, we have simulated the blood flow for Newtonian and non-Newtonian, steady and unsteady, flow conditions in three idealistic and five realistic geometries. A risk factor has been presented based on the results of wall shear stress and, then, a relation was found between geometrical features and the wall shear stress risk factor. Our main conclusions are: 1) The non-Newtonian behavior of blood elevates the value... 

This paper describes a systematic numerical investigation into the nonlinear elastic behavior of conical shells, with various types of initial imperfections, subject to a uniformly distributed axial compression. Three different patterns of imperfections, including first axisymmetric linear bifurcation mode, first non-axisymmetric linear bifurcation mode, and weld depression are studied using geometrically nonlinear finite element analysis. Effects of each imperfection shape and tapering angle on imperfection sensitivity curves are investigated and the lower bound curve is determined. Finally, an empirical lower bound relation is proposed for hand calculation in the buckling design of conical... 

The function and morphology of Endothelial Cells (ECs) play a key role in atherosclerosis. The mechanical stimuli of ECs, such as Wall Shear Stress (WSS) and arterial wall strain, greatly inuence the function and morphology of these cells. The present article deals with computations of these stimuli for a 3D model of a healthy coronary artery bifurcation. The focus of the study is to propose an accurate method for computations of WSS and strains. Two approaches are considered: Coupled simultaneous simulation of arterial wall and blood flow, called fluid-Structure Interaction (FSI) simulation, and decoupled, which simulates each domain (fluid and solid domain) separately. The study... 

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  

The main focus of this paper is on how the biped robot has a stable passive gait cycle as well as going through a stable journey on a level ground merely with push-off actuation. During recent years humanoids have been in the center of attention due to several reasons some of which are: compactness of the structure, low energy consumption, humanoid behavior and last but not least being of great use in medical field. In this paper, equations of motion regarding the passive phase as well as push-off are simulated in MATLAB software. For the next step, a comparison between these two stable gait cycles is made so as to figure out the difference between energy injected to the system by push-off... 

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... 

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  

This paper addresses the problem of aerothermoelastic behavior of a flat skin panel with wall shear stress effect in high supersonic flow. A fully coupled high-supersonic skin panel model that accounts for all thermal-fluid-structure interactions is developed. The governing equations are based on the von Kármán large deflection of Isotropic flat plates. Viscous and inviscid aerothermoelastic loading mechanisms between the fluid and structure are considered. The lumped-capacity assumption and Duhamel superposition principle are used for heat communication analysis. In addition, the effects of viscous flow shear stress, static pressure differential over the external surface, and constant axial... 

Nowadays, dynamic analysis of air-conditioner units is essential to achieve satisfactory comfort conditions in buildings with low energy consumption and operation cost. In this paper, a nonlinear multi input-multi output model (MIMO) of an air-handling unit (AHU) is considered. In the presence of realistic harmonic disturbances, nonlinear dynamics of AHU is investigated. The effect of various thermodynamics and geometrical parameters on limit cycles behaviour of the indoor temperature is investigated. It is observed that the indoor space volume plays as the bifurcation parameter of the system. Decreasing the indoor space volume leads to the occurrence of secondary Hopf (Neimark) bifurcation...