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  

We study diffusive heterogeneous predator-prey system with Holling type-II functional response in the presence of harvesting in prey equation i.e.{-δu=λu-a(x)u2-buv1+mu-ch(x)in Ω,-δv=μv-v2+duv1+muin Ω,∂νu=∂νv=0on ∂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 Ω⊂Ω and a(x)>0 on Ω\u03a90. We show that in the case of weak prey growth rate, i.e. λ less than the first eigenvalue of -δ in Ω0, the system has a positive solution for the values of μ in a bounded interval and c>0 sufficiently small. We also investigate the multiplicity of positive solutions in this case. When the prey growth rate is strong, we will show that... 

Mixing processes are widely used in industries and are being studied by a number of scientists; even though, a fundamental insight of the subject is still lacking. In this paper, some basic thoughts are set on the analogy between fluid mixing phenomena and fractal geometry/ properties/ processes. To this end, an unstable horseshoe pattern, which leads to a continuous extending boundary with maximum stretching and folding, is created and repeated. As a result, self-similarity property along with instability is imposed throughout the region, enhancing the fluid mixing. The procedures are verified computationally using the techniques of capacity and information dimensions, which are measured as... 

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... 

In this paper chaotic behavior of nonlinear viscoelastic panels in a supersonic flow is investigated. The governing equations, based on von Kàrmàn's large deflection theory of isotropic flat plates, are considered with viscoelastic structural damping of Kelvin's model included. Quasi-steady aerodynamic panel loadings are determined using piston theory. The effect of constant axial loading in the panel middle surface and static pressure differential have also been included in the governing equation. The panel nonlinear partial differential equation is transformed into a set of nonlinear ordinary differential equations through a Galerkin approach. The resulting system of equations is solved... 

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... 

We investigate the dynamics of a family of one-dimensional linearpower maps. This family has been studied by many authors mainly in the continuous case, associated with Nordmark systems. In the discontinuous case, which is much less studied, the map has vertical and horizontal asymptotes giving rise to new kinds of border collision bifurcations. We explain a mechanism of the interplay between smooth bifurcations and border collision bifurcations with singularity, leading to peculiar sequences of attracting cycles of periods n, 2n, 4n-1, 2(4n-1),···, n ≥ 3. We show also that the transition from invertible to noninvertible map may lead abruptly to chaos, and the role of organizing center in... 

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  

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... 

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... 

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  

In this paper, the occurrence of various types of bifurcation including symmetry breaking, period-doubling (flip) and secondary Hopf (Neimark) bifurcations in milling process with tool-wear and process damping effects are investigated. An extended dynamic model of the milling process with tool flank wear, process damping and nonlinearities in regenerative chatter terms is presented. Closed form expressions for the nonlinear cutting forces are derived through their Fourier series components. Non-autonomous parametrically excited equations of the system with time delay terms are developed. The multiple-scale approach is used to construct analytical approximate solutions under primary... 

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... 

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