Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 12

bifurcation Related Publications

12 CFD Analysis of the Blood Flow in Left Coronary Bifurcation with Variable Angulation

Authors: Midiya Khademi, Ali Nikoo, Shabnam Rahimnezhad Baghche Jooghi

Abstract:

Cardiovascular diseases (CVDs) are the main cause of death globally. Most CVDs can be prevented by avoiding habitual risk factors. Separate from the habitual risk factors, there are some inherent factors in each individual that can increase the risk potential of CVDs. Vessel shapes and geometry are influential factors, having great impact on the blood flow and the hemodynamic behavior of the vessels. In the present study, the influence of bifurcation angle on blood flow characteristics is studied. In order to approach this topic, by simplifying the details of the bifurcation, three models with angles 30°, 45°, and 60° were created, then by using CFD analysis, the response of these models for stable flow and pulsatile flow was studied. In the conducted simulation in order to eliminate the influence of other geometrical factors, only the angle of the bifurcation was changed and other parameters remained constant during the research. Simulations are conducted under dynamic and stable condition. In the stable flow simulation, a steady velocity of 0.17 m/s at the inlet plug was maintained and in dynamic simulations, a typical LAD flow waveform is implemented. The results show that the bifurcation angle has an influence on the maximum speed of the flow. In the stable flow condition, increasing the angle lead to decrease the maximum flow velocity. In the dynamic flow simulations, increasing the bifurcation angle lead to an increase in the maximum velocity. Since blood flow has pulsatile characteristics, using a uniform velocity during the simulations can lead to a discrepancy between the actual results and the calculated results.

Keywords: CFD, Atherosclerosis, Cardiovascular Disease, bifurcation, coronary artery, artery wall shear stress

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11 Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint

Authors: F. Rahimi Dehgolan, M. Najafi

Abstract:

In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: Stability, bifurcation, non-linear vibration, axially moving beam, multiple scales method

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10 A Qualitative Description of the Dynamics in the Interactions between Three Populations: Pollinators, Plants, and Herbivores

Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

Abstract:

In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: bifurcation, steady state, heteroclinic orbits, traveling wave

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9 Flow Transformation: An Investigation on Theoretical Aspects and Numerical Computation

Authors: Abhisek Sarkar, Abhimanyu Gaur

Abstract:

In this report we have discussed the theoretical aspects of the flow transformation, occurring through a series of bifurcations. The parameters and their continuous diversion, the intermittent bursts in the transition zone, variation of velocity and pressure with time, effect of roughness in turbulent zone, and changes in friction factor and head loss coefficient as a function of Reynolds number for a transverse flow across a cylinder have been discussed. An analysis of the variation in the wake length with Reynolds number was done in FORTRAN.

Keywords: bifurcation, attractor, intermittence, energy cascade, vortex stretching, Energy spectra

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8 Bifurcation Study and Parameter Analyses Boost Converter

Authors: S. Ben Said, K. Ben Saad, M. Benrejeb

Abstract:

This paper deals with bifurcation analyses in current programmed DC/DC Boost converter and exhibition of chaotic behavior. This phenomenon occurs due to variation of a set of the studied circuit parameters (input voltage and a reference current). Two different types of bifurcation paths have been observed as part as part of another bifurcation arising from variation of suitable chosen parameter.

Keywords: Chaos, boost converter, bifurcation, Current- programmed control, Initial parameters

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7 Complex Dynamic Behaviors in an Ivlev-type Stage-structured Predator-prey System Concerning Impulsive Control Strategy

Authors: Shunyi Li, Zhifang He, Xiangui Xue

Abstract:

An Ivlev-type predator-prey system and stage-structured for predator concerning impulsive control strategy is considered. The conditions for the locally asymptotically stable prey-eradication periodic solution is obtained, by using Floquet theorem and small amplitude perturbation skills——when the impulsive period is less than the critical value. Otherwise, the system is permanence. Numerical examples show that the system considered has more complicated dynamics, including high-order quasi-periodic and periodic oscillating, period-doubling and period-halving bifurcation, chaos and attractor crisis, etc. Finally, the biological implications of the results and the impulsive control strategy are discussed.

Keywords: Chaos, bifurcation, impulsive, permanence, Stage-structured predator-prey system

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6 Chaotic Response and Bifurcation Analysis of Gear-Bearing System with and without Porous Effect under Nonlinear Suspension

Authors: Cai-Wan Chang-Jian

Abstract:

This study presents a systematic analysis of the dynamic behaviors of a gear-bearing system with porous squeeze film damper (PSFD) under nonlinear suspension, nonlinear oil-film force and nonlinear gear meshing force effect. It can be found that the system exhibits very rich forms of sub-harmonic and even the chaotic vibrations. The bifurcation diagrams also reveal that greater values of permeability may not only improve non-periodic motions effectively, but also suppress dynamic amplitudes of the system. Therefore, porous effect plays an important role to improve dynamic stability of gear-bearing systems or other mechanical systems. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.

Keywords: Chaos, Gear, bifurcation, PSFD

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5 Dynamics and Control of a Chaotic Electromagnetic System

Authors: Shun-Chang Chang

Abstract:

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.

Keywords: bifurcation, Lyapunov exponent, chaotic motion, Poincare map

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4 Stability Analysis of Mutualism Population Model with Time Delay

Authors: Harun Budin, Rusliza Ahmad

Abstract:

This paper studies the effect of time delay on stability of mutualism population model with limited resources for both species. First, the stability of the model without time delay is analyzed. The model is then improved by considering a time delay in the mechanism of the growth rate of the population. We analyze the effect of time delay on the stability of the stable equilibrium point. Result showed that the time delay can induce instability of the stable equilibrium point, bifurcation and stability switches.

Keywords: Time Delay, bifurcation, Delay margin, Mutualism population model

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3 Nonlinear Dynamics of Cracked RC Beams under Harmonic Excitation

Authors: Atul Krishna Banik

Abstract:

Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.

Keywords: bifurcation, Incremental harmonic balance, arc-length continuation, jump phenomena

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2 Behavior of Solutions of the System of Recurrence Equations Based on the Verhulst-Pearl Model

Authors: Vladislav N. Dumachev, Vladimir A. Rodin

Abstract:

By utilizing the system of the recurrence equations, containing two parameters, the dynamics of two antagonistically interconnected populations is studied. The following areas of the system behavior are detected: the area of the stable solutions, the area of cyclic solutions occurrence, the area of the accidental change of trajectories of solutions, and the area of chaos and fractal phenomena. The new two-dimensional diagram of the dynamics of the solutions change (the fractal cabbage) has been obtained. In the cross-section of this diagram for one of the equations the well-known Feigenbaum tree of doubling has been noted.Keywordsbifurcation, chaos, dynamics of populations, fractals

Keywords: Fractals, Chaos, bifurcation, dynamics of populations

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1 Investigation of Chaotic Behavior in DC-DC Converters

Authors: Sajid Iqbal, Masood Ahmed, Suhail Aftab Qureshi

Abstract:

DC-DC converters are widely used in regulated switched mode power supplies and in DC motor drive applications. There are several sources of unwanted nonlinearity in practical power converters. In addition, their operation is characterized by switching that gives birth to a variety of nonlinear dynamics. DC-DC buck and boost converters controlled by pulse-width modulation (PWM) have been simulated. The voltage waveforms and attractors obtained from the circuit simulation have been studied. With the onset of instability, the phenomenon of subharmonic oscillations, quasi-periodicity, bifurcations, and chaos have been observed. This paper is mainly motivated by potential contributions of chaos theory in the design, analysis and control of power converters, in particular and power electronics circuits, in general.

Keywords: Chaos, boost converter, bifurcation, Buck converter, strange attractor, period- doubling

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