Search results for: Bifurcation theory
1630 Hopf Bifurcation for a New Chaotic System
Authors: Kejun Zhuang
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In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.
Keywords: Chaotic system, Hopf bifurcation, normal form theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14391629 Bifurcation Analysis in a Two-neuron System with Different Time Delays
Authors: Changjin Xu
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In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation results are given to support the theoretical predictions. Finally, main conclusions are given.
Keywords: Two-neuron system, delay, stability, Hopf bifurcation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13191628 Bifurcation Analysis for a Physiological Control System with Delay
Authors: Kejun Zhuang
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In this paper, a delayed physiological control system is investigated. The sufficient conditions for stability of positive equilibrium and existence of local Hopf bifurcation are derived. Furthermore, global existence of periodic solutions is established by using the global Hopf bifurcation theory. Finally, numerical examples are given to support the theoretical analysis.
Keywords: Physiological control system, global Hopf bifurcation, periodic solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15491627 Bifurcation Study and Parameter Analyses Boost Converter
Authors: S. Ben Said, K. Ben Saad, M. Benrejeb
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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: Bifurcation, Chaos, Boost converter, Current- programmed control, Initial parameters.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24051626 Frequency Domain Analysis for Hopf Bifurcation in a Delayed Competitive Web-site Model
Authors: Changjin Xu, Yusen Wu
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In this paper, applying frequency domain approach, a delayed competitive web-site system is investigated. By choosing the parameter α as a bifurcation parameter, it is found that Hopf bifurcation occurs as the bifurcation parameter α passes a critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.Keywords: Web-site system, stability, Nyquist criterion, Hopf bifurcation, frequency domain.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14541625 Bifurcation Analysis of a Plankton Model with Discrete Delay
Authors: Anuj Kumar Sharma, Amit Sharma, Kulbhushan Agnihotri
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In this paper, a delayed plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phytoplankton (TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, the stability of interior equilibrium point is investigated and it is shown that time delay can destabilize the otherwise stable non-zero equilibrium state by inducing Hopf-bifurcation when it crosses a certain threshold value. Explicit results are derived for stability and direction of the bifurcating periodic solution by using normal form theory and center manifold arguments. Finally, outcomes of the system are validated through numerical simulations.
Keywords: Plankton, Time delay, Hopf-bifurcation, Normal form theory, Center manifold theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19081624 Stability and Bifurcation Analysis in a Model of Hes1 Selfregulation with Time Delay
Authors: Kejun Zhuang, Hailong Zhu
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The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem.Keywords: Hes1, Hopf bifurcation, time delay, transcriptional repression loop
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13841623 Periodic Oscillations in a Delay Population Model
Authors: Changjin Xu, Peiluan Li
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In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included.
Keywords: Population model, Stability, Hopf bifurcation, Delay, Global Hopf bifurcation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17421622 Bifurcation Analysis of a Delayed Predator-prey Fishery Model with Prey Reserve in Frequency Domain
Authors: Changjin Xu
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In this paper, applying frequency domain approach, a delayed predator-prey fishery model with prey reserve is investigated. By choosing the delay τ as a bifurcation parameter, It is found that Hopf bifurcation occurs as the bifurcation parameter τ passes a sequence of critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. The length of delay which preserves the stability of the positive equilibrium is calculated. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.
Keywords: Predator-prey model, stability, Hopf bifurcation, frequency domain, Nyquist criterion.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13961621 Stability and Bifurcation Analysis of a Discrete Gompertz Model with Time Delay
Authors: Yingguo Li
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In this paper, we consider a discrete Gompertz model with time delay. Firstly, the stability of the equilibrium of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark- Sacker bifurcations occur when the delay passes a sequence of critical values. The direction and stability of the Neimark-Sacker are determined by using normal forms and centre manifold theory. Finally, some numerical simulations are given to verify the theoretical analysis.
Keywords: Gompertz system, Neimark-Sacker bifurcation, stability, time delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19301620 Nonlinear Dynamics of Cracked RC Beams under Harmonic Excitation
Authors: Atul Krishna Banik
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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: Incremental harmonic balance, arc-length continuation, bifurcation, jump phenomena.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15101619 Bifurcations of a Delayed Prototype Model
Authors: Changjin Xu
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In this paper, a delayed prototype model is studied. Regarding the delay as a bifurcation parameter, we prove that a sequence of Hopf bifurcations will occur at the positive equilibrium when the delay increases. Using the normal form method and center manifold theory, some explicit formulae are worked out for determining the stability and the direction of the bifurcated periodic solutions. Finally, Computer simulations are carried out to explain some mathematical conclusions.
Keywords: Prototype model, Stability, Hopf bifurcation, Delay, Periodic solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16551618 Stability and HOPF Bifurcation Analysis in a Stage-structured Predator-prey system with Two Time Delays
Authors: Yongkun Li, Meng Hu
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A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.
Keywords: Predator-prey system, stage structure, time delay, HOPF bifurcation, periodic solution, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15591617 Periodic Orbits in a Delayed Nicholson's Blowflies Model
Authors: Changjin Xu, Peiluan Li
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In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out.
Keywords: Nicholson's blowflies model, Stability, Hopf bifurcation, Delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15941616 Global Existence of Periodic Solutions in a Delayed Tri–neuron Network
Authors: Kejun Zhuang, Zhaohui Wen
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In this paper, a tri–neuron network model with time delay is investigated. By using the Bendixson-s criterion for high– dimensional ordinary differential equations and global Hopf bifurcation theory for functional differential equations, sufficient conditions for existence of periodic solutions when the time delay is sufficiently large are established.Keywords: Delay, global Hopf bifurcation, neural network, periodicsolutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14721615 HOPF Bifurcation of a Predator-prey Model with Time Delay and Habitat Complexity
Authors: Li Hongwei
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In this paper, a predator-prey model with time delay and habitat complexity is investigated. By analyzing the characteristic equations, the local stability of each feasible equilibria of the system is discussed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By choosing the sum of two delays as a bifurcation parameter, we show that Hopf bifurcations can occur as crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.
Keywords: Predator-prey system, delay, habitat complexity, HOPF bifurcation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18621614 Neuron Dynamics of Single-Compartment Traub Model for Hardware Implementations
Authors: J. C. Moctezuma, V. Breña-Medina, Jose Luis Nunez-Yanez, Joseph P. McGeehan
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In this work we make a bifurcation analysis for a single compartment representation of Traub model, one of the most important conductance-based models. The analysis focus in two principal parameters: current and leakage conductance. Study of stable and unstable solutions are explored; also Hop-bifurcation and frequency interpretation when current varies is examined. This study allows having control of neuron dynamics and neuron response when these parameters change. Analysis like this is particularly important for several applications such as: tuning parameters in learning process, neuron excitability tests, measure bursting properties of the neuron, etc. Finally, a hardware implementation results were developed to corroborate these results.Keywords: Traub model, Pinsky-Rinzel model, Hopf bifurcation, single-compartment models, Bifurcation analysis, neuron modeling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11961613 Characterizing the Geometry of Envy Human Behaviour Using Game Theory Model with Two Types of Homogeneous Players
Authors: A. S. Mousa, R. I. Rajab, A. A. Pinto
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An envy behavioral game theoretical model with two types of homogeneous players is considered in this paper. The strategy space of each type of players is a discrete set with only two alternatives. The preferences of each type of players is given by a discrete utility function. All envy strategies that form Nash equilibria and the corresponding envy Nash domains for each type of players have been characterized. We use geometry to construct two dimensional envy tilings where the horizontal axis reflects the preference for players of type one, while the vertical axis reflects the preference for the players of type two. The influence of the envy behavior parameters on the Cartesian position of the equilibria has been studied, and in each envy tiling we determine the envy Nash equilibria. We observe that there are 1024 combinatorial classes of envy tilings generated from envy chromosomes: 256 of them are being structurally stable while 768 are with bifurcation. Finally, some conditions for the disparate envy Nash equilibria are stated.Keywords: Game theory, Nash Equilibrium, envy Nash Equilibrium, geometric tilings, bifurcation thresholds.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8071612 Nonlinear Propagation of Acoustic Soliton Waves in Dense Quantum Electron-Positron Magnetoplasma
Authors: A. Abdikian
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Propagation of nonlinear acoustic wave in dense electron-positron (e-p) plasmas in the presence of an external magnetic field and stationary ions (to neutralize the plasma background) is studied. By means of the quantum hydrodynamics model and applying the reductive perturbation method, the Zakharov-Kuznetsov equation is derived. Using the bifurcation theory of planar dynamical systems, the compressive structure of electrostatic solitary wave and periodic travelling waves is found. The numerical results show how the ion density ratio, the ion cyclotron frequency, and the direction cosines of the wave vector affect the nonlinear electrostatic travelling waves. The obtained results may be useful to better understand the obliquely nonlinear electrostatic travelling wave of small amplitude localized structures in dense magnetized quantum e-p plasmas and may be applicable to study the particle and energy transport mechanism in compact stars such as the interior of massive white dwarfs etc.Keywords: Bifurcation theory, magnetized electron-positron plasma, phase portrait, the Zakharov-Kuznetsov equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13551611 CFD Analysis of the Blood Flow in Left Coronary Bifurcation with Variable Angulation
Authors: Midiya Khademi, Ali Nikoo, Shabnam Rahimnezhad Baghche Jooghi
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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: Coronary artery, cardiovascular disease, bifurcation, atherosclerosis, CFD, artery wall shear stress.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9351610 Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions
Authors: Hailong Zhu, Zhaoxiang Li
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Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).
Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16391609 Haemodynamics Study in Subject Specific Carotid Bifurcation Using FSI
Authors: S. M. Abdul Khader, Anurag Ayachit, Raghuvir Pai, K. A. Ahmed, V. R. K. Rao, S. Ganesh Kamath
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The numerical simulation has made tremendous advances in investigating the blood flow phenomenon through elastic arteries. Such study can be useful in demonstrating the disease progression and hemodynamics of cardiovascular diseases such as atherosclerosis. In the present study, patient specific case diagnosed with partially stenosed complete right ICA and normal left carotid bifurcation without any atherosclerotic plaque formation is considered. 3D patient specific carotid bifurcation model is generated based on CT scan data using MIMICS-4.0 and numerical analysis is performed using FSI solver in ANSYS-14.5. The blood flow is assumed to be incompressible, homogenous and Newtonian, while the artery wall is assumed to be linearly elastic. The two-way sequentially coupled transient FSI analysis is performed using FSI solver for three pulse cycles. The hemodynamic parameters such as flow pattern, Wall Shear Stress, pressure contours and arterial wall deformation are studied at the bifurcation and critical zones such as stenosis. The variation in flow behavior is studied throughout the pulse cycle. Also, the simulation results reveal that there is a considerable increase in the flow behavior in stenosed carotid in contrast to the normal carotid bifurcation system. The investigation also demonstrates the disturbed flow pattern especially at the bifurcation and stenosed zone elevating the hemodynamics, particularly during peak systole and later part of the pulse cycle. The results obtained agree well with the clinical observation and demonstrates the potential of patient specific numerical studies in prognosis of disease progression and plaque rupture.Keywords: Fluid-Structure Interaction, arterial stenosis, Wall Shear Stress, Carotid Artery Bifurcation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22861608 Bifurcation and Stability Analysis of the Dynamics of Cholera Model with Controls
Authors: C. E. Madubueze, S. C. Madubueze, S. Ajama
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Cholera is a disease that is predominately common in developing countries due to poor sanitation and overcrowding population. In this paper, a deterministic model for the dynamics of cholera is developed and control measures such as health educational message, therapeutic treatment, and vaccination are incorporated in the model. The effective reproduction number is computed in terms of the model parameters. The existence and stability of the equilibrium states, disease free and endemic equilibrium states are established and showed to be locally and globally asymptotically stable when R0 < 1 and R0 > 1 respectively. The existence of backward bifurcation of the model is investigated. Furthermore, numerical simulation of the model developed is carried out to show the impact of the control measures and the result indicates that combined control measures will help to reduce the spread of cholera in the population.Keywords: Backward bifurcation, cholera, equilibrium, dynamics, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27381607 Effect of Time Delay on the Transmission of Dengue Fever
Authors: K. Patanarapelert, I.M. Tang
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The effect of a time delay on the transmission on dengue fever is studied. The time delay is due to the presence of an incubation period for the dengue virus to develop in the mosquito before the mosquito becomes infectious. The conditions for the existence of a Hopf bifurcation to limit cycle behavior are established. The conditions are different from the usual one and they are based on whether a particular third degree polynomial has positive real roots. A theorem for determining whether for a given set of parameter values, a critical delay time exist is given. It is found that for a set of realistic values of the parameters in the model, a Hopf bifurcation can not occur. For a set of unrealistic values of some of the parameters, it is shown that a Hopf bifurcation can occur. Numerical solutions using this last set show the trajectory of two of the variables making a transition from a spiraling orbit to a limit cycle orbit.Keywords: Dengue fever transmission, time delay, Hopfbifurcation, limit cycle behavior
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17841606 Hopf Bifurcation Analysis for a Delayed Predator–prey System with Stage Structure
Authors: Kejun Zhuang
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In this paper, a delayed predator–prey system with stage structure is investigated. Sufficient conditions for the system to have multiple periodic solutions are obtained when the delay is sufficiently large by applying Bendixson-s criterion. Further, some numerical examples are given.Keywords: Predator-prey system, Stage structure, Hopf bifurcation, Periodic solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13231605 Chaotic Response and Bifurcation Analysis of Gear-Bearing System with and without Porous Effect under Nonlinear Suspension
Authors: Cai-Wan Chang-Jian
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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: Gear, PSFD, bifurcation, chaos.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21301604 Dynamics and Feedback Control for a New Hyperchaotic System
Authors: Kejun Zhuang, Hailong Zhu
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In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results.Keywords: Feedback control, Hopf bifurcation, hyperchaotic system, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17411603 Bifurcations for a FitzHugh-Nagumo Model with Time Delays
Authors: Changjin Xu, Peiluan Li
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In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given.
Keywords: FitzHugh-Nagumo model, Time delay, Stability, Hopf bifurcation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16831602 Chatter Stability Characterization of Full-Immersion End-Milling Using a Generalized Modified Map of the Full-Discretization Method, Part 1: Validation of Results and Study of Stability Lobes by Numerical Simulation
Authors: Chigbogu G. Ozoegwu, Sam N. Omenyi
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The objective in this work is to generate and discuss the stability results of fully-immersed end-milling process with parameters; tool mass m=0.0431kg,tool natural frequency ωn = 5700 rads^-1, damping factor ξ=0.002 and workpiece cutting coefficient C=3.5x10^7 Nm^-7/4. Different no of teeth is considered for the end-milling. Both 1-DOF and 2-DOF chatter models of the system are generated on the basis of non-linear force law. Chatter stability analysis is carried out using a modified form (generalized for both 1-DOF and 2-DOF models) of recently developed method called Full-discretization. The full-immersion three tooth end-milling together with higher toothed end-milling processes has secondary Hopf bifurcation lobes (SHBL’s) that exhibit one turning (minimum) point each. Each of such SHBL is demarcated by its minimum point into two portions; (i) the Lower Spindle Speed Portion (LSSP) in which bifurcations occur in the right half portion of the unit circle centred at the origin of the complex plane and (ii) the Higher Spindle Speed Portion (HSSP) in which bifurcations occur in the left half portion of the unit circle. Comments are made regarding why bifurcation lobes should generally get bigger and more visible with increase in spindle speed and why flip bifurcation lobes (FBL’s) could be invisible in the low-speed stability chart but visible in the high-speed stability chart of the fully-immersed three-tooth miller.
Keywords: Chatter, flip bifurcation, modified full-discretization map stability lobe, secondary Hopf bifurcation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18251601 Data Traffic Dynamics and Saturation on a Single Link
Authors: Reginald D. Smith
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The dynamics of User Datagram Protocol (UDP) traffic over Ethernet between two computers are analyzed using nonlinear dynamics which shows that there are two clear regimes in the data flow: free flow and saturated. The two most important variables affecting this are the packet size and packet flow rate. However, this transition is due to a transcritical bifurcation rather than phase transition in models such as in vehicle traffic or theorized large-scale computer network congestion. It is hoped this model will help lay the groundwork for further research on the dynamics of networks, especially computer networks.Keywords: congestion, packet flow, Internet, traffic dynamics, transcritical bifurcation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1605