scholarly journals Modelling HIV dynamics with cell-to-cell transmission and CTL response

2021 ◽  
Author(s):  
Zirui Zhu ◽  
Ranchao Wu ◽  
Yu Yang ◽  
Yancong Xu
Keyword(s):  
Hopf Bifurcation ◽  
Cell Interaction ◽  
Backward Bifurcation ◽  
Hiv Treatment ◽  
Hiv Model ◽  
Ctl Response ◽  
Hiv Dynamics ◽  
Subcritical Hopf Bifurcation ◽  
Cell Transmission ◽  
New Type

In most HIV models, the emergence of backward bifurcation means that the control for basic reproduction number less than one is no longer effective for HIV treatment. In this paper, we study an HIV model with CTL response and cell-to-cell transmission by using the dynamical approach. The local and global stability of equilibria is investigated, the relations of subcritical Hopf bifurcation and supercritical bifurcation points are revealed, especially, the so-called new type bifurcation is also found with two Hopf bifurcation curves meeting at the same Bogdanov-Takens bifurcation point. Forward and backward bifurcation, Hopf bifurcation, saddle-node bifurcation, Bogdanov-Takens bifurcation are investigated analytically and numerically. Two limit cycles are also found numerically, which indicates that the complex behavior of HIV dynamics. Interestingly, the role of cell-to-cell interaction is fully uncovered, it may cause the oscillations to disappear and keep the so-called new type bifurcation persist. Finally, some conclusions and discussions are also given.

Vectored Immunoprophylaxis and Cell-to-Cell Transmission in HIV Dynamics

2020 ◽  
Vol 30 (13) ◽  
pp. 2050185
Author(s):  
Yancong Xu ◽  
Zirui Zhu ◽  
Yu Yang ◽  
Fanwei Meng
Keyword(s):  
Hopf Bifurcation ◽  
Homoclinic Bifurcation ◽  
Hiv Disease ◽  
Hiv Model ◽  
Hiv Dynamics ◽  
Dynamical Behaviors ◽  
Cell Transmission ◽  
Parameter Interval ◽  
Local And Global Bifurcations ◽  
Main Factor

We consider local and global bifurcations in a HIV model with cell-to-cell transmission and vectored immunoprophylaxis. Both theoretical and numerical analyses are conducted to explore various dynamical behaviors including backward bifurcation, Hopf bifurcation, homoclinic bifurcation, Bogdanov–Takens bifurcation, hysteresis and isola bifurcation. The isola bifurcation of periodic orbits was first detected numerically in HIV model, which means that there is a parameter interval with the same oscillations. It is shown that the effect of vectored immunoprophylaxis in this model is the main cause of the periodic symptoms of HIV disease. Moreover, it is shown that the increase of cell-to-cell transmission may be the main factor causing Hopf bifurcation to disappear, and thus eliminating oscillation behavior. Also, several patterns of dynamical behaviors are found in different parameter intervals including the bistability.

Dynamic Analysis of a Bistable Bi-Local Active Memristor and Its Associated Oscillator System

2018 ◽  
Vol 28 (08) ◽  
pp. 1850105 ◽  
Author(s):  
Hui Chang ◽  
Zhen Wang ◽  
Yuxia Li ◽  
Guanrong Chen
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Theory ◽  
Hysteresis Loops ◽  
Oscillator System ◽  
Local Activity ◽  
Edge Of Chaos ◽  
Bifurcation Phenomenon ◽  
Subcritical Hopf Bifurcation ◽  
New Type ◽  
Pinched Hysteresis

This paper proposes a new type of memristor with two distinct stable pinched hysteresis loops and twin symmetrical local activity domains, named as a bistable bi-local active memristor. A detailed and comprehensive analysis of the memristor and its associated oscillator system is carried out to verify its dynamic behaviors based on nonlinear circuit theory and Hopf bifurcation theory. The local-activity domains and the edge-of-chaos domains of the memristor, which are both symmetric with respect to the origin, are confirmed by utilizing the mathematical cogent theory. Finally, the subcritical Hopf bifurcation phenomenon is identified in the subcritical Hopf bifurcation region of the memristor.

Hopf bifurcation for a discontinuous HTLV-1 model

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6247-6267 ◽  
Author(s):  
Elham Shamsara ◽  
Zahra Afsharnezhad ◽  
Reihaneh Mostolizadeh
Keyword(s):  
Hopf Bifurcation ◽  
Sliding Mode ◽  
Early Stage ◽  
Time Lag ◽  
Discontinuous System ◽  
Steady State Condition ◽  
Ctl Response ◽  
Optimal Drug ◽  
Long Time ◽  
Immunosuppressive Diseases

Developing accurate mathematical models for host immune response in immunosuppressive diseases such as HIV and HTLV-1 are essential to achieve an optimal drug therapy regime. Since for HTLV-1 specific CTL response typically occurs after a time lag, we consider a discontinuous response function to better describe this lagged response during the early stage of the infectious, thus the system of HTLV-1 model will be a discontinuous system. For analyzing the dynamic of the system we use Filippov theory and find conditions in which the Filippov system undergoes a Hopf bifurcation. The Hopf bifurcation help us to find stable and unstable periodic oscillations and can be used to predict whether the CTL response can return to a steady state condition. Also, Hopf bifurcation in sliding mode is investigated. In this case the solutions will remain in the hyper-surface of discontinuity and as a consequence the disease cannot progress, at least for a long time. Finally we use numerical simulations to demonstrate the results by example.

Subcritical Hopf bifurcation in NeNd hollow cathode discharge

1994 ◽  
Vol 196 (3-4) ◽  
pp. 191-194 ◽  
Author(s):  
P.R. Sasi Kumar ◽  
V.P.N. Nampoori ◽  
C.P.G. Vallabhan
Keyword(s):  
Hopf Bifurcation ◽  
Hollow Cathode ◽  
Hollow Cathode Discharge ◽  
Subcritical Hopf Bifurcation

Nonlinear Vibration Analysis of a Flexible Rotor Supported by a Flexure Pivot Tilting Pad Journal Bearing in Comparison to a Fixed Profile Journal Bearing with Experimental Verification

2021 ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Hopf Bifurcation ◽  
Journal Bearing ◽  
Flexible Rotor ◽  
Maximum Test ◽  
Operating Region ◽  
Stable Operating ◽  
Subcritical Hopf Bifurcation ◽  
Tilting Pad ◽  
Calculation Results ◽  
Tilting Pad Journal Bearing

Abstract In this paper, an efficient numerical method consisting of the real mode component mode synthesis (CMS) model reduction, shooting method with parallel computing, and Floquet analysis was developed for nonlinear rotordynamics analysis of a flexible rotor supported by a 4-lobe flexure pivot tilting pad journal bearing (FPTPJB) in load-on-pad (LOP) and load-between-pad (LBP) orientations in comparison to a fixed profile journal bearing (JB) of the same pad geometry. The method used the rotor's finite elements and bearing forces obtained from directly solving the Reynolds equation to determine the limit cycles and Hopf bifurcation types. For the investigated rotor and bearing parameters, the numerical results indicated that the onset speed of instability (OSI) of FPTPJB is considerably higher than that of JB of the same orientation. Also, FPTPJB in LOP orientation yielded higher OSI than the LBP one, whereas the OSI of JB in LOP orientation was substantially higher than the LBP counterpart. Nonlinear calculation results indicated that all bearing types and orientations gave subcritical Hopf bifurcation. The FPTPJB in LOP orientation produced the largest stable operating region, whereas the JB in LBP configuration yield the smallest one. The experiment showed subcritical Hopf bifurcation occurred at speed close to the calculated OSI in all cases except FPTPJB in LOP orientation that the OSI is higher than the maximum test rig speed. The whirling orbit had the same frequency as the first critical speed and precessed in the direction of shaft rotation.

scholarly journals Rendering a subcritical Hopf bifurcation supercritical

1996 ◽  
Vol 317 ◽  
pp. 91-109 ◽  
Author(s):  
Po Ki Yuen ◽  
Haim H. Bau
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycle ◽  
Thermal Convection ◽  
Control Strategy ◽  
Chaotic Motion ◽  
Feedback Controller ◽  
Nonlinear Feedback ◽  
Naturally Occurring ◽  
Subcritical Hopf Bifurcation ◽  
Stable Periodic

It is demonstrated experimentally and theoretically that through the use of a nonlinear feedback controller, one can render a subcritical Hopf bifurcation supercritical and thus dramatically modify the nature of the flow in a thermal convection loop heated from below and cooled from above. In particular, we show that the controller can replace the naturally occurring chaotic motion with a stable, periodic limit cycle. The control strategy consists of sensing the deviation of fluid temperatures from desired values at a number of locations inside the loop and then altering the wall heating to counteract such deviations.

Global Stability and Hopf Bifurcation in a Delayed Viral Infection Model with Cell-to-Cell Transmission and Humoral Immune Response

2019 ◽  
Vol 29 (12) ◽  
pp. 1950161 ◽  
Author(s):  
Jinhu Xu ◽  
Yan Geng ◽  
Suxia Zhang
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Viral Infection ◽  
Humoral Immune Response ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Humoral Immune ◽  
Cell Transmission ◽  
Viral Infection Model ◽  
Intracellular Delays

We have developed a class of viral infection model with cell-to-cell transmission and humoral immune response. The model addresses both immune and intracellular delays. We also constructed Lyapunov functionals to establish the global dynamical properties of the equilibria. Theoretical results indicate that considering only two intracellular delays did not affect the dynamical behavior of the model, but incorporating an immune delay greatly affects the dynamics, i.e. an immune delay may destabilize the immunity-activated equilibrium and lead to Hopf bifurcation, oscillations and stability switches. Our results imply that an immune delay dominates the intracellular delays in the model. We also investigated the direction of the Hopf bifurcation and the stability of the periodic solutions by applying normal form and center manifold theory, and investigated the existence of global Hopf bifurcation by regarding the immune delay as a bifurcation parameter. Numerical simulations are carried out to support the analytical conclusions.

Study of Dynamic Characteristics of Friction: A Comparative Analysis of the Velocity Dependent and the LuGre Friction Model

2005 ◽  
Author(s):  
Firoz Ali Jafri ◽  
David F. Thompson
Keyword(s):  
Hopf Bifurcation ◽  
Friction Model ◽  
Continuation Methods ◽  
Bifurcation Parameter ◽  
Lugre Model ◽  
Lugre Friction Model ◽  
Subcritical Hopf Bifurcation ◽  
Fold Bifurcation ◽  
Dependent Model ◽  
Lugre Friction

In this paper, we conduct numerical analysis to study the effects of friction on the dynamic response of a single degree of freedom mechanical system. Two different friction models, the velocity dependent friction model and the LuGre friction model, have been used to model the friction interface. Bifurcation analysis has been conducted using equilibrium and limit cycle continuation methods. With system viscous damping as the bifurcation parameter, a reverse subcritical Hopf bifurcation is observed in the case of velocity dependent model. In the case of the LuGre model for the same bifurcation parameter, a reverse supercritical Hopf bifurcation is observed at lower velocities but at higher velocities it changes to a reverse subcritical Hopf bifurcation. A fold bifurcation of the limit cycles is also seen at higher velocities for the LuGre model.

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