Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical...Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.展开更多
The study of viral dynamics of HIV/AIDS has resulted in a deep understanding of host-pathogenesis of HIV infection from which numerous mathematical modeling have been derived. Most of these models are based on nonline...The study of viral dynamics of HIV/AIDS has resulted in a deep understanding of host-pathogenesis of HIV infection from which numerous mathematical modeling have been derived. Most of these models are based on nonlinear ordinary differential equations. In Bangladesh, the rate of increase of HIV infection comparing with the other countries of the world is not so high. Bangladesh is still considered to be a low prevalent country in the region with prevalence and shown the local and global stability at disease free and chronic infected equilibrium points. Also we have shown that if the basic reproduction number , then HIV infection is cleared from T cell population and it converges to disease free equilibrium point. Whereas if , then HIV infection persists.展开更多
HIV infection is one of the most serious causes of death throughout the world.CD4+T cells which play an important role in immune protection,are the primary targets for HIV infection.The hallmark of HIV infection is th...HIV infection is one of the most serious causes of death throughout the world.CD4+T cells which play an important role in immune protection,are the primary targets for HIV infection.The hallmark of HIV infection is the progressive loss in population of CD4+T cells.However,the pathway causing this slow T cell decline is poorly understood[16].This paper studies a discontinuous mathematical model for HIV-1 infection,to investigate the effect of pyroptosis on the disease.For this purpose,we use the theory of discontinuous dynamical systems.In this way,we can better analyze the dynamical behavior of the HIV-1 system.Especially,considering the dynamics of the system on its discontinuity boundary enables us to obtain more comprehensive results rather than the previous researches.A stability region for the system,corresponding to its equilibria on the discontinuity boundary,will be determined.In such a parametric region,the trajectories of the system will be trapped on the discontinuity manifold forever.It is also shown that in the obtained stability region,the disease can lead to a steady state in which the population of uninfected T cells and viruses will preserve at a constant level of cytokines.This means that the pyroptosis will be restricted and the disease cannot progress for a long time.Some numerical simulations based on clinical and experimental data are given which are in good agreement with our theoretical results.展开更多
I stepped down as president of the Institute for Systems Biol- ogy （ISB） on Jan 1, 2018. As I think about my 17-year term as President, I am astounded at how much I have learned, not only about science but also abou...I stepped down as president of the Institute for Systems Biol- ogy （ISB） on Jan 1, 2018. As I think about my 17-year term as President, I am astounded at how much I have learned, not only about science but also about, among other things, what it takes to build a unique world-class institution.展开更多
文摘Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.
文摘The study of viral dynamics of HIV/AIDS has resulted in a deep understanding of host-pathogenesis of HIV infection from which numerous mathematical modeling have been derived. Most of these models are based on nonlinear ordinary differential equations. In Bangladesh, the rate of increase of HIV infection comparing with the other countries of the world is not so high. Bangladesh is still considered to be a low prevalent country in the region with prevalence and shown the local and global stability at disease free and chronic infected equilibrium points. Also we have shown that if the basic reproduction number , then HIV infection is cleared from T cell population and it converges to disease free equilibrium point. Whereas if , then HIV infection persists.
文摘HIV infection is one of the most serious causes of death throughout the world.CD4+T cells which play an important role in immune protection,are the primary targets for HIV infection.The hallmark of HIV infection is the progressive loss in population of CD4+T cells.However,the pathway causing this slow T cell decline is poorly understood[16].This paper studies a discontinuous mathematical model for HIV-1 infection,to investigate the effect of pyroptosis on the disease.For this purpose,we use the theory of discontinuous dynamical systems.In this way,we can better analyze the dynamical behavior of the HIV-1 system.Especially,considering the dynamics of the system on its discontinuity boundary enables us to obtain more comprehensive results rather than the previous researches.A stability region for the system,corresponding to its equilibria on the discontinuity boundary,will be determined.In such a parametric region,the trajectories of the system will be trapped on the discontinuity manifold forever.It is also shown that in the obtained stability region,the disease can lead to a steady state in which the population of uninfected T cells and viruses will preserve at a constant level of cytokines.This means that the pyroptosis will be restricted and the disease cannot progress for a long time.Some numerical simulations based on clinical and experimental data are given which are in good agreement with our theoretical results.
文摘I stepped down as president of the Institute for Systems Biol- ogy （ISB） on Jan 1, 2018. As I think about my 17-year term as President, I am astounded at how much I have learned, not only about science but also about, among other things, what it takes to build a unique world-class institution.
