Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of term...Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of terminally differentiated effector T cells to an existing model of autoimmune disease and investigate the stability and Hopf branching phenomenon in a model of multiple sclerosis with a saturable functional response. First, we explore the local asymptotic stability of the equilibrium point and propose conditions for the existence of Hopf branching. Finally, with the help of canonical type theory and the central manifold theorem, we analyze the direction of Hopf branching and the stability of branching periodic solutions.展开更多
In this paper,the stability and Hopf bifurcation of multiple sclerosis model with time delay and saturation function reaction are studied.At first,the stability condition of trivial equilibrium point is given,and the ...In this paper,the stability and Hopf bifurcation of multiple sclerosis model with time delay and saturation function reaction are studied.At first,the stability condition of trivial equilibrium point is given,and the stability of nonnegative equilibrium point is discussed.Then,the existence condition of Hopf bifurcation is given by choosing the added time delay τ as the bifurcation parameter.The direction of Hopf bifurcation and the stability of its periodic solution are analyzed by using canonical form theory and central manifold theorem.Finally,the conclusion is drawn by numerical analysis.展开更多
文摘Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of terminally differentiated effector T cells to an existing model of autoimmune disease and investigate the stability and Hopf branching phenomenon in a model of multiple sclerosis with a saturable functional response. First, we explore the local asymptotic stability of the equilibrium point and propose conditions for the existence of Hopf branching. Finally, with the help of canonical type theory and the central manifold theorem, we analyze the direction of Hopf branching and the stability of branching periodic solutions.
文摘In this paper,the stability and Hopf bifurcation of multiple sclerosis model with time delay and saturation function reaction are studied.At first,the stability condition of trivial equilibrium point is given,and the stability of nonnegative equilibrium point is discussed.Then,the existence condition of Hopf bifurcation is given by choosing the added time delay τ as the bifurcation parameter.The direction of Hopf bifurcation and the stability of its periodic solution are analyzed by using canonical form theory and central manifold theorem.Finally,the conclusion is drawn by numerical analysis.
