In this paper, we investigate the complex dynamics of two-species Ricker-type discrete-time competitive model. We perform a local stability analysis for the fixed points and we will discuss about its persistence for b...In this paper, we investigate the complex dynamics of two-species Ricker-type discrete-time competitive model. We perform a local stability analysis for the fixed points and we will discuss about its persistence for boundary fixed points. This system inherits the dynamics of one-dimensional Ricker model such as cascade of period-doubling bifurcation, periodic windows and chaos. We explore the existence of chaos for the equilibrium points for a specific case of this system using Marotto theorem and proving the existence of snap-back repeller. We use several dynamical systems tools to demonstrate the qualitative behaviors of the system.展开更多
A new viral infection model with cell-to-cell infection and periodic antiretroviral therapy was proposed and analyzed.With the help of defined basic reproduction number Ro,we proved that if R_(0)<1,then the infecti...A new viral infection model with cell-to-cell infection and periodic antiretroviral therapy was proposed and analyzed.With the help of defined basic reproduction number Ro,we proved that if R_(0)<1,then the infection-free steady state is globally attractive.If R_(0)>1,then the infection is uniformly persistent.Furthermore,the globally asymptotical stability of infection-free steady state has been established for the critical case of R_(0)=1.Also,the global asymptotic stability of the infection steady state for a special case of the model has been established by applying the method of Lyapunov.Numerical simulations show that increasing the drug efficacy for blocking virus-to-cell infection,cell-to-cell infection and producing non-infectious virus contributes to weakening the severity ofviral infection.展开更多
文摘In this paper, we investigate the complex dynamics of two-species Ricker-type discrete-time competitive model. We perform a local stability analysis for the fixed points and we will discuss about its persistence for boundary fixed points. This system inherits the dynamics of one-dimensional Ricker model such as cascade of period-doubling bifurcation, periodic windows and chaos. We explore the existence of chaos for the equilibrium points for a specific case of this system using Marotto theorem and proving the existence of snap-back repeller. We use several dynamical systems tools to demonstrate the qualitative behaviors of the system.
基金This work was supported by the National Natural Science Foundation of China(#11701445)the Natural Science Basic Research Program in Shaanxi Province of China(2022JM-042,2022JM-038,2022JQ-033,2020JQ-831,2022JQ-043).
文摘A new viral infection model with cell-to-cell infection and periodic antiretroviral therapy was proposed and analyzed.With the help of defined basic reproduction number Ro,we proved that if R_(0)<1,then the infection-free steady state is globally attractive.If R_(0)>1,then the infection is uniformly persistent.Furthermore,the globally asymptotical stability of infection-free steady state has been established for the critical case of R_(0)=1.Also,the global asymptotic stability of the infection steady state for a special case of the model has been established by applying the method of Lyapunov.Numerical simulations show that increasing the drug efficacy for blocking virus-to-cell infection,cell-to-cell infection and producing non-infectious virus contributes to weakening the severity ofviral infection.
