We consider a reaction-diffusion model which describes the spatial Wolbachia spread dynamics for a mixed population of infected and uninfected mosquitoes. By using linearization method, comparison principle and Leray-...We consider a reaction-diffusion model which describes the spatial Wolbachia spread dynamics for a mixed population of infected and uninfected mosquitoes. By using linearization method, comparison principle and Leray-Schauder degree theory, we investigate the influence of diffusion on the Wolbachia infection dynamics.After identifying the system parameter regions in which diffusion alters the local stability of constant steadystates, we find sufficient conditions under which the system possesses inhomogeneous steady-states. Surprisingly,our mathematical analysis, with the help of numerical simulations, indicates that diffusion is able to lower the threshold value of the infection frequency over which Wolbachia can invade the whole population.展开更多
We investigate the stability of steady states of a size- and stage-structured population model, which is a hybrid system of ordinary and partial differential equations with global integral feedbacks. After the formula...We investigate the stability of steady states of a size- and stage-structured population model, which is a hybrid system of ordinary and partial differential equations with global integral feedbacks. After the formulation of a criterion by spectrum method, we derive conditions for global stability of the trivial state and local stability of the positive equilibrium via the basic reproduction rate. Furthermore, some examples and simulations ure .presented to illustrate the obtained results.展开更多
We propose two models of one hyper-connected mutualistic-species described by delay differential equations of Lotka-Volterra type. An hyper-connected model comprises a central species interacting with a number of peri...We propose two models of one hyper-connected mutualistic-species described by delay differential equations of Lotka-Volterra type. An hyper-connected model comprises a central species interacting with a number of peripheral species around it, that is to say, one animal species （pollinators or dispersers） that interacts with several plant species （flowering plants or fruit trees）, or several animal species that interact with one plant species. We derive a necessary and sufficient condition for the global asymptotic stability of the unique coexisting steady state of hyper-connected systems by means of novel Lyapunov functionals.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11471085, 91230104 and 11301103)Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT1226)+1 种基金Program for Yangcheng Scholars in Guangzhou (Grant No. 12A003S)Guangdong Innovative Research Team Program (Grant No. 2011S009)
文摘We consider a reaction-diffusion model which describes the spatial Wolbachia spread dynamics for a mixed population of infected and uninfected mosquitoes. By using linearization method, comparison principle and Leray-Schauder degree theory, we investigate the influence of diffusion on the Wolbachia infection dynamics.After identifying the system parameter regions in which diffusion alters the local stability of constant steadystates, we find sufficient conditions under which the system possesses inhomogeneous steady-states. Surprisingly,our mathematical analysis, with the help of numerical simulations, indicates that diffusion is able to lower the threshold value of the infection frequency over which Wolbachia can invade the whole population.
文摘We investigate the stability of steady states of a size- and stage-structured population model, which is a hybrid system of ordinary and partial differential equations with global integral feedbacks. After the formulation of a criterion by spectrum method, we derive conditions for global stability of the trivial state and local stability of the positive equilibrium via the basic reproduction rate. Furthermore, some examples and simulations ure .presented to illustrate the obtained results.
文摘We propose two models of one hyper-connected mutualistic-species described by delay differential equations of Lotka-Volterra type. An hyper-connected model comprises a central species interacting with a number of peripheral species around it, that is to say, one animal species （pollinators or dispersers） that interacts with several plant species （flowering plants or fruit trees）, or several animal species that interact with one plant species. We derive a necessary and sufficient condition for the global asymptotic stability of the unique coexisting steady state of hyper-connected systems by means of novel Lyapunov functionals.
