A predator-prey system in a polluted environment is studied in this paper.Surveying the transformation of toxicants from prey to predator and the effects of toxicants on functional response of predator comprehensively...A predator-prey system in a polluted environment is studied in this paper.Surveying the transformation of toxicants from prey to predator and the effects of toxicants on functional response of predator comprehensively, the thresholds between the weak persistence in the mean and extinction of populations are established.展开更多
A four-dimensional delay differential equations(DDEs)model of malaria with standard incidence rate is proposed.By utilizing the limiting system of the model and Lyapunov direct method,the global stability of equilibri...A four-dimensional delay differential equations(DDEs)model of malaria with standard incidence rate is proposed.By utilizing the limiting system of the model and Lyapunov direct method,the global stability of equilibria of the model is obtained with respect to the basic reproduction number R_(0).Specifically,it shows that the disease-free equilibrium E^(0)is globally asymptotically stable(GAS)for R_(0)<1,and globally attractive(GA)for R_(0)=1,while the endemic equilibrium E^(*)is GAS and E^(0)is unstable for R_(0)>1.Especially,to obtain the global stability of the equilibrium E^(*)for R_(0)>1,the weak persistence of the model is proved by some analysis techniques.展开更多
文摘A predator-prey system in a polluted environment is studied in this paper.Surveying the transformation of toxicants from prey to predator and the effects of toxicants on functional response of predator comprehensively, the thresholds between the weak persistence in the mean and extinction of populations are established.
基金supported in part by the National Natural Science Foundation of China (Nos.11901027,11871093 and 12171003)the China Postdoctoral Science Foundation (No.2021M703426)+1 种基金the Pyramid Talent Training Project of BUCEA (No.JDYC20200327)the BUCEA Post Graduate Innovation Project (No.PG2022143)。
文摘A four-dimensional delay differential equations(DDEs)model of malaria with standard incidence rate is proposed.By utilizing the limiting system of the model and Lyapunov direct method,the global stability of equilibria of the model is obtained with respect to the basic reproduction number R_(0).Specifically,it shows that the disease-free equilibrium E^(0)is globally asymptotically stable(GAS)for R_(0)<1,and globally attractive(GA)for R_(0)=1,while the endemic equilibrium E^(*)is GAS and E^(0)is unstable for R_(0)>1.Especially,to obtain the global stability of the equilibrium E^(*)for R_(0)>1,the weak persistence of the model is proved by some analysis techniques.
