In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are...In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are also considered.in particular,the conditions for the existence of Hopf bifurcation can be given in terms of the coefficients of the characteristic equation.The method extends the application of the Hopf bifurcation theorem to higher differential equations which occur in biological models,chemical models,and epidemiological models etc.展开更多
A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population,infected with Ebola virus,on human-to-human transmission of Ebola Virus Disease(EVD)in a disease-free area.In view of t...A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population,infected with Ebola virus,on human-to-human transmission of Ebola Virus Disease(EVD)in a disease-free area.In view of the dynamics of Ebola virus disease,here,the infected class is supposed to be divided into subclasses,viz.primary and secondary infected.The proposed model is analyzed qualitatively using the stability theory of differential equations and quantitatively using numerical simulation.The obtained results,qualitatively and quantitatively,suggest that migration and contact rates play an important role in controlling the spreading of disease.Critical values for migration and contact rates are evaluated and it is revealed that if these rates go beyond their critical values,it leads to delay in the stabilization of the system.It is also found that primary reproductive number increases with increase in migration rate.Besides this,the approximate time required to attain stability of the disease model system is also determined.The model analysis recommends quarantining the noninfected from the secondary infected in order to control the spreading out of disease.展开更多
In this paper, supposing that the received signals at the input are of the formv（t）=s<sub>1</sub>[t, x<sub>1</sub>（t）]s<sub>2</sub>[t, x<sub>2</sub>（t）]+n（t） whe...In this paper, supposing that the received signals at the input are of the formv（t）=s<sub>1</sub>[t, x<sub>1</sub>（t）]s<sub>2</sub>[t, x<sub>2</sub>（t）]+n（t） where s<sub>i</sub> are FM signals （i=1, 2）, a novel cross-coupledphase-locked loop （CCPLL（M）） and its mathematical model are obtained. The globalqualitativestructural analysis of the mathematical model of the first-order loop, the acqui-sition region and synchronization region of the first-order loop, and the synchronizationregion of the second-order loop are obtained.展开更多
基金This project is supported by the National Science Foundation "Tian Yuan" Terms and LNM Institute of Mechanics Academy of ScienceThis project is supported by the NationalYunnan Province Natural Science Foundation of China
文摘In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are also considered.in particular,the conditions for the existence of Hopf bifurcation can be given in terms of the coefficients of the characteristic equation.The method extends the application of the Hopf bifurcation theorem to higher differential equations which occur in biological models,chemical models,and epidemiological models etc.
文摘A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population,infected with Ebola virus,on human-to-human transmission of Ebola Virus Disease(EVD)in a disease-free area.In view of the dynamics of Ebola virus disease,here,the infected class is supposed to be divided into subclasses,viz.primary and secondary infected.The proposed model is analyzed qualitatively using the stability theory of differential equations and quantitatively using numerical simulation.The obtained results,qualitatively and quantitatively,suggest that migration and contact rates play an important role in controlling the spreading of disease.Critical values for migration and contact rates are evaluated and it is revealed that if these rates go beyond their critical values,it leads to delay in the stabilization of the system.It is also found that primary reproductive number increases with increase in migration rate.Besides this,the approximate time required to attain stability of the disease model system is also determined.The model analysis recommends quarantining the noninfected from the secondary infected in order to control the spreading out of disease.
文摘In this paper, supposing that the received signals at the input are of the formv（t）=s<sub>1</sub>[t, x<sub>1</sub>（t）]s<sub>2</sub>[t, x<sub>2</sub>（t）]+n（t） where s<sub>i</sub> are FM signals （i=1, 2）, a novel cross-coupledphase-locked loop （CCPLL（M）） and its mathematical model are obtained. The globalqualitativestructural analysis of the mathematical model of the first-order loop, the acqui-sition region and synchronization region of the first-order loop, and the synchronizationregion of the second-order loop are obtained.
