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  • 1990-1994  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Hopf bifurcation and other dynamical behaviors for a fourth order differential equation in models of infectious disease (1994)
    Springer
    Acta mathematicae applicatae sinica 10 (1994), S. 401-410 
    Details
    ISSN: 1618-3932
    Keywords: Model of infections disease ; existence and stability of equilibria ; Hopf bifurcation value ; periodic solutions of Hopf type
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Periodic solutions of Hopf type and other dynamical behaviors for a four-order differential equation which occurs in the model of infections disease are investigated. The extended theorem about the conditions for the existence of Hopf bifurcation is proved in higher-order differential equations with several parameters. The Hopf bifurcation value is given through the medium of the corresponding coordinate at the Hopf bifurcation point, and depends on one parameter. The paper reveals that the model of Holt and Picker has periodic solutions, and proves the reliability of the numerical solution which is given by Liu Winmin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02016330
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Qualitative analysis for a mathematical model of aids (1993)
    Springer
    Acta mathematicae applicatae sinica 9 (1993), S. 302-316 
    Details
    ISSN: 1618-3932
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02005919
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    Paper (German National Licenses)
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