论文信息 - Stability and bifurcation analysis on a Logistic model with discrete and distributed delays

Stability and bifurcation analysis on a Logistic model with discrete and distributed delays

In this paper, a Logistic model with discrete and distributed delays is investigated. We first consider the stability of the positive equilibrium and the existence of local Hopf bifurcations. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions. A numerical simulation for supporting the theoretical analysis is also given.

Yongli Song | Yahong Peng | Yongli Song | Yahong Peng

[1] Shui-Nee Chow,et al. Integral averaging and bifurcation , 1977 .

[2] S. Yau. Mathematics and its applications , 2002 .

[3] B. Hassard,et al. Theory and applications of Hopf bifurcation , 1981 .

[4] K. Gopalsamy. Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[5] Harlan W. Stech,et al. Hopf bifurcation calculations for functional differential equations , 1985 .

[6] Jack K. Hale,et al. Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[7] K. Cooke,et al. Discrete delay, distributed delay and stability switches , 1982 .

[8] G. Ladas,et al. Oscillation Theory of Delay Differential Equations: With Applications , 1992 .

[9] W. D. Evans,et al. PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[10] G.Stephen Jones,et al. The existence of periodic solutions of f′(x) = − αf(x − 1){1 + f(x)} , 1962 .