Stability and bifurcation of a discrete red blood cell survival model

A kind of a discrete red blood cell survival model obtained by Euler method is investigated. Firstly, the linear stability of the model is studied. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived by using the normal form method and center manifold theorem. Finally, computer simulations are performed to illustrate the analytical results found.

[1]  Toshiyuki Koto.  Naimark-Sacker Bifurcations in the Euler Method for a Delay Differential Equation , 1999 .

[2]  Ricard V. Solé,et al.  Control, synchrony and the persistence of chaotic populations , 2001 .

[3]  José Manuel Gutiérrez,et al.  Chaos suppression through changes in the system variables and numerical rounding errors , 1996 .

[4]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[5]  S. Ruan,et al.  On the zeros of transcendental functions with applications to stability of delay differential equations with two delays , 2003 .

[6]  H. El-Owaidy,et al.  Asymptotic behaviour of the chemostat model with delayed response in growth , 2002 .

[7]  Mingshu Peng,et al.  The use of the Euler method in identification of multiple bifurcations and chaotic behavior in numerical approximation of delay-differential equations ☆ , 2004 .

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

[9]  Mingzhu Liu,et al.  Hopf bifurcation in numerical approximation of a class delay differential equations , 2003, Appl. Math. Comput..

[10]  Neville J. Ford,et al.  Numerical Hopf bifurcation for a class of delay differential equations , 2000 .

[11]  Chunrui Zhang,et al.  Hopf bifurcation in numerical approximation of a n-dimension neural network model with multi-delays , 2005 .

[12]  K. Gopalsamy,et al.  Almost Periodic Solutions of Lasota–Wazewska-type Delay Differential Equation , 1999 .

[13]  Neville J. Ford,et al.  The Use of Boundary Locus Plots in the Identification of Bifurcation Points in Numerical Approximati , 1998 .

[14]  Mustafa R. S. Kulenovic,et al.  Global attractivity in population dynamics , 1989 .