Existence of Multiple Positive Periodic Solutions of Delayed Predator-Prey Models with Functional Responses

In this paper, by applying the continuation theorem of coincidence degree theory, we establish some new criteria for the existence of multiple positive periodic solutions for the delayed predator-prey model.x^'(t)=x(t)(r(t)-a(t)x(t))-b(t)f(x(t))y(t),y^'(t)=y(t)(c(t)f(x([email protected]))-d(t)), when functional response function f is monotonic or nonmonotonic.

[1]  S. Hsu,et al.  Global analysis of the Michaelis–Menten-type ratio-dependent predator-prey system , 2001, Journal of mathematical biology.

[2]  Yang Kuang,et al.  Global qualitative analysis of a ratio-dependent predator–prey system , 1998 .

[3]  Yuming Chen,et al.  Multiple periodic solutions of delayed predator–prey systems with type IV functional responses , 2004 .

[4]  Dongmei Xiao,et al.  Multiple Bifurcations in a Delayed Predator–prey System with Nonmonotonic Functional Response , 2022 .

[5]  Wan-Tong Li,et al.  Periodic solutions of delayed ratio-dependent predator–prey models with monotonic or nonmonotonic functional responses , 2004 .

[6]  A. Bush,et al.  The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater. , 1976, Journal of theoretical biology.

[7]  Y. Kuang,et al.  Global analyses in some delayed ratio-dependent predator-prey systems , 1998 .

[8]  Alan A. Berryman,et al.  The Orgins and Evolution of Predator‐Prey Theory , 1992 .

[9]  Yang Kuang,et al.  Periodic Solutions of Periodic Delay Lotka–Volterra Equations and Systems☆ , 2001 .

[10]  W. Sokol,et al.  Kinetics of phenol oxidation by washed cells , 1981 .

[11]  Christian Jost,et al.  About deterministic extinction in ratio-dependent predator-prey models , 1999 .

[12]  Li Yongkun,et al.  PERIODIC SOLUTIONS OF A PERIODIC DELAY PREDATOR-PREY SYSTEM , 1999 .

[13]  Ke Wang,et al.  Periodicity in a Delayed Ratio-Dependent Predator–Prey System☆☆☆ , 2001 .

[14]  Shigui Ruan,et al.  Global Analysis in a Predator-Prey System with Nonmonotonic Functional Response , 2001, SIAM J. Appl. Math..

[15]  John F. Andrews,et al.  A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates , 1968 .

[16]  R. Gaines,et al.  Coincidence Degree and Nonlinear Differential Equations , 1977 .