Periodicity in A Predator-Prey System with Hassell-Varley Type Functional Response on Time Scales

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ZENG Zhi-jun(School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024 China)
Journal Title:
Journal of Biomathematics
Volume 27, Issue 01, 2012
Key Word:
Time scales;Hassell-Varley type;Continuation theorem;Periodic solution;Functional response

Abstract´╝Ü In this paper,by using the continuation theorem of coincidence degree theory,sufficient conditions are obtained for the existence of positive periodic solution for non-autonomous predator-prey systems with Hassell-Varley type functional response.Our results substantially extend some known criteria.

  • [1]Pathak S,Maitib A,Samanta G P.Rich dynamics of a food chain model with Hassell-Varley type functional responses[J].Applied Mathematics and Computation,2009,208(2):303-317.
  • [2]Fan M,Wang Q,Zou X F.Dynamics of a non-autonomous ratio-dependent predator-prey system[J].Proceedings of the Royal Society of Edinburgh:Section A Mathematics,2003,133(1):97-118.
  • [3]Hsu S B,Huang T W,Kuang Y.Global qualitative of a predator-prey model with Hassell-Varley type functional response[J].Discrete and continuous dynamical systems,Series B,2008,10(4):857-871.
  • [4]Hassell M P,Varley G C.New inductive population model for insect parasites and its bearing on biological control[J].Nature (London),1969,233(5211):1133-1137.
  • [5]Arditi R,Ginzburg L R.Coupling in predator-prey dynamics:ratio-dependence[J].Journal of Theoretical Biology,1989,139(3):311-326.
  • [6]Freedman H I.Deterministic Mathematical Models in Population Ecology[M].New York:Marcel Dekker,1980.
  • [7]Bohner M,Fan M,Zhang J M.Peridicity of scalar dynamic equations and applications to population models[J].Journal of Mathematical Analysis and Applications,2007,330(1):1-9.
  • [8]Bohner M,Fan M,Zhang J M.Existence of periodic solutions in predator-prey and competition dynamic systems[J].Nonlinear Analysis:Real World Applications,2006,7(5):1193-1204.
  • [9]Zhang W P,Bi P,Zhu D M.Periodicity in a ratio-dependent predator-prey system with stage-structured predator on time scales[J].Nonlinear Analysis:Real World Applications,2008,9(2):344-353.
  • [10]Hilger S.Analysis on measure chains-a unified approach to continuous and discrete calculus[J].Results in Mathematics,1990,18(1-2):18-56.
  • [11]Aulbach B,Hilger S.Linear dynamical processes with inhomogeneous time scale[M].Nonlinear dynamics and quantum dynamical systems,Berlin:Akademie Verlag,1990.
  • [12]Bohner M,Peterson A.Dynamic Equations on Time Scales:An Introduction with Application[M].Boston:Birkh(a)user,2001.
  • [13]Gaines R E,Mawhin J L.Coincidence Degree and Nolinear Differential Equations[M].New York:SpringerVerlag,1977.
  • [14]Zhao L C,Zhang Q L,Yang Q C.Dissipation control of three species food chain systems[J].Journal of Biomathematics,2003,18(1):82-92.
  • [15]Ye D,Fan M,Zhang W P.Existence of positive periodic solution of a predator-prey system[J].Journal of Biomathematics,2004,19(2):161-168.
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