Rocky Mountain Journal of Mathematics

Some Global Qualitative Analyses of a Single Species Neutral Delay Differential Population Model

H.I. Freedman and Yang Kuang

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 25, Number 1 (1995), 201-215.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181072278

Digital Object Identifier
doi:10.1216/rmjm/1181072278

Mathematical Reviews number (MathSciNet)
MR1340003

Zentralblatt MATH identifier
0831.34074

Subjects
Primary: 34K15
Secondary: 34K20: Stability theory 92A15

Keywords
Neutral delay differential equation single species population model global stability

Citation

Freedman, H.I.; Kuang, Yang. Some Global Qualitative Analyses of a Single Species Neutral Delay Differential Population Model. Rocky Mountain J. Math. 25 (1995), no. 1, 201--215. doi:10.1216/rmjm/1181072278. https://projecteuclid.org/euclid.rmjm/1181072278


Export citation

References

  • J.M. Cushing, Integrodifferential equations and delay models in population dynamics, Lect. Notes in Biomath. 20, Springer, New York-Berlin, 1977.
  • J.C.F. De Oliveira, Hopf bifurcation for functional differential equations, Nonlinear Anal. 4 (1980), 217 -229.
  • H. I. Freedman, Deterministic mathematical models in population ecology, Marcel Dekker, New York, 1980.
  • H.I. Freedman and K. Gopalsamy, Global stability in time delayed single species dynamics, Bull. Math. Biol. 48 (1986), 485-492.
  • H.I. Freedman and Y. Kuang, Stability switches in linear scalar neutral delay equations, Funkcial. Ekvac. 34 (1991), 187-209.
  • K. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics, Kluwer Academic Publisher, Boston, 1992.
  • K. Gopalsamy, X. He and L. Wen, On a periodic neutral logistic equation, Glasgow Math. J. 33 (1991), 281-286.
  • K. Gopalsamy and B.G. Zhang, On a neutral delay logistic equation, Dynamical Stability Systems 2 (1988), 183-195.
  • I. Gyori and J. Wu, A neutral equation arising from compartmental systems with pipes, J. Dynamics Differential Equations 3 (1991), 289-311.
  • J.R. Haddock and Y. Kuang, Asymptotic theory for a class of nonautonomous delay differential equations, J. Math. Anal. Appl., to appear.
  • J.K. Hale, Theory of functional differential equations, Springer-Verlag, New York-Berlin, 1977.
  • G.E. Hutchinson, Circular causal systems in ecology, Ann. N.Y. Acad. Sci. 50 (1948), 221-246.
  • Y. Kuang, On neutral delay logistic Gause-type predator-prey systems, Dynamics Stability Systems 6 (1991), 173-189.
  • --------, On neutral delay two-species Lotka-Volterra competitive systems, J. Austral. Math. Soc. 32 (1991), 311-326.
  • --------, Qualitative analysis of one or two species neutral delay population models, SIAM J. Math. Anal. 23 (1992), 181-200.
  • --------, Global stability in one or two species neutral delay population models, Canad. Appl. Math. Quart. 1 (1993), 23-45.
  • Y. Kuang and A. Feldstein, Boundedness of solutions of nonlinear nonautonomous neutral delay equations, J. Math. Anal. Appl. 156 (1991), 193-204.
  • Y. Kuang and H.L. Smith, Global stability for infinite delay Lotka-Volterra type systems, J. Differential Equations 103 (1993), 221-246.
  • --------, Convergence in Lotka-Volterra type delay systems without instantaneous feedbacks, Proc. Roy. Soc. Edinburgh Sect. A 123A (1993), 45-58.
  • O.J. Staffans, Hopf bifurcation for functional and functional differential equations with infinite delay, J. Differential Equations 70 (1987), 114-151.
  • J. Wu and H.I. Freedman, Monotone semiflows generated by neutral functional differential equations with application to compartmental systems, Canad. J. Math. 43 (1991), 1098-1120.