Periodic solutions of single-species models with periodic delay

A single-species population growth model is considered, where the growth rate response to changes in its density has a periodic delay. It is shown that if the self-inhibition rate is sufficiently large compared to the reproduction rate, then the model equation has a globally asymptotically stable positive periodic solution.

[1]  John Caperon,et al.  Time Lag in Population Growth Response of Isochrysis Galbana to a Variable Nitrate Environment , 1969 .

[2]  W. Gurney,et al.  Stability switches in distributed delay models , 1985 .

[3]  D. Cohen,et al.  Stable oscillations in single species growth models with hereditary effects , 1979 .

[4]  Periodic solutions of functional differential equations , 1970 .

[5]  Udo Halbach,et al.  Life Table Data and Population Dynamics of the Rotifer Brachionus calyciflorus Pallas as Influenced by Periodically Oscillating Temperature , 1973 .

[6]  Roger D. Nussbaum,et al.  Periodic solutions of some nonlinear, autonomous functional differential equations. II , 1973 .

[7]  Jim M Cushing,et al.  Integrodifferential Equations and Delay Models in Population Dynamics , 1977 .

[8]  Bo Zhang.  Boundedness in functional differential equations , 1994 .

[9]  J. Cushing.  Stable positive periodic solutions of the time-dependent logistic equation under possible hereditary influences , 1977 .

[10]  S. Lefschetz.  Contributions to the theory of nonlinear oscillations , 1950 .

[11]  William Gurney,et al.  Instability and complex dynamic behaviour in population models with long time delays , 1982 .

[12]  John Maynard Smith.  Models in ecology , 1974 .

[13]  Bernard D. Coleman,et al.  Nonautonomous logistic equations as models of the adjustment of populations to environmental change , 1979 .

[14]  Kondalsamy Gopalsamy,et al.  Global attractivity and oscillations in a periodic delay-logistic equation , 1990 .

[15]  H. Walther.  Existence of a non-constant periodic solution of a non-linear autonomous functional differential equation representing the growth of a single species population , 1975, Journal of mathematical biology.

[16]  T. Burton.  Uniform stabilities for Volterra equations , 1980 .

[17]  Robert M. May,et al.  Time delays, density-dependence and single-species oscillations , 1974 .

[18]  W. Kilmer,et al.  Oscillatory depletion models for renewable ecosystems , 1977 .

[19]  H. I. Freedman.  Deterministic mathematical models in population ecology , 1982 .

[20]  V. A. Pliss.  Nonlocal Problems of the Theory of Oscillations , 1966 .

[21]  E. M. Wright.  A non-linear difference-differential equation. , 1946 .

[22]  James A. Yorke,et al.  On the Stability of a Periodic Solution of a Differential Delay Equation , 1975 .

[23]  C. Wissel,et al.  Population dynamics of rotifers as bioassay tool for toxic effects of organic Pollutants: With 9 figures in the text , 1981 .

[24]  Gregory Dunkel.  Single species model for population growth depending on past history , 1968 .

[25]  Global stability in time-delayed single-species dynamics. , 1986, Bulletin of mathematical biology.

[26]  D. Jillson.  Insect populations respond to fluctuating environments , 1980, Nature.

[27]  Robert M. May,et al.  Time delays are not necessarily destabilizing , 1975 .

[28]  W. A. Horn.  Some fixed point theorems for compact maps and flows in Banach spaces. , 1970 .

[29]  The null space and the range of a convolution operator in a fading memory space , 1984 .

[30]  H. I. Freedman,et al.  ASYMPTOTIC BEHAVIOR OF A TIME-DEPENDENT SINGLE-SPECIES MODEL , 1989 .

[31]  Ying-Hen Hsieh,et al.  On the optimal choice of r for a population in a periodic environment , 1979 .