Periodic solutions for scalar functional differential equations

Suf ficient criteria are established f or the existence ofpositive periodic solutions ofscalar f tional differential equations, which improve and generalize some related results in the literature. The approach is based on the Krasnoselskii’s fixed point theorem. Numerical simulations are presented to support the analytical analysis. 2005 Elsevier Ltd. All rights reserved. MSC: 34K13; 92D25

[1]  Colin W. Clark,et al.  Mathematical Bioeconomics: The Optimal Management of Renewable Resources. , 1993 .

[2]  Jianhong Wu,et al.  Periodic solutions of single-species models with periodic delay , 1992 .

[3]  S. P. Blythe,et al.  Nicholson's blowflies revisited , 1980, Nature.

[4]  Shui-Nee Chow,et al.  Existence of periodic solutions of autonomous functional differential equations , 1974 .

[5]  Junjie Wei,et al.  Existence of positive periodic solutions for Volterra intergo-differential equations , 2001 .

[6]  Haiyan Wang Positive periodic solutions of functional differential equations , 2004 .

[7]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[8]  Lawrence F. Shampine,et al.  Solving ODEs with MATLAB , 2002 .

[9]  A. Nicholson,et al.  The Balance of Animal Populations.—Part I. , 1935 .

[10]  Yongkun Li,et al.  Existence and global attractivity of a positive periodic solution of a class of delay differential equation , 1998 .

[11]  Guang Zhang,et al.  Existence of Positive Periodic Solutions for Non-Autonomous Functional Differential Equations , 2001 .

[12]  Global attractivity in an RBC survival model of Wazewska and Lasota , 2002 .

[13]  Leo F. Boron,et al.  Positive solutions of operator equations , 1964 .

[14]  F. J. Richards A Flexible Growth Function for Empirical Use , 1959 .

[15]  M. Fan,et al.  Optimal harvesting policy for single population with periodic coefficients. , 1998, Mathematical biosciences.

[16]  Daqing Jiang,et al.  EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS , 2002 .

[17]  A. Nicholson,et al.  The Self-Adjustment of Populations to Change , 1957 .

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