Periodic solution and oscillation in a competition model with diffusion and distributed delay effects

Nonlinear Analysis, Theory, Methods and Applications

Volumn 27, Issue 6, 1996, Pages 699-709

  Lu, Xin ^a   Feng, Wei ^a  

^a UNIVERSITY OF NORTH CAROLINA WILMINGTON   (United States)

Author keywords

Periodic solutions; Population dynamics; Reaction diffusion systems; Stability and asymptotic behavior; Time delays

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; DYNAMICS; EIGENVALUES AND EIGENFUNCTIONS; FINITE DIFFERENCE METHOD; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; TIME VARYING CONTROL SYSTEMS;

COMPETITION DELAY SYSTEM; DIRICHLET BOUNDARY CONDITIONS; DISTRIBUTED DELAY EFFECTS MODELING; GLOBAL STABILITY; HOLDER CONTINUOUS FUNCTIONS; MONOTONE ITERATIVE SCHEME; PERIODIC SOLUTIONS; POPULATION DYNAMICS; REACTION DIFFUSION SYSTEMS; TIME DELAYS;

EQUATIONS OF MOTION;

EID: 0030241483     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(95)00067-6     Document Type: Article

References (22)

1. AHMAD S. & LAZER A. C., Asymptotic behaviour of solutions of periodic competition diffusion systems, Non-linear Analysis 13, 263-283 (1989).
2. CANTRELL R. S. & COSNER C., Practical persistence in ecological models via comparison methods, preprint.
3. HESS P., Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Research Notes in Mathematics Series, Vol. 247. Pitman, New York (1991).
4. MORGAN J. J. & HOLLIS S. L., The existence of periodic solutions to reaction-diffusion systems with periodic data, SIAM J. math Analysis (to appear).
5. MOTTONI DE P. & SCHIAFFINO A., Competition systems with periodic coefficients: A geometrical approach, J. math. Biol. 11, 319-335 (1981).
6. CUSHING J. M., Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomath., No. 20. Springer, Berlin.
7. WEI FENG & XIN LU, Asymptotic periodicity in logistic equations with discrete delays, Nonlinear Analysis 26(2), 171-178 (1996).
8. GOPALSAMY K. & PEI-XUAN WENG, Global attractivity and "level crossings" in a periodic partial integrodifferential equation, Houston J. Math. 18, 551-575 (1992).
9. GOPALSAMY K., XUE-ZHONG HE & DA-QING SUN, Oscillations and covergence in a diffusive delay logistic equation, Math. Nachr. 164, 219-237 (1993).
10. YANG KUANG, Delay Differential Equations with Applications in Population Dynamics. Academic Press, New York (1993).
11. LENHART S. M. & TRAVIS C. C., Global stability of a biological model with time delay, Proc. Am. math. Soc. 96(1), 75-58 (1986).
12. XIN LU, Persistence and extinction in a competition-diffusion system with time delays, Can. Appl. math. Quart. 2(2), 231-246 (1994).
13. LUCKHAUS S., Global boundedness for a delay differential equation, Trans. Am. math. Soc. 294(2), 767-774 (1986).
14. SEIFERT G., On a delay-differential equation for single species population variations, Nonlinear Analysis, 11(9), 1051-1059 (1987).
15. ZHANG B. G. & GOPALSAMY K., Global attractivity and oscillations in a periodic delay-logistic equation, J. math. Analysis. Applic. 150, 274-283 (1990).
16. WIENER J. & COOKE K. L., Oscillations in systems of differential equations with piecewise constant arguments, J. math. Analysis Applic. 137, 221-239 (1989).
17. PAO C. V., On Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York (1992).
18. WEI FENG, Coexistence, stability, and limiting behavior in a one-predator-two-prey model, J. math. Analysis Applic. 179(2), 592-609 (1993).
19. WEI FENG & XIN LU, Some coexistence and extinction results for a three-species ecological system, Diff. Integral Eqns 8, 617-626 (1995).
20. XIN LU, Monotone method and convergence acceleration for finite difference solutions of parabolic problems with time delays, Numer. Meth. part. diff. Eqns (to appear).
21. XIN LU & WEI FENG, Dynamics and numerical simulations of foodchain populations, Appl. Math. Comp. 65, 335-344 (1994).
22. PAO C. V., Numerical methods for semilinear parabolic equations, SIAM J. numer. Analysis 24, 24-35 (1987).