Asymptotic Behavior of a Competition-Diffusion System with Variable Coefficients and Time Delays
Miguel Uh Zapata, Eric Avila Vales, and Angel G. Estrella
Source: J. Appl. Math. Volume 2008
(2008), Article ID
537284, 17 pages.
Abstract
A class of time-delay reaction-diffusion systems with variable coefficients which arise from the model of two competing ecological species is discussed. An asymptotic global attractor is established in terms of the variable coefficients, independent of the time delays and the effect of diffusion by the upper-lower solutions and iteration method.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jam/1220969291
Digital Object Identifier: doi:10.1155/2008/537284
Mathematical Reviews number (MathSciNet): MR2399308
Zentralblatt MATH identifier: 1149.35373
References
S. G. Ruan and X.-Q. Zhao, ``Persistence and extinction in two species reaction-diffusion systems with delays,'' Journal of Differential Equations, vol. 156, no. 1, pp. 71--92, 1999.
Mathematical Reviews (MathSciNet): MR1701810
Zentralblatt MATH: 0936.35092
Digital Object Identifier: doi:10.1006/jdeq.1998.3599
X. Lu, ``Persistence and extinction in a competition-diffusion system with time delays,'' The Canadian Applied Mathematics Quarterly, vol. 2, no. 2, pp. 231--246, 1994.
Mathematical Reviews (MathSciNet): MR1285911
Zentralblatt MATH: 0817.35043
S. A. Gourley and S. Ruan, ``Convergence and travelling fronts in functional differential equations with nonlocal terms: a competition model,'' SIAM Journal on Mathematical Analysis, vol. 35, no. 3, pp. 806--822, 2003.
Mathematical Reviews (MathSciNet): MR2048407
Zentralblatt MATH: 1040.92045
Digital Object Identifier: doi:10.1137/S003614100139991
W. Feng and F. Wang, ``Asymptotic periodicity and permanence in a competition-diffusion system with discrete delays,'' Applied Mathematics and Computation, vol. 89, no. 1--3, pp. 99--110, 1998.
Mathematical Reviews (MathSciNet): MR1491696
Zentralblatt MATH: 0968.35020
Digital Object Identifier: doi:10.1016/S0096-3003(97)81650-5
L. Zhou, Y. Tang, and S. Hussein, ``Periodic bifurcation solution for a delay competition diffusion system,'' Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 9, pp. 6073--6084, 2001.
Mathematical Reviews (MathSciNet): MR1970779
Zentralblatt MATH: 1042.35578
W. Feng and X. Lu, ``Harmless delays for permanence in a class of population models with diffusion effects,'' Journal of Mathematical Analysis and Applications, vol. 206, no. 2, pp. 547--566, 1997.
Mathematical Reviews (MathSciNet): MR1433956
Zentralblatt MATH: 0871.92030
Digital Object Identifier: doi:10.1006/jmaa.1997.5265
C. V. Pao, ``Global asymptotic stability of Lotka-Volterra 3-species reaction-diffusion systems with time delays,'' Journal of Mathematical Analysis and Applications, vol. 281, no. 1, pp. 186--204, 2003.
Mathematical Reviews (MathSciNet): MR1980084
Zentralblatt MATH: 1031.35071
C. V. Pao, ``Global asymptotic stability of Lotka-Volterra competition systems with diffusion and time delays,'' Nonlinear Analysis: Real World Applications, vol. 5, no. 1, pp. 91--104, 2004.
Mathematical Reviews (MathSciNet): MR2004088
Zentralblatt MATH: 1066.92054
Digital Object Identifier: doi:10.1016/S1468-1218(03)00018-X
Y. Wang and Y. Meng, ``Asymptotic behavior of a competition-diffusion system with time delays,'' Mathematical and Computer Modelling, vol. 38, no. 5-6, pp. 509--517, 2003.
Mathematical Reviews (MathSciNet): MR2007621
Zentralblatt MATH: 1078.35135
Digital Object Identifier: doi:10.1016/S0895-7177(03)90023-9
J. Wu and X.-Q. Zhao, ``Diffusive monotonicity and threshold dynamics of delayed reaction diffusion equations,'' Journal of Differential Equations, vol. 186, no. 2, pp. 470--484, 2002.
Mathematical Reviews (MathSciNet): MR1942218
Zentralblatt MATH: 1022.35082
Digital Object Identifier: doi:10.1016/S0022-0396(02)00012-8
B. Shi and Y. Chen, ``A prior bounds and stability of solutions for a Volterra reaction-diffusion equation with infinite delay,'' Nonlinear Analysis: Theory, Methods & Applications, vol. 44, no. 1, pp. 97--121, 2001.
Mathematical Reviews (MathSciNet): MR1815694
Zentralblatt MATH: 0981.35095
C. V. Pao, ``Systems of parabolic equations with continuous and discrete delays,'' Journal of Mathematical Analysis and Applications, vol. 205, no. 1, pp. 157--185, 1997.
Mathematical Reviews (MathSciNet): MR1426986
Zentralblatt MATH: 0880.35126
Digital Object Identifier: doi:10.1006/jmaa.1996.5177
C. V. Pao, Nonlinear Parabolic and Elliptic Equations, New York, NY, USA, Plenum Press, 1992.
Mathematical Reviews (MathSciNet): MR1212084
Zentralblatt MATH: 0777.35001
Journal of Applied Mathematics
