A Single Species Model with Symmetric Bidirectional Impulsive Diffusion and Dispersal Delay

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References

[1] Z. Teng and Z. Lu, “The Effect of Dispersal on SingleSpecies Nonautonomous Dispersal Models with Delays,” Journal of Mathematical Biology, Vol. 42, No. 5, 2001, pp. 439-454. doi:10.1007/s002850000076

[2] Z. Teng and L. Chen, “Permanence and Extinction of Periodic Predator-Prey Systems in a Patchy Environment with Delay,” Nonlinear Analysis: Real World Applications, Vol. 4, No. 2, 2003, pp. 335-364.
doi:10.1016/S1468-1218(02)00026-3

[3] L. Buttel, R. Durrett and S. Levin, “Competition and Species Packing in Patchy Environments,” Theoretical Population Biology, Vol. 61, No. 3, 2002, pp. 265-276.
doi:10.1006/tpbi.2001.1569

[4] J. Cui, Y. Takeuchi and Z. Lin, “Permanence and Extinction for Dispersal Population Systems,” Journal of Mathematical Analysis and Applications, Vol. 298, No. 1, 2004, pp. 73-93. doi:10.1016/j.jmaa.2004.02.059

[5] Y. Takeuchi, “Diffusion Effect on Stability of LotkaVolterra Models,” Bulletin of Mathematical Biology, Vol. 48, No. 5-6, 1986, pp. 585-601.

[6] Y. Takeuchi, J. Cui, R. Miyazak and Y. Saito, “Permanence of Delayed Population Model with Dispersal Loss,” Mathematical Biosciences, Vol. 201, No. 1-2, 2006, pp. 143-156. doi:10.1016/j.mbs.2005.12.012

[7] E. Beretta and Y. Takeuchi, “Global Stability of SingleSpecies Diffusion Volterra Models with Continuous Time Delays,” Bulletin of Mathematical Biology, Vol. 49, 1987, pp. 431-448.

[8] E. Beretta and Y. Takeuchi, “Global Asymptotic Stability of Lotka-Volterra Diffusion Models with Continuous Time Delays,” SIAM Journal on Applied Mathematics, Vol. 48, No. 3, 1998, pp. 627-651. doi:10.1137/0148035

[9] E. Beterra, P. Fergola and C. Tenneriello, “Ultimate Boundedness of Nonautonomous Diffusive Lotka-Volterra Patches,” Mathematical Biosciences, Vol. 92, No. 1, 1988, pp. 29-53. doi:10.1016/0025-5564(88)90004-1

[10] H. I. Freedman, J. Shukla and Y. Takeuchi, “Population Diffusion in a Two-Patch Environment,” Mathematical Biosciences, Vol. 95, No. 1, 1989, pp. 111-123.
doi:10.1016/0025-5564(89)90055-2

[11] A. Hastings, “Dynamics of a Single Species in a Spatially Varying Environment: The Stability Role of High Dispersal Rates,” Journal of Mathematical Biology, Vol. 16, No. 1, 1982, pp. 49-55. doi:10.1007/BF00275160

[12] W. Wang and L. Chen, “Global Stability of a Population Dispersal in a Two-Patch Environment,” Dynamic Systems & Applications, Vol. 6, 1997, pp. 207-216.

[13] L. Zhang and Z. Teng, “Permanence for a Class of Periodic Time-Dependent Competitive System with Delays and Dispersal in a Patchy-Environment,” Applied Mathematics and Computation, Vol. 188, No. 1, 2007, pp. 855-864. doi:10.1016/j.amc.2006.10.037

[14] L. Zhang and Z. Teng, “Permanence for a Delayed Periodic Predator-Prey Model with Prey Dispersal in MultiPatches and Predator Density-Independent,” Journal of Mathematical Analysis and Applications, Vol. 338, No. 1, 2008, pp. 175-193.
doi:10.1016/j.jmaa.2007.05.016

[15] E. Beretta, F. Solimano and Y. Takeuchi, “Global Stability and Periodic Orbits for Two Patch Predator-Prey Diffusion-Delay Models,” Mathematical Biosciences, Vol. 85, No. 2, 1987, pp. 153-183.
doi:10.1016/0025-5564(87)90051-4

[16] R. Mahbuba and L. Chen, “On the Nonautonomous Lotka-Volterra Competion System with Diffusion,” Differential Equations and Dynamical Systems, Vol. 2, 1994, pp. 243-253.

[17] J. G. Skellam, “Random Dispersal in Theoretical Population,” Biometrika, Vol. 38, 1951, pp. 196-218.

[18] J. Hui and L. Chen, “A Single Species Model with Impulsive Diffusion,” Acta Mathematicae Applicatae Sinica. English Series, Vol. 21, No. 1, 2005, pp. 43-48.
doi:10.1007/s10255-005-0213-3

[19] L. Wang and L. Chen, “Impulsive Diffusion in Single Species Model,” Chaos Solitons, Fractals, Vol. 33, No. 4, 2007, pp. 1213-1219. doi:10.1016/j.chaos.2006.01.102

[20] A. Lakmeche and O. Arino, “Bifurcation of Nontrivial Periodic Solution of Impulsive Differential Equations Arising Chemotherapeutic Treatment,” Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 7, 2000, pp. 265-287.

[21] L. Zhang and Z. Teng, “N-Species Non-Autonomous Lotka-Volterra Competitive Systems with Delays and Impulsive Perturbations,” Nonlinear Analysis: Real World Applications, Vol. 12, No. 6, 2011, pp. 3152-3169.
doi:10.1016/j.nonrwa.2011.05.015

[22] J. Vandermeer, L. Stone and B. Blasius, “Categories of Chaos and Fractal Basin Boundaries in Forced Predator-Preymodels,” Chaos Solitons, Fractals, Vol. 12, No. 2, 2001, pp. 265-276. doi:10.1016/S0960-0779(00)00111-9

[23] L. Dong, L. Chen and L. Sun, “Optimal Harvesting Policy for Inshore-Offshore Fishery Model with Impulsive Diffusion,” Acta Mathematica Scientia, Vol. 27, No. 2, 2007, pp. 405-412. doi:10.1016/S0252-9602(07)60040-X

[24] Z. Zhao, X. Zhang and L. Chen, “The Effect of Pulsed Harvesting Policy on the Inshore-Offshore Fishery Model with the Impusive Diffusion,” Nonlinear Dynamic, Vol. 63, No. 4, 2011, pp. 537-545.
doi:10.1007/s11071-009-9527-7

[25] Y. Kuang, “Delay Differential Equations with Applications in Population Dynamics,” Academic Press, New York, 1993.

[26] X. Zhao, “Dynamical Systems in Population Biology,” Springer-Verlag, New York, 2003.

[27] H. L. Smith, “Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems,” Mathematical Surveys and Monographs, Vol. 41, 1995.

[28] X. Zhao, “Global Attractivity in a Class of Non-Monotone Reaction? Diffusion Equations with Time Delay,” Canadian Applied Mathematics Quarterly, Vol. 17, 2009, pp. 271-281.

[29] X. Meng and L. Chen, “Permanence and Global Stability in an Impulsive Lotka-Volterra N-Species Competitive System with Both Discrete Delays and Continuous Delays,” International Journal of Biomathematics, Vol. 1, No. 2, 2008, pp. 179-196.
doi:10.1142/S1793524508000151

[30] H. L. Smith, “Cooperative Systems of Differential Equations with Concave Nonlinearities,” Nonlinear Analysis: Theory, Methods & Applications, Vol. 10, 1986, pp. 1037-1052.

[31] V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, “Theory of Impulsive Differential Equations,” World Scientific, Singapore, 1989.

[32] D. Bainov and P. Simeonov, “Impulsive Differential Equations: Periodic Solutions and Applications,” Longman, England, 2003.