References
- D. Alonso, F. Bartumeus and J. Catalan, Mutual interference between predators can give rise to Turing spatial patterns, Ecology, 83(1)(2002), 28-34. https://doi.org/10.1890/0012-9658(2002)083[0028:MIBPCG]2.0.CO;2
- R. M. Anderson and R. M. May, The population dynamics of microparasites and their invertebrate hosts, Phil. Tran. R. Soc. Lond. B, 291(1981), 451-524. https://doi.org/10.1098/rstb.1981.0005
- H. Baek, On the dynamical behavior of a two-prey one-predator system with two-type functional responses, Kyungpook Math. J., 53(4)(2013), 647-660. https://doi.org/10.5666/KMJ.2013.53.4.647
- H. Baek, Spatiotemporal Dynamics of a Predator-Prey System with Linear Harvesting Rate, Math. Probl. Eng., (2014), Art. ID 625973, 9 pp.
- M. Baurmann, T. Gross and U. Feudel, Instabilities in spatially extended predator-prey systems : Spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations, J. Theoret. Biol., 245(2007), 220-229. https://doi.org/10.1016/j.jtbi.2006.09.036
- I. Berenstein, M. Dolnik, L. Yang, A. M. Zhabotinsky, and I. R. Epstein, Turing pattern formation in a two-layer system: Superposition and superlattice patterns, Physical Review E, 70(2004), 046219. https://doi.org/10.1103/PhysRevE.70.046219
- B. I. Camara and M. A. Aziz-Alaoui, Turing and Hope patterns formation in a predator-prey model with Leslie-Gower-type functional response, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Algorithms and Applications, 16(2009), 479-488.
- D. Ebert, M. Lipsitch and K. L. Mangin, The effect of parasites on host population density and extinction: experimental epidemiology with Daphnia and six microparasites, Am. Nat., 156(2000), 459-477. https://doi.org/10.1086/303404
- M. R. Garvie, Finite-Difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB, Bull. Math. Biol., 69(2007), 931-956. https://doi.org/10.1007/s11538-006-9062-3
- D. A. Garzon-Alvarado, C. H. Galeano and J. M. Mantilla, Turing pattern formation for reaction-convection-diffusion systems in fixed domains submitted to toroidal velocity fields, Appl. Math. Model., 35(2011), 4913-4925. https://doi.org/10.1016/j.apm.2011.03.040
- J. Hale and H. Kocak, Dynamics and bifurcations, Springer-Verlag, New York, 1991.
- T.-W. Hwang and Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol., 46(2003), 17-30. https://doi.org/10.1007/s00285-002-0165-7
- I. Kozlova, M. Singh, A. Easton and P. Ridland, Twospotted spider mite predator-prey model, Math. Comput. Model., 42(2005), 1287-1298. https://doi.org/10.1016/j.mcm.2005.01.036
- L. Li, Patch invasion in a spatial epidemic model, Appl. Math. Comput., 258(2015), 342-349. https://doi.org/10.1016/j.amc.2015.02.006
- L. Li and Z. Jin, Pattern dynamics of a spatial predator-prey model with noise, Nonliear Dynam., 67(3)(2012), 1737-1744. https://doi.org/10.1007/s11071-011-0101-8
- J. Li, Y. Xiao and Y. Yang, Global analysis of a simple parasite-host model with homoclinic orbits, Math. Biosci. Eng., 9(4)(2012), 767-784. https://doi.org/10.3934/mbe.2012.9.767
- A. B. Medvinsky, S. V. Petrovskii, I. A. Tikhonova, H. Malchow and B.-L. Li, Spatiotemporal complexity of plankton and fish dynamics, SIAM Rev., 44(3)(2002), 311-370. https://doi.org/10.1137/S0036144502404442
- F. Rao, W. Wang and Z. Li, Spatiotemporal complexity of a predator-prey system with the effect of noise and external forcing, Chaos, Solitons Fractals, 41(2009), 1634-1644. https://doi.org/10.1016/j.chaos.2008.07.005
- M. J. Smith, J. D. M. Rademacher and J. A. Sherratt, Absolutes stability of wavetrains can explain spatiotemporal dynamics in reaction-diffusion systems of lambda-omega type, SIAM J. Appl. Dyn. Syst., 8(3)(2009), 1136-1159. https://doi.org/10.1137/090747865
- M. J. Smith, J. A. Sherratt, The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction-diffusion systems, Physica D, 236(2007), 90-103. https://doi.org/10.1016/j.physd.2007.07.013
- K. Wang and Y. Kuang, Fluctuation and extinction dynamics in host-microparasite systems, Commun. Pure Appl. Anal., 10(5)(2011), 1537-1548. https://doi.org/10.3934/cpaa.2011.10.1537
- W. Wang, W. Li, Z. Li and H. Zhang, The effect of colored noise on spatiotemporal dynamics of biological invasion in a diffusive predator-prey system, Biosystems, 104(2011), 48-56. https://doi.org/10.1016/j.biosystems.2010.12.011
- W. Wang, Q.-X. Liu and Z. Jin, Spatiotemporal complexity of a ratio-dependent predator-prey system, Phys. Rev. E, 75(2007), 051913, 9 pp. https://doi.org/10.1103/PhysRevE.75.051913
- Y. Wang, J. Wang and L. Zhang, Cross diffusion-induced pattern in an SI model, Appl. Math. Comput., 217(2010), 1965-1970. https://doi.org/10.1016/j.amc.2010.06.052
- W. Wang, L. Zhang, H. Wang and Z. Li, Pattern formation of a predator-prey system with Ivlev-type functional response, Ecological Modelling, 221(2010), 131-140. https://doi.org/10.1016/j.ecolmodel.2009.09.011
- L. Yang, M. Dolnik, A. M. Zhabotinsky and I. R. Epstein, Pattern formation arising from interactions between Turing and wave instabilities, J. Chem. Phys., 117(15)(2002), 7259-7265. https://doi.org/10.1063/1.1507110
- Z. F. Zhang, T. R. Ding, W. Z. Huang, Zh. X. Dong, Qualitative theory of differential equations, Translations of Mathematical Monographs 101, AMS, Providence, RI, 1992.