참고문헌
- E. Baker, E. A. Gaffney, and P. K. Maini, Partial differential equations for self-organization in cellular and developmental biology, Nonlinearity 21 (2008), no. 11, 251-290. https://doi.org/10.1088/0951-7715/21/11/R05
- M. Banerjee and L. Zhang, Influence of discrete delay on pattern formation in a ratio-dependent prey-predator model, Chaos, Soliton Fractals 67 (2014), 73-81. https://doi.org/10.1016/j.chaos.2014.06.012
- Q. Y. Bie, Q. R. Wang, and Z. A. Yao, Cross-diffusion induced instability and pattern formation for a Holling type-II predator-prey model, Appl. Math. Comput. 247 (2014), 1-12. https://doi.org/10.1016/j.amc.2014.08.088
- W. Z. Gan, P. Zhu, and J. Bao, Cross-diffusion induced instability in Lvlev-Tanner model, Int. J. Biomath. 4 (2011), no. 4, 431-442. https://doi.org/10.1142/S1793524511001301
- D. Horstmann, Remarks on some Lotka-Volterra type cross-diffusion models, Nonlinear Anal. Real World Appl. 8 (2007), no. 1, 90-117. https://doi.org/10.1016/j.nonrwa.2005.05.008
- K. Kishimoto and H. F.Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains, J. Differential Equations 58 (1985), no.1, 15-21. https://doi.org/10.1016/0022-0396(85)90020-8
- X. Lian, H. Wang, andW. Wang, Delay-driven pattern formation in a reaction-diffusion predator-prey model incorporating a prey refuge, J. Stat. Mech. Theory Exp. (2013), no. 4, P04006, 16 pp.
- X. Z. Lian, S. L. Yan, and H. L. Wang, Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion, Abstr. Appl. Anal. 2013 (2013), Art. ID 147232, 10 pp.
- A. Madzvamuse and R. Barreia, Exhibiting cross-difussion-induced patterns for reaction-diffusion systems on evolving domains and surfaces, Phys. Rev. E 90 (2014), 043307. https://doi.org/10.1103/PhysRevE.90.043307
- J. D. Murray, Mathematical Biology, Vol 19. Biomathematics Texts, Springer, Berlin, 1993.
- K. J. Painter, P. K. Maini, and H. G. Othmer, Development and applications of a model for cellular response to multiple chemotactic cues, J. Math. Biol. 41 (2000), no. 4, 285-314. https://doi.org/10.1007/s002850000035
- P. Y. H. Pang and M. X. Wang, Strategy and stationary pattern in a three-species predator-prey model, J. Differential Equations 200 (2004), no. 2, 245-273. https://doi.org/10.1016/j.jde.2004.01.004
- S. Sen, P. Ghosh, S. S. Riaz, and D. S. Ray, Time-delay-induced instabilities in reaction diffusion system, Phys. Rev. E 80 (2009), 046212. https://doi.org/10.1103/PhysRevE.80.046212
- J. P. Shi, Z. F. Xie, and K. Little, Cross-diffusion induced instability and stability in reactiond-diffusions systems, J. Appl. Anal. Comput. 24 (2010), 95-119.
- C. R. Tian, Delay-driven spatial patterns in a plankton allelopathic system, Chaos 22 (2012), 013129. https://doi.org/10.1063/1.3692963
- C. R. Tian and L. Zhang, Delay-driven irregular spatiotemporal patterns in a plankton system, Phys. Rev. E 88 (2013), 012713.
- C. R. Tian and L. Zhang, Hopf bifurcation analysis in a diffusive food-chain model with time delay, Comput. Math. Appl. 66 (2013), no. 10, 2139-2153. https://doi.org/10.1016/j.camwa.2013.09.002
- C. R. Tian, L. Zhang, and Z. G. Lin, Pattern formation for a model of plankton allelopathy with cross-diffusion, J. Franklin Inst. 348 (2011), no. 8, 1947-1964. https://doi.org/10.1016/j.jfranklin.2011.05.013
- A. M. Turing, The chemical basisi of morphogenesis, Phil. Trans. London Ser. B 237 (1952), 37-72. https://doi.org/10.1098/rstb.1952.0012
- J. F. Wang, J. P. Shi, and J. J. Wei, Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey, J. Differential Equations 251 (2011), no. 4-5, 1276-1304. https://doi.org/10.1016/j.jde.2011.03.004
- W. M. Wang, L. Zhang, H. L. Wang, and Q. L. Zheng, 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. Wolpert, The development of pattern and form in animals, Carol. Biol. Read. 1 (1977), 1-16.
- X. C. Zhang, G. Q. Sun, and Z. Jin, Spatial dynamics in a predator-prey model with Beddington-DeAngelis functional response, Phys. Rev. E 85 (2012), 021924. https://doi.org/10.1103/PhysRevE.85.021924