Mathematical Biosciences and Engineering (MBE)

The spatial dynamics of a zebrafish model with cross-diffusions
Pages: 1035 - 1054, Issue 4, August 2017

doi:10.3934/mbe.2017054      Abstract        References        Full text (2810.4K)           Related Articles

Hongyong Zhao - Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China (email)
Qianjin Zhang - Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China (email)
Linhe Zhu - Department of Mathematics, Nanjing University of Aeronautics and Astronautics, School of Mathematical and Natural Sciences, Arizona State University, Nanjing 210016, China (email)

1 R. Asai, R. Taguchi, Y. Kume, M. Saito and S. Kondo, Zebrafish Leopard gene as a component of the putative reaction-diffusion system, Mech. Dev., 89 (1999), 87-92.
2 V. Dufiet and J. Boissonade, Dynamics of turing pattern monolayers close to onset, Phys. Rev. E., 53 (1996), 1-10.
3 M. Fras and M. Gosak, Spatiotemporal patterns provoked by environmental variability in a predator-prey model, Biosystems, 114 (2013), 172-177.
4 A. Gierer and H. Meinhardt, A theory of biological pattern formation, Kybernetika, 12 (1972), 30-39.
5 P. Gray and S. K. Scott, Autocatalytic reactions in the isothermal continuous stirred tank reactor, Chem. Eng. Sci., 39 (1984), 1087-1097.
6 G. H. Gunaratne, Q. Ouyang and H. L. Swinney, Pattern formation in the presence of symmetries, Phys. Rev. E., 50 (1994), 4-15.       
7 O. Jensen, V. C. Pannbacker, G. Dewel and P. Borckmans, Subcritical transitions to Turing structures, Phys. Lett. A., 179 (1993), 91-96.
8 C. T. Klein and F. F. Seelig, Turing structures in a system with regulated gap-junctions, Biosystems, 35 (1995), 15-23.
9 S. Kondo, The reaction-diffusion system: A mechanism for autonomous pattern formation in the animal skin, Genes. Cells., 7 (2002), 535-541.
10 S. Kondo and R. Asia, A reaction-diffusion wave on the skin of the marine angelfish Pomacanthus, Nature, 376 (1995), 765-767.
11 S. Kondo and H. Shirota, Theoretical analysis of mechanisms that generate the pigmentation pattern of animals, Semin. Cell. Dev. Biol., 20 (2009), 82-89.
12 H. Meinhardt, Reaction-diffusion system in development, Appl. Math. Comput Appl. Math. Comput., 32 (1989), 103-135.       
13 S. Miyazawa, M. Okamoto and S. Kondo, Blending of animal colour patterns by hybridization, Nat. Commun, 10 (2010), 1-6.
14 M. Nguyen, A. M. Stewart and A. V. Kalueff, Aquatic blues: Modeling depression and antidepressant action in zebrafish, Prog. Neuro-Psychoph, 55 (2014), 26-39.
15 Q. Ouyang, Pattern Formation in Reaction-diffusion Systems, (Shanghai: Shanghai Sci-Tech Education Publishing House)(in Chinese), 2000.
16 D. M. Parichy, Pigment patterns: Fish in stripes and spots current, Biology, 13 (2003), 947-950.
17 J. Schnackenberg, Simple chemical reaction systems with limit cycle behavior, J. Theor. Biol., 81 (1979), 389-400.       
18 H. Shoji and Y. Iwasa, Labyrinthine versus straight-striped patterns generated by two-dimensional Turing systems, J. Theor. Biol., 237 (2005), 104-116.       
19 H. Shoji and Y. Iwasa, Pattern selection and the direction of stripes in two-dimensional turing systems for skin pattern formation of fishes, Forma, 18 (2003), 3-18.       
20 H. Shoji, Y. Iwasa and S. Kondo, Stripes, spots, or reversedspots in two-dimensional Turing systems, J. Theor. Biol., 224 (2003), 339-350.       
21 H. Shoji, Y. Iwasa, A. Mochizuki and S. Kondo, Directionality of stripes formed by anisotropic reaction-diffusion models, J. Theor. Biol., 214 (2002), 549-561.       
22 H. Shoji, A. Mochizuki, Y. Iwasa, M. Hirata, T. Watanabe, S. Hioki and S. Kondo, Origin of directionality in the fish stripe pattern, Dev. Dynam., 226 (2003), 627-633.
23 A. M. Stewart, E. Yang, M. Nguyen and A. V. Kalueff, Developing zebrafish models relevant to PTSD and other trauma- and stressor-related disorders, Prog. Neuro-Psychoph, 55 (2014), 67-79.
24 G. Q. Sun, Z. Jin, Q. X. Liu and B. L. Li, Rich dynamics in a predator-prey model with both noise and periodic force, Biosystems, 100 (2010), 14-22.
25 W. M. Wang, H. Y. Liu, Y. L. Cai and Z. Q. Liu, Turing pattern selection in a reaction diffusion epidemic model, Chin. Phys. B., (2011), 074702, 12pp.
26 M. Yamaguchi, E. Yoshimoto and S. Kondo, Pattern regulation in the stripe of zebrafish suggests an underlying dynamic and autonomous mechanism, PNAS, 104 (2007), 4790-4793.
27 X. Y. Yang, T. Q. Liu, J. J. Zhang and T. S. Zhou, The mechanism of Turing pattern formation in a positive feedback system with cross diffusion, J. Stat. Mech-Theory. E., 14 (2014), 1-16.
28 X. C. Zhang, G. Q. Sun and Z. Jin, Spatial dynamics in a predator-prey model with Beddington-DeAngelis functional response, Phys. Rev. E., (2012), 021924, 14pp.

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