Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 1
130
Views
2
CrossRef citations to date
0
Altmetric
Articles

Patterns in a freshwater tussock sedge model

ORCID Icon, &
Pages 118-135 | Received 09 Jul 2019, Accepted 13 Feb 2020, Published online: 24 Feb 2020

References

  • Wang Y, Zhao M, Yu HG, et al. Analysis of spatiotemporal dynamic and bifurcation in a wetland ecosystem. Discrete Dyn Nat Soc. 2015;2015: 1854321–15.
  • van de Koppel J, Rietkerk M, Dankers N, et al. Scale-dependent feedback and regular spatial patterns in young mussel beds. Am Nat. 2005;165(3):E66–E67.
  • van de Koppel J, Crain CM. Scale-dependent inhibition drives regular tussock spacing in a freshwater marsh. Am Nat. 2006;168(5):E136–E147.
  • Wang JL, Hou XJ, Li Y. Patterns in a fresh water tussock sedge model with two limit cycles. Dyn Contin Discrete Impuls Syst. 2019;26:231–260.
  • Li Y, Wang JL, Hou XJ. Stripe and spot patterns for the Gierer-Meinhardt model with saturated activator production. J Math Anal Appl. 2017;449(2):1863–1879.
  • Wang JL, Hou XJ, Jing ZJ. Stripe and spot patterns in a Gierer-Meinhardt activator-inhibitor model with different sources. Int J Bifurcation Chaos. 2015;25(8): 15501081–16.
  • Yu BG. Dynamic behavior of a plant-wrack model with spatial diffusion. Commun Nonlinear Sci Numer Simul. 2010;15(8):2201–2205.
  • Li Y, Wang JL, Hou XJ. Stripe and spot patterns for general Gierer-Meinhardt model with common sources. Int J Bifurcation Chaos. 2017;27(2): 1750018–18.
  • Wang JL, Li Y, Hou XJ. Supercritical Hopf bifurcation and Turing patterns for an activator and inhibitor model with different sources. Adv Differ Equ. 2018;2018(241):1–24.
  • Kang JH, Lee J, Oh YM. The existence, nonexistence and uniqueness of golobal positive coexistence of a nonlinear elliptic biological interacting model. Kangweon-Kyungki Math J. 2004;12(1):77–90.
  • Pang PYH, Wang MX. Non-constant positive steady states of a predator–prey system with non-monotonic functional response and diffusion. Proc London Math Sci. 2004;88(1):135–157.
  • Peng R, Wang MX. Pattern formation in the Brusselator system. J Math Anal Appl. 2005;309(1):151–166.
  • Ni WM, Tang M. Turing patterns in the Lengyel-Epstein system for the CIMA reaction. Trans AMS. 2005;357(10):3953–3969.
  • Li Y, Wang MX. Stationary pattern of a diffusive prey-predator model with trophic interactions of three levels. Nonlinear Anal Real World Appl. 2013;14(3):1806–1816.
  • Li HL, Pang PYH, Wang MX. Qualitative analysis of a diffusive pre-predator model with trophic interactions of three levels. Discrete Contin Dyn Syst Ser B. 2012;17(1):127–152.
  • Turing AM. The chemical basis of morphogenesis. Philos Trans Roy Soc London Ser B. 1952;237(641):37–72.
  • Sun GQ, Li L, Jin Z, et al. Pattern formation in a spatial plant-wrack model with tide effect on the wrack. J Biol Phys. 2010;36(2):161–174.
  • Li B, Wang MX. Stationary patterns of the stage-structured predator–prey model with diffusion and cross diffusion. Math Comput Model. 2011;54(5–6):1380–1393.
  • Lou Y, Ni WM. Diffusion, self-diffusion, and cross diffusion. J Differ Equ. 1996;131(1):79–131.
  • Murray JD. Mathematical biology I: an introduction. New York (NY): Springer-Verlag; 1989.
  • Gierer A, Meinhardt H. A theory of biological pattern formation. Kybernetik. 1972;12(1):30–39.
  • Hartman Ph. Ordinary differential equations. 2nd ed. Boston, Basel, Stuttgart: Birkhäuser; 1982.
  • Henry D. Geometric theory of semilinear parabolic equations. Berlin, Heidelberg: Springer-Verlag; 1981. (Lecture notes in mathematics).
  • Weinberger HF. Invariant sets for weakly coupled parabolic and elliptic systems. Rend Mat. 1975;8(6):295–310.
  • Lin CS, Ni WM, Takagi I. Large amplitude stationary solutions to a chemotaxis system. J Differ Equ. 1988;72(1):1–27.
  • Hsu S-H. A survey of constructing Lyapunov functions for mathematical models in population biology. Taiwan J Math. 2005;9(2):151–173.
  • Smoller J. Shock waves and reaction diffusion equations. 2nd ed. New York: Springer-Verlag; 1999.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.