Journal of Hebei University(Natural Science Edition) >

2018 , Vol. 38 >Issue 5: 454 - 459

DOI: https://doi.org/10.3969/j.issn.1000-1565.2018.05.002

Bifurcation study of a class of nonlocal reaction diffusion equation

  • LI Congrui ,
  • CAO Jianzhi ,
  • BAO Junyan
Expand
  • Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received date: 2017-08-09

  Online published: 2018-09-25

Fold

Abstract

A Fisher-KPP equation with nonlocal competition term is considered, by using the Lyapunov-Schmidt reduction and singularity theory, some bifurcation problems with homogeneous Dirichlet boundary conditions are analyzed in detail.

Key words： nonlocal influence; reaction-diffusion; Lyapunov-Schmidt reduction; bifurcation

Cite this article

LI Congrui , CAO Jianzhi , BAO Junyan . Bifurcation study of a class of nonlocal reaction diffusion equation[J]. Journal of Hebei University(Natural Science Edition), 2018 , 38(5) : 454 -459 . DOI: 10.3969/j.issn.1000-1565.2018.05.002

References

[1] FISHER R A. The wave of advance of advantageous genes[J]. Ann Eugenics, 1937, 7(4): 355-369. DOI:10.1111/j. 1469-1809. 1937.tb02153.x.
[2] KOLMOGOROFF A, PETROVSKY I, PISCOUNOFF N. Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem[J]. Moscow University Bulletin of Mathematics, 1937(1): 1-25. DOI: 10.1016/B978-0-08-092523-3.50014-9.
[3] FUENTE M A, KUPERMAN M N, KENKRE V M. Nonlocal interaction effects on pattern formation in population dynamics[J]. Physical Review Letters, 2003, 91(15): 158104. DOI: 10.1103/PhysRevLett.91.158104.
[4] FUENTE M A, KUPERMAN M N, KENKRE V M. Analytical considerations in the study of spatial patterns arising from no nonlocal interaction effects[J]. Journal of Physical Chemistry B, 2004, 108(29): 10505-10508. DOI:10.1021/jp040090k.
[5] KENKRE V M. Results from variants of the fisher equation in the study of epidemics and bacteria[J]. Physica A, 2004,342(1): 242-248. DOI: 10.1016/j.physa.2004.04.084.
[6] CHEN S S, YU J S. Stability and bifurcation on predator-prey systems with nonlocal prey competition[J]. Discrete and Continuous Dynamical Systems, 2017, 38(1): 43-62. DOI: 10.3934/dcds.2018002.
[7] 陆启韶.分岔与奇异性[M]. 上海:上海科技教育出版社,1995: 40-43.
[8] SUN L N, SHI J P, WANG Y W. Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equaction[J]. Z Angew Math Phys, 2013, 64(4): 1267-1278. DOI:10.1007/s00033-012-0286-9.
Options
Outlines

/

〈 〉