JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 74-78.doi: 10.6040/j.issn.1671-9352.0.2015.450
Previous Articles Next Articles
LI Yue-xia, ZHANG Li-na, ZHANG Xiao-jie
CLC Number:
[1] TURING A M. The chemical basis of morphogenesis[J]. Phil Trans Roy Soc Londonser, 1952, B237:37-72. [2] CASTETS V, DULOS E, BOISSONADE J, et al. Experimental evidence of a sustained Turing-type equilibrium chemical pattern[J]. Phys Rev Lett, 1990, 64:2953-2956. [3] LENGYEL I, EPSTEIN I R. Modeling of turing structures in the chlorite-iodidemalonic acid-starch reaction system[J]. Science, 1991, 251:650-652. [4] JANG Jaeduck, NI Weiming, TANG Moxun. Global bifurcation and structure of turing patterns in the 1-D Lengyel-Epstein model[J]. J Dyn Diff Equ, 2005, 16(2):297-320. [5] DU Linglong, WANG Mingxin. Hopf bifurcation analysis in the 1-D Lengyel-Epsteinreaction-diffusion model[J]. J Math Anal Appl, 2010, 366:473-485. [6] WEI Minghua, WU Jianhua, GUO Gaihui. Turing structures and stability for the 1-D Lengyel-Epstein system[J]. J Math Chem, 2012, 50:2374-2396. [7] JIN Jianyin, SHI Junping, WEI Junjie, et al. Bifurcations of patterned solutions in diffusive Lengyel-Epstein system of CIMA chemical reaction[J]. Rocky Mt J Math, 2013, 43(5):1637-1674. [8] KAR S, BHATTACHARJEE J K, RAY D D. A model reaction-diffusion system under spatial perturbation: theoretical and numerical investigation[J]. Eur Phys J, 2005, 43B:109-114. [9] NI Weiming, TANG Moxun. Turing patterns in the Lengyel-Epstein system for the CIMA reaction[J]. Trans Am Math Soc, 2005, 357:3953-3969. [10] CRANDALL M G, RABINOWITZ P H. Bifurcation from simple eigenvalues[J]. J Funct Anal, 1997, 8:321-340. |
[1] | LIU Hua, YE Yong, WEI Yu-mei, YANG Peng, MA Ming, YE Jian-hua, MA Ya-lei. Study of dynamic of a discrete host-parasitoid model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 30-38. |
[2] | DONG Ya-ying. Global bifurcation structure in a predator-prey model with a spatial degeneracy [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 76-84. |
[3] | ZHANG Dao-xiang, SUN Guang-xun, MA Yuan, CHEN Jin-qiong, ZHOU Wen. Hopf bifurcation and spatial patterns in a delayed diffusive predator-prey system with Holling-III functional response and linear harvesting effect [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 85-94. |
[4] | BAI Bao-li, ZHANG Jian-gang, DU Wen-ju, YAN Hong-ming. Dynamic behavior analysis of a stochastic SIR epidemic model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 72-82. |
[5] | SHI Xue-wei, JIA Jian-wen. Study on an SIR epidemic model with information variable and graded cure rate [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(3): 51-59. |
[6] | LI Xiao-yan, XU Man. Existence and multiplicity of nontrivial solutions of Dirichlet problems for second-order impulsive differential equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 29-35. |
[7] | LI Hai-xia. Coexistence solutions for a predator-prey model with additive Allee effect and a protection zone [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(09): 88-94. |
[8] | WU Dai-yong, ZHANG Hai. Stability and bifurcation analysis for a single population discrete model with Allee effect and delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 88-94. |
[9] | ZHANG Lu, MA Ru-yun. Bifurcation structure of asymptotically linear second-order #br# semipositone discrete boundary value problem#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 79-83. |
[10] | FENG Xiao-zhou1,2, NIE Hua2. Bifurcation solutions and stability of a predator-prey system with predator saturation and competition [J]. J4, 2012, 47(5): 103-107. |
[11] | CHEN Si-yang, LIU Xiao-na. Stability and bifurcation analysis of the model with interference and piecewise constant variables [J]. J4, 2012, 47(11): 109-118. |
[12] | ZHANG Wei-qiang, LIU Yang-zheng*. Generation and circuit implementation of a unified hyperchaotic system [J]. J4, 2011, 46(7): 30-34. |
[13] | ZHANG Zhi-Reng. The uniqueness of the limit cycle and the bifurcation of singular points for a class of polynomial systems [J]. J4, 2009, 44(9): 90-92. |
[14] |
HOU Qiang, JIN Zhen.
Analysis of a HollingTanner model with ratiodependence incorporating a prey refuge [J]. J4, 2009, 44(3): 56-60 . |
[15] | LIU Hua ,LIU Zhi-guang ,SU Min ,LI Zi-zhen , . Clumping effect in a host—parasitoid interaction model [J]. J4, 2008, 43(8): 31-34 . |
|