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Equilibriums' linear stability of a diffusive model of pioneer and climax species interaction[J]. Journal of South China Normal University (Natural Science Edition), 2014, 46(6): 16-22.
Citation: Equilibriums' linear stability of a diffusive model of pioneer and climax species interaction[J]. Journal of South China Normal University (Natural Science Edition), 2014, 46(6): 16-22.

Equilibriums' linear stability of a diffusive model of pioneer and climax species interaction

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  • Received Date: May 18, 2014
  • Revised Date: August 25, 2014
  • The linear stability of equilibria for a diffused pioneer and climax species competition model is discussed. This system has at least 4 and at most 6 equilibria with two possible positive equilibria, and thus the dynamical behaviors are very rich. All the constant equilibria of the model are given in the second section, and then the linear stabilities of these equilibria are analyzed in the third section. The sufficient condition or sufficient and necessary condition of the stability for every equilibrium is given. The linearization method is used accompanied with the eigenvalue skill. At the last, an example is given to illustrate the application of the results, with numerical simulation and conclusion discussion are given.
  • [1] W.E. Ricker, Stock and recruitment[J],
    { J. Fish. Res. Board Can,} 1954, {\bf 11:}559-623.
    [2] J.E. Franke, A.A. Yakubu, Pioneer exclusion in a one-hump discrete pioneer-climax competing system[J],,
    {J.Math . Biol,}1994, {\bf 32:} 771-787.
    [3]J.R. Buchanan, Asymptotic behavior of two interacting pioneer-climax species[J].
    {Fields 1nst.comm,} 1999, {\bf 21:}51-63.
    [4]J.F. Selgrade, G. Namkong, Stable periodic behavior in a pioneer-climax models[J].
    { Nature. Resource Modeling,}1990, {\bf 4:}215-227.
    [5] S. Summer, Hopf bifurcation in pioneer-climax species models[J].
    { Math. Biosci,}1996,{\bf 137:} 1-24.
    [6] S. Summer, Stable periodic behavior in pioneer-climax competing species models with constant rate forcing[J].
    { Nature. Resource Modeling, }1998, {\bf 11:} 155-171.
    [7] J.X. Liu, J.J. Wei, Bifurcation analysis of a diffusive model of pioneer and climax species interaction[J].
    {Advance in Difference Equation,} 2001,{\bf 24:} 11-52.
    [8] J. Robert Buchanan, Turning instability in pioneer-climax species interactions[J].
    { Math. Biosci,} 2005,{\bf 194:} 126-199.
    [9] 马知恩, 周义仓, 常微分方程定性与稳定性方法[M]. 北京:科学出版社, 2004.
    [10] N. Shigesada, K. Kawasaki, Biology Invasions: Theory and Practice[M]. { Oxford University Press}, Oxford, 1997.
    [11] {J.D. Murray, Mathematical Biology: I and II[M]. Spriner-Verlag, New York, 2002.}

    [1] W.E. Ricker, Stock and recruitment[J],
    { J. Fish. Res. Board Can,} 1954, {\bf 11:}559-623.
    [2] J.E. Franke, A.A. Yakubu, Pioneer exclusion in a one-hump discrete pioneer-climax competing system[J],,
    {J.Math . Biol,}1994, {\bf 32:} 771-787.
    [3]J.R. Buchanan, Asymptotic behavior of two interacting pioneer-climax species[J].
    {Fields 1nst.comm,} 1999, {\bf 21:}51-63.
    [4]J.F. Selgrade, G. Namkong, Stable periodic behavior in a pioneer-climax models[J].
    { Nature. Resource Modeling,}1990, {\bf 4:}215-227.
    [5] S. Summer, Hopf bifurcation in pioneer-climax species models[J].
    { Math. Biosci,}1996,{\bf 137:} 1-24.
    [6] S. Summer, Stable periodic behavior in pioneer-climax competing species models with constant rate forcing[J].
    { Nature. Resource Modeling, }1998, {\bf 11:} 155-171.
    [7] J.X. Liu, J.J. Wei, Bifurcation analysis of a diffusive model of pioneer and climax species interaction[J].
    {Advance in Difference Equation,} 2001,{\bf 24:} 11-52.
    [8] J. Robert Buchanan, Turning instability in pioneer-climax species interactions[J].
    { Math. Biosci,} 2005,{\bf 194:} 126-199.
    [9] 马知恩, 周义仓, 常微分方程定性与稳定性方法[M]. 北京:科学出版社, 2004.
    [10] N. Shigesada, K. Kawasaki, Biology Invasions: Theory and Practice[M]. { Oxford University Press}, Oxford, 1997.
    [11] {J.D. Murray, Mathematical Biology: I and II[M]. Spriner-Verlag, New York, 2002.}

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