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Preface
Exact travelling wave solutions of three-species competition--diffusion systems
1. | Department of Mathematics, National Taiwan University, and National Center for Theoretical Sciences (Taipei Office), No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan |
2. | Department of Mathematics, National Taiwan University, and National Center for Theoretical Sciences (Taipei Office), No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan |
3. | Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 1-1-1 Higashimita, Tamaku, Kawasaki 214-8571, Japan |
4. | Meiji Institute for Advanced Study of Mathematical Sciences, and Graduate School of Advanced Mathematical Sciences, Meiji University, 1-1-1 Higashimita, Tamaku, Kawasaki 214-8571, Japan |
References:
[1] |
E. J. Doedel, B. E. Oldeman, A. R. Champneys, F. Dercole, T. F. Fairgrieve, Y. Kuznetsov, R. C. Paffenroth, B. Sandstede, X. J. Wang and C. H. Zhang, "AUTO-07p: Continuation and Bifurcation Software for Ordinary Differential Equations," Concordia Univ., Version 0.7, 2010. Available from: http://sourceforge.net/projects/auto-07p/files/auto07p/ |
[2] |
S.-I. Ei, R. Ikota and M. Mimura, Segregating partition problem in competition-diffusion systems, J. Interfaces and Free Boundaries, 1 (1999), 57-80. |
[3] |
M. W. Hirsch, Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math., 383 (1988), 1-53. |
[4] |
J. Hofbauer and K. Sigmund, "Evolutionary Games and Population Dynamics," Cambridge University Press, Cambridge, 1998. |
[5] | |
[6] |
Y. Kannon, Traveling waves in systems of two competing species, Sūgaku, 49 (1997), 379-392. |
[7] |
K. Kishimoto and H. F. Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains, J. Differential Equations, 58 (1985), 15-21.
doi: 10.1016/0022-0396(85)90020-8. |
[8] |
M. Rodrigo and M. Mimura, Exact solutions of a competition-diffusion system, Hiroshima Math. J., 30 (2000), 257-270. |
[9] |
M. Rodrigo and M. Mimura, Exact solutions of reaction-diffusion systems and nonlinear wave equations, Japan J. Indust. Appl. Math., 18 (2001), 657-696.
doi: 10.1007/BF03167410. |
[10] |
S. Wolfram, "Mathematica: A System for Doing Mathematics by Computer," Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1988. |
[11] |
M. L. Zeeman, Hopf bifurcations in competitive three-dimensional Lotka-Volterra systems, Dynam. Stability Systems, 8 (1993), 189-217. |
show all references
References:
[1] |
E. J. Doedel, B. E. Oldeman, A. R. Champneys, F. Dercole, T. F. Fairgrieve, Y. Kuznetsov, R. C. Paffenroth, B. Sandstede, X. J. Wang and C. H. Zhang, "AUTO-07p: Continuation and Bifurcation Software for Ordinary Differential Equations," Concordia Univ., Version 0.7, 2010. Available from: http://sourceforge.net/projects/auto-07p/files/auto07p/ |
[2] |
S.-I. Ei, R. Ikota and M. Mimura, Segregating partition problem in competition-diffusion systems, J. Interfaces and Free Boundaries, 1 (1999), 57-80. |
[3] |
M. W. Hirsch, Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math., 383 (1988), 1-53. |
[4] |
J. Hofbauer and K. Sigmund, "Evolutionary Games and Population Dynamics," Cambridge University Press, Cambridge, 1998. |
[5] | |
[6] |
Y. Kannon, Traveling waves in systems of two competing species, Sūgaku, 49 (1997), 379-392. |
[7] |
K. Kishimoto and H. F. Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains, J. Differential Equations, 58 (1985), 15-21.
doi: 10.1016/0022-0396(85)90020-8. |
[8] |
M. Rodrigo and M. Mimura, Exact solutions of a competition-diffusion system, Hiroshima Math. J., 30 (2000), 257-270. |
[9] |
M. Rodrigo and M. Mimura, Exact solutions of reaction-diffusion systems and nonlinear wave equations, Japan J. Indust. Appl. Math., 18 (2001), 657-696.
doi: 10.1007/BF03167410. |
[10] |
S. Wolfram, "Mathematica: A System for Doing Mathematics by Computer," Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1988. |
[11] |
M. L. Zeeman, Hopf bifurcations in competitive three-dimensional Lotka-Volterra systems, Dynam. Stability Systems, 8 (1993), 189-217. |
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