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A simple regulatory circuit that can simultaneously generate excitability of two different mechanisms
A periodic reaction-diffusion model with a quiescent stage
1. | Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan |
References:
[1] |
J. Cook, "Dispersive Variability and Invasion Wave Speeds," unpublished manuscript, 1993. |
[2] |
K. Deimling, "Nonlinear Functional Analysis," Springer-Verlag, Berlin, 1985. |
[3] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin-New York, 1981. |
[4] |
J. K. Hale, "Ordinary Differential Equations," Second edition, Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980. |
[5] |
P. Hess, "Periodic-Parabolic Boundary Value Problems and Positivity," Pitman Res. Notes Math. Series, 247, Longman Scientific & Technical, Harlow, copublished in the United States with John Wiley & Sons, Inc., New York, 1991. |
[6] |
K. P. Hadeler and M. A. Lewis, Spatial dynamics of the diffusive logistic equation with a sedentary compartment, Can. Appl. Math. Q., 10 (2002), 473-499. |
[7] |
J. Jiang, X. Liang and X.-Q. Zhao, Saddle-point behavior for monotone semiflows and reaction-diffusion models, J. Diff. Eqns., 203 (2004), 313-330.
doi: 10.1016/j.jde.2004.05.002. |
[8] |
X. Liang, Y. Yi and X.-Q. Zhao, Spreading speeds and traveling waves for periodic evolution system, J. Diff. Eqns., 231 (2006), 57-77.
doi: 10.1016/j.jde.2006.04.010. |
[9] |
X. Liang and X.-Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, J. Funct. Anal., 259 (2010), 857-903.
doi: 10.1016/j.jfa.2010.04.018. |
[10] |
R. H. Martin, "Nonlinear Operators and Differential Equations in Banach Spaces," New York, 1976. |
[11] |
R. H. Martin and H. L. Smith, Abstract functional-differential equations and reaction-diffusion systems, Trans. of AMS, 321 (1990), 1-44.
doi: 10.2307/2001590. |
[12] | |
[13] |
P. Magal and X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM. J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[14] |
K. F. Zhang and X.-Q. Zhao, Asymptotic behaviour of a reaction-diffusion model with a quiescent stage, Proc. R. Soc. A., 463 (2007), 1029-1043.
doi: 10.1098/rspa.2006.1806. |
[15] |
X.-Q. Zhao, "Dynamical Systems in Population Biology," CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 16, Springer-Verlag, New York, 2003. |
show all references
References:
[1] |
J. Cook, "Dispersive Variability and Invasion Wave Speeds," unpublished manuscript, 1993. |
[2] |
K. Deimling, "Nonlinear Functional Analysis," Springer-Verlag, Berlin, 1985. |
[3] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin-New York, 1981. |
[4] |
J. K. Hale, "Ordinary Differential Equations," Second edition, Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980. |
[5] |
P. Hess, "Periodic-Parabolic Boundary Value Problems and Positivity," Pitman Res. Notes Math. Series, 247, Longman Scientific & Technical, Harlow, copublished in the United States with John Wiley & Sons, Inc., New York, 1991. |
[6] |
K. P. Hadeler and M. A. Lewis, Spatial dynamics of the diffusive logistic equation with a sedentary compartment, Can. Appl. Math. Q., 10 (2002), 473-499. |
[7] |
J. Jiang, X. Liang and X.-Q. Zhao, Saddle-point behavior for monotone semiflows and reaction-diffusion models, J. Diff. Eqns., 203 (2004), 313-330.
doi: 10.1016/j.jde.2004.05.002. |
[8] |
X. Liang, Y. Yi and X.-Q. Zhao, Spreading speeds and traveling waves for periodic evolution system, J. Diff. Eqns., 231 (2006), 57-77.
doi: 10.1016/j.jde.2006.04.010. |
[9] |
X. Liang and X.-Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, J. Funct. Anal., 259 (2010), 857-903.
doi: 10.1016/j.jfa.2010.04.018. |
[10] |
R. H. Martin, "Nonlinear Operators and Differential Equations in Banach Spaces," New York, 1976. |
[11] |
R. H. Martin and H. L. Smith, Abstract functional-differential equations and reaction-diffusion systems, Trans. of AMS, 321 (1990), 1-44.
doi: 10.2307/2001590. |
[12] | |
[13] |
P. Magal and X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM. J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[14] |
K. F. Zhang and X.-Q. Zhao, Asymptotic behaviour of a reaction-diffusion model with a quiescent stage, Proc. R. Soc. A., 463 (2007), 1029-1043.
doi: 10.1098/rspa.2006.1806. |
[15] |
X.-Q. Zhao, "Dynamical Systems in Population Biology," CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 16, Springer-Verlag, New York, 2003. |
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