On the Behavior of Certain Turing System
On the Behavior of Certain Turing System
摘要
The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coefficient D = 0 and the solution blows up ifD= 0. The method of linearization is applied to derive the existence of Hopfs bifurcation which is the signature of instability of Turing system. The increasing of the size of the attractor and the existence of Hopf＇ s bifurcation indicate that there is a threshold that initiates the instability.
参考文献9
-
1F.A. Davidson, B.D. Sleeman, J.W. Crawford, Travelling waves in a reaction-diffusion system modeling fungal mycelia, IMA Journal of Applied Mathematics 58 (1997) 237-257.
-
2A. Gierer, Generation of biological patterns and form: Some physical, mathematical and logical aspects, Progress in Biophysics and Molecular Biology 37 (1981) 1-47.
-
3H. Meinhardt, Models of Biological Pattern Formation, London Academic Press, London, 1982.
-
4Y. Lou, W.M. Ni, Diffusion, self-diffusion and cross-diffusion, Journal of Differential Equations 131.(1996) 79-131.
-
5A.M. Turing, The chemical basis of morphogenesis, Philosophical Transactions of the Royal Society B 237 (1952) 37-72.
-
6T. Kolokolnikova, T. Emeuxa, J. Weib, Mesa-type patterns in the one-dimensional Brusselator and their stability, Physica D 214 (2006) 63-77.
-
7P. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics 28, Springer-Verlag, Berlin, Heidelberg, New York, 1979.
-
8J.D. Murray, Mathematical Biology, Springer-Verlag, Berlin, Heidelberg, New York, 1993.
-
9Y. Yang, Solitons in Field Theory and Nonlinear Analysis, Springer-Verlag, New York, 2001.
-
1刘富成,贺亚峰,潘宇扬.Superlattice Patterns in Coupled Turing Systems[J].Communications in Theoretical Physics,2010(5):971-976. 被引量：1
-
2熊利芝,梁凯,何则强.锂离子在LiVOPO_4中的扩散系数的测定[J].吉首大学学报（自然科学版）,2011,32(1):85-87. 被引量：3
-
3陈继乾.一类高阶椭圆方程的极值原理与解的唯一性[J].西南科技大学学报,1989,16(3):1-6.
-
4王向东,梁廷.抛物型方程广义解的弱最大值原理[J].自然杂志,1991,14(4):314-315.
-
5王向东,梁廷.拟线性椭圓型方程广义解的Liouville定理[J].自然杂志,1992,15(1):72-72.
-
6郑学永.拟线性具间断系数抛物型方程柯西问题解的渐近性质[J].上饶师范学院学报,1989,15(5):15-19.
-
7赵红宙,于赛发,赵颖坤.战术通信训练电磁环境模拟与仿真研究[J].河北科技大学学报,2011,32(S1):175-177. 被引量：1
-
8廖福成,李安贵,唐远炎.一般Lorenz型系统的特性分析及混沌[J].辽宁工程技术大学学报（自然科学版）,2009,28(1):158-160.
-
9郑慧峰,王吉,张雅卓.四阶时延耦合振子系统的分岔研究[J].哈尔滨师范大学自然科学学报,2007,23(5):11-13.
-
10J.Oke,N.Vlachopoulos,M.S.Diederichs.Numerical analyses in the design of umbrella arch systems[J].Journal of Rock Mechanics and Geotechnical Engineering,2014,6(6):546-564. 被引量：3
