抑素作用下三分量组织生长模型的行波解

本文运用反应扩散系统的行波解理论,研究一个受抑素影响的三分量Logistic型组织生长模型方程.讨论了方程定态的稳定性和行波解的存在性,运用小参数展开法求出近似波前解,并通过数值模拟证明波速为2.0的波是全局稳定的.最后得出结论;生长组织中的自分泌抑素并不影响Logistic组织的整体增殖速度,而只改变组织的局域生长速度和减小组织的最大密度.

TRAVELLING WAVE SOLUTIONS 0F A THREE COMPONENT-TISSUE GROWTH MODEL UNDER INHIBITION BY CHALONES

The theory of travelling wave solutions of reaction-diffusion systems is applied in the study of a three-component model equations describing logistic tissue growth under inhibition by chalones. The linear stability of steady states and the existence of the travelling wave solutions are first discussed, then the small parameter expansion technique is employed to get the approximate wavefront solution and the global stability of the wavefront with c=2.0 is demonstrated by nume-rical simulations. Finally the conclusion is reached that the self secreted chalo-nes can hardly affect the global proliferation speed of the logist c tissue,but modify the local growth rate and supress the maximum density of the ussue.