A weakly nonlinear analysis of a model of avascular solid tumour growth
A weakly nonlinear analysis of a model of avascular solid tumour growth
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DOI：
10.1007/s002850050163
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发表时间：
1999-07-01
影响因子：
1.9
通讯作者：
Byrne, HM
中科院分区：
文献类型：
--
作者：
Byrne, HM
在本文中，我们研究了一个数学模型，描述了无血管实体瘤的生长。我们的分析集中在稳定的，径向对称模型的解决方案，相对于从类球谐函数的扰动。使用弱非线性分析，以前的结果被扩展到显示的振幅的非对称模式的相互作用。注意力集中在一个特殊的情况下，模型方程简化。简化的模型方程的分析导致识别的两个参数的家庭的非对称稳定的解决方案，其稳定和不稳定的流形的尺寸取决于系统参数。非对称定常解限制了径向对称定常状态线性稳定时的吸引域。在这些数值和分析结果的基础上，我们假设存在完全非线性稳定的解决方案，这是稳定的时间依赖的扰动。
In this paper we study a mathematical model that describes the growth of an avascular solid tumour. Our analysis concentrates on the stability of steady, radially-symmetric model solutions with respect to perturbations taken from the class of spherical harmonics. Using weakly nonlinear analysis, previous results are extended to show how the amplitudes of the asymmetric modes interact. Attention focuses on a special case for which the model equations simplify. Analysis of the simplified model equations leads to the identification of a two-parameter family of asymmetric steady solutions, the dimensions of whose stable and unstable manifolds depend on the system parameters. The asymmetric steady solutions limit the basin of attraction of the radially-symmetric steady state when it is linearly stable. On the basis of these numerical and analytical results we postulate the existence of fully nonlinear steady solutions which are stable with respect to time-dependent perturbations.