Banasiak Jacek, Lachowicz Mirosław, Moszyński Marcin
School of Mathematical Sciences, University of KwaZulu-Natal, Durban, South Africa.
Math Biosci. 2007 Apr;206(2):200-15. doi: 10.1016/j.mbs.2005.08.004. Epub 2005 Sep 30.
In the last few years there has been a renewed interest in infinite systems of differential equations, similar to the classical birth-and-death system of population dynamics, due to their rôle in modelling the evolution of drug resistance in cancer cells. In [J. Banasiak, M. Lachowicz, Topological chaos for birth-and-death models with proliferation, Math. Models Methods Appl. Sci. 12 (6) (2002) 755] such systems were shown to generate a chaotic dynamics under, however, very restrictive assumptions on the growth of coefficients. In this paper, using recently developed concept of subspace chaos [J. Banasiak, M. Moszyński, A generalization of Desch-Schappacher-Webb criteria for topological chaos with applications, Discrete Contin. Dyn. Syst. - A 12 (5) (2005) 959], we show that for a linear growth of the coefficients, which are more acceptable from biological point of view, the dynamics of these systems is chaotic in some subspaces of the original state space.
在过去几年中，人们对微分方程的无穷系统重新产生了兴趣，这类似于种群动态学中的经典生死系统，因为它们在模拟癌细胞耐药性的演变中发挥了作用。在[J. 巴纳西亚克，M. 拉乔维茨，具有增殖的生死模型的拓扑混沌，《数学模型与应用科学方法》12 (6) (2002) 755]中，这类系统在系数增长的非常严格的假设下被证明会产生混沌动力学。在本文中，我们使用最近发展的子空间混沌概念[J. 巴纳西亚克，M. 莫辛斯基，具有应用的拓扑混沌的德施 - 沙帕彻 - 韦伯准则的推广，《离散与连续动力系统 - A》12 (5) (2005) 959]，表明从生物学角度来看更可接受的系数线性增长情况下，这些系统的动力学在原始状态空间的某些子空间中是混沌的。
