Weinberger Hans F, Lewis Mark A, Li Bingtuan
School of Mathematics, University of Minnesota, 514 Vincent Hall, 206 Church Street SE, Minneapolis, Minnesota 55455, USA.
J Math Biol. 2002 Sep;45(3):183-218. doi: 10.1007/s002850200145.
The discrete-time recursion system u_[n+1]=Q[u_n] with u_n(x) a vector of population distributions of species and Q an operator which models the growth, interaction, and migration of the species is considered. Previously known results are extended so that one can treat the local invasion of an equilibrium of cooperating species by a new species or mutant. It is found that, in general, the resulting change in the equilibrium density of each species spreads at its own asymptotic speed, with the speed of the invader the slowest of the speeds. Conditions on Q are given which insure that all species spread at the same asymptotic speed, and that this speed agrees with the more easily calculated speed of a linearized problem for the invader alone. If this is true we say that the recursion has a single speed and is linearly determinate. The conditions are such that they can be verified for a class of reaction-diffusion models.
考虑离散时间递归系统(u_{[n + 1]} = Q[u_n])，其中(u_n(x))是物种种群分布的向量，(Q)是一个对物种的生长、相互作用和迁移进行建模的算子。先前已知的结果得到了扩展，以便能够处理新物种或突变体对合作物种平衡的局部入侵。研究发现，一般来说，每个物种平衡密度的变化以其自身的渐近速度传播，入侵者的速度是所有速度中最慢的。给出了关于(Q)的条件，这些条件确保所有物种以相同的渐近速度传播，并且该速度与仅针对入侵者的线性化问题的更容易计算的速度一致。如果是这样，我们就说该递归具有单一速度并且是线性确定的。这些条件使得它们可以针对一类反应扩散模型进行验证。
