Coarse Dynamics for Coarse Modeling: An Example From Population Biology
Coarse Dynamics for Coarse Modeling: An Example From Population Biology
复制标题
粗略建模的粗略动力学：群体生物学的一个例子
作者：
J. Bush;K. Mischaikow
网络已成为一种流行的方式来简明地表示复杂的非线性系统，其中相互作用和参数是不精确的。一项挑战是如何最好地描述相关的动力学，它可以表现出对参数的微小变化敏感的复杂行为。最近开发的一种计算方法（我们称之为动力学数据库）为大范围参数空间上的全局动力学提供了稳健且数学上严格的描述。为了证明这种方法的潜力，我们考虑两个经典的年龄结构人口模型，它们共享相同的网络图并具有类似的非线性过度补偿项，但仍然会根据参数产生不同的定性行为模式。通过对这些模型的概括，我们将在生物学相关问题（例如群体的稳定振荡、双稳定性和持久性）中观察到的动态的不同结构联系起来。
Networks have become a popular way to concisely represent complex nonlinear systems where the interactions and parameters are imprecisely known. One challenge is how best to describe the associated dynamics, which can exhibit complicated behavior sensitive to small changes in parameters. A recently developed computational approach that we refer to as a database for dynamics provides a robust and mathematically rigorous description of global dynamics over large ranges of parameter space. To demonstrate the potential of this approach we consider two classical age-structured population models that share the same network diagram and have a similar nonlinear overcompensatory term, but nevertheless yield different patterns of qualitative behavior as a function of parameters. Using a generalization of these models we relate the different structure of the dynamics that are observed in the context of biologically relevant questions such as stable oscillations in populations, bistability, and permanence.