A Mathematical Framework for Agent Based Models of Complex Biological Networks
A Mathematical Framework for Agent Based Models of Complex Biological Networks
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DOI：
10.1007/s11538-010-9582-8
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发表时间：
2011-07-01
影响因子：
3.5
通讯作者：
Laubenbacher, Reinhard
中科院分区：
文献类型：
--
作者：
Hinkelmann, Franziska;Murrugarra, David;Laubenbacher, Reinhard
基于Agent的建模和仿真是研究从分子生物学到生态学等广泛领域中的生物现象的有用方法。由于目前还没有一个公认的标准方法来指定这样的模型，因此使用已发布的模型并不总是那么容易。此外，由于模型描述通常不是用数学术语给出的，因此很难使用数学分析工具，因此通常通过模拟来研究模型。为了解决这个问题，Grimm等人提出了一个用于模型规范的协议，即所谓的ODD协议，它提供了一种描述模型的标准方法。本文提出了一个除了ODD协议，它允许描述的一个基于代理的模型作为一个动态系统，它提供了访问的计算和理论工具，其分析。数学框架是代数模型，即具有代数结构的时间离散动力系统。它是通过几个例子，这个数学规范可以帮助模型分析。这个数学框架也可以容纳其他模型类型，如布尔网络和更一般的逻辑模型，以及Petri网。
Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.