Chaos and Microbial Systems

近十年来，在非线性动力学领域出现了许多新的成果，其中最引人注目的是混沌现象。许多最近的结果来自数学家和理论和实验物理学家；然而，早期的许多工作都是由人口动态问题推动的。最近研究的一个反复出现的主题是，看似随机的波动往往是简单的确定性机制的结果。因此，非线性动力学最近的大部分工作都集中在识别看似混乱系统中的秩序的新技术上。当这些技术应用于生态学时，对几个系统产生了新的见解，最引人注目的是各种儿童流行病。为了确定这些技术的稳健性，在某种程度上，必须将混沌带入实验室。对强制双monod方程（一个具有流入底物浓度周期性变化的趋化器中捕食者和猎物的模型）的初步研究表明，简单的微生物系统可能为确定处理复杂种群动态的新非线性动力学的有效性和相关性提供了完美的框架。本建议将提供一个彻底的检查的数学性质的强迫双莫诺模型和自同系统的实验研究。

The last ten years have seen a host of new results in the field of nonlinear dynamics, most notably regarding the phenomenon called chaos. Many recent results have come from mathematicians and from theoretical and experimental physicists; yet much of the early work was motivated by issues in population dynamics. A recurrent theme of this recent resarch is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in non-linear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. These techniques when applied in ecology have led to new insights for several systems, most notably various childhood epidemics. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This proposal will provide a thorough examination of the mathematical properties of the forced double-Monod model and an experimental investigation of the self- same system.