SGER: Real-Population Data for Evaluating Chaos-Detection Methods

9505343 Hairston博士申请探索性研究（SGER）小额资助，该项目具有将混沌研究推向新领域的巨大潜力：检测非线性和混沌方法的真实实验验证。最终目标是发展方法来确定是否混沌是自然种群动态的基础。在这个项目中，真实的生物体将被用来创建数据集，这些数据集明显表现出复杂的非线性动力学（要么是混沌，要么是复杂的周期振荡）。这些数据将用于实验测试现有的和新的方法来表征复杂的动力学。本实验系统采用单态恒化器培养轮虫及其藻类食物，以可变供给速率限制藻类生长的养分。有实验证据表明，这个系统可以表现出捕食者-猎物的振荡。数学理论表明，这种振荡可以被驱动成复杂的模式锁定振荡，并最终进入混沌，通过脉冲或周期性变化的营养供应率。SGER拨款将用于为期一年的试点研究，以证明建造和维持实验系统的可行性；改变条件以获得有用的种群动态；并进行实验。在这些研究中，原本打算用于自然种群的统计方法将首次通过在真实生物体上的实验得到验证。与使用模拟数据的传统测试相比，这是向现实迈出的重要一步。

9505343 Hairston Dr. Hairston requests funding for a Small Grant for Exploratory Research (SGER) for a project which has great potential to move research on chaos to a new arena: real experimental validation of methods for detecting nonlinearity and chaos. The ultimate goal is the development of methods for determining whether chaos underlies the dynamics of natural populations. In this project, real organisms will be used to create data sets that demonstrably exhibit complex nonlinear dynamics (either chaos or complicated periodic oscillations). These data will be used to experimentally test existing and new methods for characterizing complex dynamics. The experimental system is a single-state chemostat culturing rotifers and their algal food with variable supply rate of the nutrient limiting algal growth. There is experimental evidence that this system can exhibit predator-prey oscillation. Mathematical theory suggests that such oscillations can be driven into complex mode-locking oscillations, and eventually into chaos, by pulsed or periodically varying nutrient supply rate. SGER funding will be used for a one-year pilot study to demonstrate the feasibility to: construct and maintain the experimental system; vary conditions to obtain useful population dynamics; and conduct experiments. These will be the first studies in which statistical methods, intended for use on natural populations, are validated through experiments on real organisms. This represents a major step towards reality, compared with conventional tests using simulated data.