Stochastic nonlinear dynamics in the environment and biology

环境和生物学中的随机非线性动力学

• 批准号: RGPIN-2015-03892
• 负责人: Kuske, Rachel
• 金额: $ 2.26万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=612637
• 关键词: Stochastic; nonlinear; dynamics; environment; biology

Realistic models of biology and the environment are essential to understanding observations about our world, predicting phenomena, and making improvements. We focus on areas of stochastic nonlinear dynamics that have received minimal attention from past dynamical analyses, but are necessary for realistical environmental and biological models - namely, nonsmooth dynamics, delays, and transitions driven by interaction of complex dynamics and noise. Our objectives are to identify conditions where noise drives qualitative changes in biological and environmental dynamics, to create a better understanding of the underlying mechanisms, to develop better models and analyses, and to predict unexpected behaviours. We combine modern approaches based on applied analysis, computations, and integrated probabilistic, statistical, dynamical and geometrical analyses to develop novel techniques that can translate across application areas. We focus on several key areas that are virtually unexplored or under-explored, where we need creative new approaches for understanding, measuring, and predicting novel interactions of randomness and nonlinear complex dynamics. There are opportunities for research training throughout. Transitions: Present measures for abrupt or dramatic transitions, such as stochastic facilitation in neuroscience, tipping in environmental contexts, and outbreaks in epidemiology, do not all capture the interaction of nonlinear dynamics and noise. We propose new methodologies for capturing these effects. Nonsmooth dynamics: Interactions of noise and novel nonlinear phenomenon for nonsmooth systems are virtually unexplored even though nonsmooth behavior is commonly seen in systems with on-off switches, phase transitions, or patchy environments. Delayed Feedback: In models with delayed feedback, e.g. optics, human balance, disease, and cellular dynamics, noise can interact to either stabilize or destabilize desired behavior. Preliminary results point to new directions for studying spatial phenomenon, such as resilience of vegetation patterns or biochemical and electrophysiological waves. Multiple Scales: Multiple time scale concepts are ripe for translation to new areas such as epidemiology, genetics, and the environment, as well as disease dynamics with rare events on long time scales, such as in HIV or tuberculosis. Optimization and control: Robustness in control systems is often dependent on features such as delayed feedback, on-off control, and noise, that are captured by our novel approaches. In stochastic optimization we develop new, efficient methods by viewing the iterations themselves as a dynamical system, with nonlinearities interacting with sampling.

现实的生物学和环境模型对于理解我们世界的观察、预测现象和做出改进至关重要。我们专注于领域的随机非线性动力学，已收到最小的关注，从过去的动力学分析，但有必要realtimes环境和生物模型-即，非光滑动力学，延迟和过渡驱动的复杂动力学和噪声的相互作用。 我们的目标是确定噪声驱动生物和环境动力学发生质变的条件，更好地了解潜在机制，开发更好的模型和分析，并预测意外行为。我们结合联合收割机基于应用分析、计算和综合概率、统计、动力学和几何分析的现代方法，开发可以跨应用领域转化的新技术。我们专注于几个几乎未开发或开发不足的关键领域，在这些领域，我们需要创造性的新方法来理解、测量和预测随机性和非线性复杂动力学的新相互作用。有机会在整个研究培训。 过渡：目前的措施，突然或戏剧性的转变，如随机促进神经科学，在环境背景下的小费，和流行病学的爆发，并不都捕捉到非线性动力学和噪声的相互作用。我们提出了新的方法来捕捉这些影响。 非光滑动力学：非光滑系统的噪声和新的非线性现象的相互作用几乎是未知的，即使非光滑行为是常见的系统与开关，相变，或斑块环境。 延迟反馈：在具有延迟反馈的模型中，例如光学、人体平衡、疾病和细胞动力学，噪声可以相互作用以稳定或不稳定期望的行为。初步结果指出了研究空间现象的新方向，如植被模式或生物化学和电生理波的弹性。 多尺度：多时间尺度的概念已经成熟，可以转化为新的领域，如流行病学，遗传学和环境，以及在长时间尺度上罕见事件的疾病动力学，如艾滋病毒或结核病。 优化和控制：控制系统的鲁棒性通常取决于延迟反馈、开关控制和噪声等特征，这些特征都是我们的新方法所捕获的。在随机优化中，我们开发了新的，有效的方法，通过查看迭代本身作为一个动态系统，非线性与采样相互作用。