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.

生物学和环境的现实模型对于理解有关我们世界，预测现象和改进的观察至关重要。我们专注于随机非线性动力学的领域，这些动力学从过去的动态分析中受到了最少的关注，但对于现实的环境和生物模型是必需的 - 即，由复杂动态和噪声的相互作用驱动的非平滑动力学，延迟和过渡。 我们的目标是确定噪声驱动生物学和环境动力学的质量变化的条件，以更好地理解潜在机制，开发更好的模型和分析并预测意外行为。我们根据应用分析，计算以及综合概率，统计，动态和几何分析来结合现代方法，以开发可在应用领域转化的新技术。我们专注于几乎是意外或探索不足的几个关键领域，在这些领域中，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型相互作用。整个过程中都有研究培训的机会。 过渡：目前针对突然或戏剧性转变的措施，例如神经科学中的随机设施，在环境环境中的小费以及流行病学中的爆发，并不全部捕获非线性动力学和噪声的相互作用。我们提出了捕获这些效果的新方法。 非平滑动力学：噪声与新型非平滑系统的新型非线性现象的相互作用实际上是出乎意料的，即使在具有开关开关，相变或斑点环境的系统中通常可以看到非滑动行为。 延迟反馈：在具有延迟反馈的模型中，例如光学，人类平衡，疾病和细胞动力学，噪声可以相互作用以稳定或破坏所需的行为。初步结果指出了研究空间现象的新方向，例如植被模式的弹性或生化和电生理波。 多个尺度：多个时间尺度概念已经成熟，可以转化为新领域，例如流行病学，遗传学和环境，以及在长期尺度上（例如HIV或结核病）上具有罕见事件的疾病动态。 优化和控制：控制系统中的鲁棒性通常取决于我们的新方法捕获的延迟反馈，关闭控制和噪声等功能。在随机优化中，我们通过将迭代本身视为动态系统来开发新的，有效的方法，而非线性与采样相互作用。