The Study of Supertransients in Spatiotemporal Chaotic Dynamical Systems with Applications to Nonequilibrial Species Coexistence in Ecology

赖9626529混沌动力学的研究为理解从物理学到气象学到生物科学的广泛学科中的复杂动力学提供了一个新的范式。这一建议集中于一个在非线性动力学中具有重要意义的问题，并且在生态系统中具有潜在的重要意义：空间扩展混沌系统中的超瞬变现象。具体地说，我们将研究超瞬变的起源，并发展一个定量标度理论来解释超瞬变的寿命如何以及为什么会随着系统的大小而增加。这一理论将首先发展为一个简单的、可分析的模型，然后在一些模型时空混沌系统上测试该理论。我们将研究几个现实生态模型系统中的超瞬变现象，重点关注超瞬变现象促进竞争物种长期(尽管不是无限期)共存的可能性，以及这种共存如何受到系统大小的影响。ME模型涉及斑块中物种之间的竞争，以及斑块之间的局部扩散。这项工作将有助于生态学中关于非平衡动力学在理解物种多样性模式方面的重要性以及空间尺度对物种共存的影响的长期辩论。充分理解物理和生物系统的动力学需要考虑脱离平衡的瞬时动力学。最近，人们认识到，现实的空间分布生态系统模型在达到平衡之前可能会表现出超长的‘混沌’瞬变，在所有实际目的中，系统永远不会达到最终平衡。我们的研究集中于定量刻画数学模型中的超瞬变现象，使用数学分析和广泛的数值模拟，并确定超瞬变与重要的、未解决的生态学问题的潜在相关性，特别是竞争有限资源的物种的长期共存，但能够在异质、斑驳的景观中分散在空间中。

Lai 9626529 The study of chaotic dynamics provides a new paradigm for understanding complicated dynamics in a wide range of disciplines, ranging from physics to meteorology to the biological sciences. This proposal focuses on one problem that is of fundamental importance in nonlinear dynamics, and is potentially of great importance in ecological systems: the phenomenon of supertransients in spatially-extended chaotic systems. Specifically, we will investigate the origin of supertransients, and develop a quantitative scaling theory to explain how and why the lifetime of supertransients increases with system size. This theory will be developed first for a simple, analyzable model, then to test this theory on a number of model spatiotempral chaotic systems. We will investigate supertransients in several realistic ecological model systems, and focus on the potential for supertransiency to promote the long term (though not indefinite) coexistence of competing species, and how such coexistence is influenced by system size. 'Me models involve competition among species in patches, with localized dispersal among patches. This work will contribute to a long-standing debate in ecology about the importance of nonequilibrial dynamics in understanding patterns in species diversity, and the influence of spatial scale on species coexistence. A full understanding of the dynamics of physical and biological systems requires a consideration of transient dynamics away from equilibrium. Recently, it has become recognized that realistic models of spatially-distributed ecological systems can exhibit superlong 'chaotic' transients before equilibrium is reached, wherein for all practical purposes a system never reaches its ultimate equilibrium. Our research focuses on characterizing quantitatively the phenomenon of supertransient behaviors in mathematical models, using both mathematical analyses and extensive numerical simulations, and on ascertaining the potential relevance of supertransients for import ant, unresolved questions in ecology, in particular the long-term coexistence of species competing for limiting resources, but able to disperse in space in heterogeneous, patchy landscapes.