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

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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.