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- W4249194610 abstract "The idea of a community matrix was introduced in 1968 by R. Levins [L]. If a model has n compartments, then the community matrix is an n×n matrix of functions of time A(t). As in the previous chapter, A(t) is defined relative to a special trajectory $${rm{hat x}}$$ (t), a trajectory of observed, “normal,” or, on the basis of experience, predicted compartment values. Recall the definition of A(t): $${{A}_{{ij}}}(t) = frac{{partial {{f}_{i}}}}{{partial {{x}_{j}}}}left( {hat{x}(t),t} right)$$ where $${hat{x}}$$ (t) is a trajectory of the ecosystem model (dynamical system) $${{{dot{x}}}_{i}} = {{f}_{i}}left( {x,t} right)$$ In the very special and unrealistic case that A(t) is actually a matrix of constants, certain mathematical tests (the Hurwitz tests of the previous chapter) can be performed on A which indicate the qualitative nature of nearby trajectories, namely, whether or not relative to nearby trajectories $${hat{x}}$$ (t) is an attractor trajectory." @default.
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- W4249194610 date "1989-01-01" @default.
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- W4249194610 title "Introduction to Ecosystem Models" @default.
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- W4249194610 doi "https://doi.org/10.1007/978-1-4612-4550-6_5" @default.
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