State monitoring of a population system in changing environment
For Lotka-Volterra population systems, a general model of state monitoring is presented. The model includes time-dependent environmental effects or direct human intervention (“treatment”) as control functions and, instead of the whole state vector, the densities of certain indicator species (distinguished or lumped together) are observed. Mathematical systems theory offers a sufficient condition for local observability in such systems. The latter means that, based on the above (dynamic) partial observation, the state of the population can be recovered, at least near equilibrium. The application of this sufficient condition is illustrated by three-species examples such as a one-predator two-prey system and a simple food chain.
KeywordsLotka-Volterra model Non-linear system Observability Predator/prey systems
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