Mathematical Modelling of Natural Phenomena · 2014 · 11 citations · 28 references
Life SciencesBiologyMathematicsDifferential EquationsDynamical SystemsPopulation EcologyAge StructurePartial Differential Equation ModelsPopulation Dynamics ModelingPredator-prey InteractionsTime Delay EffectsDelay Differential SystemsDelay EquationsPopulation Dynamics With DelayPredator - Prey DynamicsPredator DynamicsPredator-prey DynamicsPredator-prey ModelsPrey Dynamics
A general framework for age-structured predator-prey systems is introduced. Individuals are distinguished into two classes, juveniles and adults, and several possible interactions are considered. The initial system of partial differential equations is reduced to a system of (neutral) delay differential equations with one or two delays. Thanks to this approach, physically correct models for predator-prey with delay are provided. Previous models are considered and analysed in view of the above results. A Rosenzweig-MacArthur model with delay is presented as an example.
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R. D. Carmichael, Alfred J. Lotka · American Mathematical Monthly · 1926 · 2.8K citations
E. W. Kopf, Alfred J. Lotka · Journal of the American Statistical Association · 1925 · 2.4K citations
The Natural Control of Animal Populations
M. E. Solomon · Journal of Animal Ecology · 1949 · 1.5K citations
Life Sciences, Biology, Ecology +12