LotkaVolterraSystemsPredatorprey dynamics 
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This is the basic two species model of predation from ecology—the so called LotkaVolterraModel [17].
In the upper model we recognize more explicitly that both populations, rabbits and foxes, have independent processes of exponential growth (the prey population's net rate of growth) and exponential decline (the predator's net rate of negative growth when there is no prey). The predation is modeled using an an →interaction (a special kind of flow element). It introduces nonlinearity, as there is some fractional rate (beta, delta
) that is multiplied with rabbits(t) ⋅ foxes(t). Predation results in an outflow from the rabbit population (increased deaths) and an inflow to the prey population (increased reproduction).
The model below shows the same model structure in a generalized, more compact fashion using the interaction flow component →LotkaVolterra .
0.1 [1/yr]
using the displayUnit
attribute and conversion tables. All calculations in a simulation will always use SIunits for time so that rates are in unit 1/s
and times in unit s
.modelOutput
) where the variables rabbits, foxes, prey, predators
are explicitly declared with appropriate units.The model presented here comes from Michael Tiller's excellent introduction "Modelica by Example" (see Describing Behavior>Basic Equations>Examples>LotkaVolterra System), which ships with SystemModeler and can also be found online.
LotkaVolterra, NonlinearInteraction, ExponentialGrowth, ExponentialDecline
alpha 
Value: 3.16887385068114e09 Type: Rate (1/s) Description: Reproduction rate of prey 

beta 
Value: 6.33774770136229e10 Type: Rate (1/s) Description: Mortality rate of prey per predator 
gamma 
Value: 1.26754954027246e08 Type: Rate (1/s) Description: Mortality rate of predator 
delta 
Value: 6.33774770136229e10 Type: Rate (1/s) Description: Reproduction rate of predators per prey 
modelOutput 
Type: ModelOutput Description: Main output of the model 

modelSettings 
Type: ModelSettings Description: Setting important global variables within a model 


prey 
Type: MaterialStock Description: Prey population 

predators 
Type: MaterialStock Description: Predator population 

rabbits 
Type: MaterialStock Description: Rabbit population 

foxes 
Type: MaterialStock Description: Fox population 

reproducing 
Type: ExponentialGrowth Description: Growth of rabbit population 

starving 
Type: ExponentialDecline Description: Foxes mortality in absense of prey 

predation 
Type: NonlinearInteraction Description: Foxes predating on rabbits 

predating 
Type: LotkaVolterra Description: Compact interaction flow that combines all processes of growth and decline 
foxes
does not need unit="foxes"
, diagram and simulation plots in v2.0.0.