Flow* Lotka_Volterra.model

Model description

The 2-dimensional Lotka-Volterra system depicts the populations change of a class of predators and a class of preys. The growth rate of preys’ population  x over time is given by  \dot{x} = x\cdot (\alpha - \beta \cdot y) wherein  \alpha, \beta are constant parameters and  y is the population of predators. It gives that the number of preys grows exponentially without predation. The population growth of predators is governed by the differential equation  \dot{y} = -y\cdot (\gamma - \delta\cdot x) wherein  \gamma, \delta are constant parameters. We set those parameters as  \alpha = 1.5 ,  \beta = 1 ,  \gamma = 3 and  \delta = 1 .

Reachability setting

We consider the initial set  x\in [4.8,5.2], y \in [1.8,2.2] .


The following figure shows an overapproximation computed by Flow* for the time horizon  [0,5] :