Lotka-Volterra model¶
- class pints.toy.LotkaVolterraModel(y0=None)[source]¶
Lotka-Volterra model of Predatory-Prey relationships [1].
This model describes cyclical fluctuations in the populations of two interacting species.
\[\begin{split}\frac{dx}{dt} = ax - bxy \\ \frac{dy}{dt} = -cy + dxy\end{split}\]where
x
is the number of prey, andy
is the number of predators.Real data is included via
suggested_values()
, which was taken from [2], and includes hare and lynx pelt count data collected by the Hudson’s Bay Company, in Canada in the early twentieth century.Extends
pints.ForwardModelS1
,pints.toy.ToyODEModel
.- Parameters:
y0 – The initial population, given as a vector
[a, b]
such thata >= 0
andb >= 0
.
References
- n_states()¶
Returns number of states in underlying ODE. Note: will not be same as
n_outputs()
for models where only a subset of states are observed.
- simulate(parameters, times)¶
- simulateS1(parameters, times)¶