Find predator–prey equilibria and the instantaneous rates of change from the classic four parameters.
| Prey equilibrium | – |
| Predator equilibrium | – |
| dx/dt | – |
| dy/dt | – |
Use this calculator for the classic Lotka–Volterra model when you have prey growth, predation, predator death, and conversion, plus a current pair of densities.
The rates are: dx/dt = αx − βxy and dy/dt = δxy − γy. The interior equilibrium is prey* = γ/δ and predators* = α/β. α is prey growth without predators, β is the attack rate, γ is predator death without prey, and δ is how much eaten prey becomes predator growth. Densities are in the same arbitrary units you used to fit the parameters.
This is the unbounded textbook model: no carrying capacity, no delays, no spatial structure. β and δ must be positive.
α (prey growth): Prey growth rate with no predators.
β (attack): Predation rate coefficient.
γ (predator death): Predator death rate with no prey.
δ (conversion): Conversion of eaten prey into predator growth.
Prey x: Current prey density.
Predators y: Current predator density.
Prey equilibrium: γ/δ.
Predator equilibrium: α/β.
dx/dt, dy/dt: Instantaneous rates at the current (x, y).
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