Lotka–Volterra equations
E645178
The Lotka–Volterra equations are a pair of nonlinear differential equations that model the dynamics of biological systems in which two species interact as predator and prey.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical model
ⓘ
nonlinear dynamical system ⓘ predator–prey model ⓘ system of differential equations ⓘ |
| assumes |
no environmental carrying capacity
ⓘ
no intraspecific competition ⓘ predators depend solely on prey for food ⓘ unlimited prey food supply ⓘ |
| describes |
biological systems with two interacting species
ⓘ
population dynamics ⓘ predator–prey interactions ⓘ |
| equationForm |
dx/dt = αx − βxy
ⓘ
dy/dt = δxy − γy ⓘ |
| field |
dynamical systems theory
ⓘ
ecology ⓘ mathematical biology ⓘ |
| hasComponent |
predator population equation
ⓘ
prey population equation ⓘ |
| hasEquilibrium | coexistence equilibrium of predator and prey ⓘ |
| hasUse |
chemical reaction modeling analogs
ⓘ
economics analog competition models ⓘ epidemiology analog models ⓘ population biology ⓘ theoretical ecology ⓘ |
| historicalPeriod | early 20th century ⓘ |
| inspired |
Lotka–Volterra competition equations
NERFINISHED
ⓘ
generalized predator–prey models ⓘ |
| mathematicalType |
autonomous system
ⓘ
first-order ordinary differential equations ⓘ |
| namedAfter |
Alfred J. Lotka
NERFINISHED
ⓘ
Vito Volterra NERFINISHED ⓘ |
| predicts |
closed orbits in phase space under ideal conditions
ⓘ
oscillatory population dynamics ⓘ |
| property |
continuous-time
ⓘ
deterministic ⓘ nonlinear ⓘ |
| relatedConcept |
bifurcation analysis
ⓘ
fixed point ⓘ limit cycle ⓘ phase portrait ⓘ |
| solutionBehavior | neutrally stable cycles in the linearized ideal model ⓘ |
| timeVariable | t (time) ⓘ |
| usesParameter |
α (prey growth rate)
ⓘ
β (predation rate coefficient) ⓘ γ (predator mortality rate) ⓘ δ (predator reproduction rate per prey eaten) ⓘ |
| usesVariable |
x (prey population size)
ⓘ
y (predator population size) ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.