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Predator-prey relationship using ODE

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maha ezzat

on 31 May 2016

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Transcript of Predator-prey relationship using ODE

Predator-Prey Model 1
Lotka–Volterra equations
Equilibrium:

Eliminating time from Differential Equations:

Team Members
Basma Bashir

Bassma Hassan

Eman Mohamed

Shrouk Shalaby

Maha Ezzat
predator–prey Model
Describes the dynamics of a biological system consists of predator and pray by two first order non-linear Differential Equations.

x is the number of prey
y is the number of predator
t is time
dx/dt and dy/dt are the growth rate over time
α, β, γ, δ are non-negative constants represent the interaction between predator and prey.
Applying this Model on lion as predator and zebra as prey :

Eliminating time from equations:
Results
Separation of variables:
Solution:
Zebra
lion
stability
jacobian and eigen values:
first solution:
second solution:
Thank You!
Assumption
Prey’s population find available food all the time
Predators’ population depend entirely on the size of prey population available
Population’s rate of change is proportional to its own size
The environment does not change
Perdator’s appetite is limitless
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