by:
Rudy C Tarumingkeng

Reference:
Edelstein-Keshet, L (1988): Mathematical Models in Biology.

Random
House, New York. p. 218-219

The equations along
with the time are converted into the following sumultaneous descrete
equation:

Values given for a,
b, c and d:

h = step,

This
is a simulation of the Lotka-Volterra two species interaction (i.e. predator and
prey) with simple assumptions as follow (Edelstein-Keshet,
1988):

1.
Prey population grow in an unlimited way when there is no
predators

2.
For the prey to survive predator must be present

3.
The rate of predation depends on the likelihood that a victim is encountered by
a predator

4.
The growth rate of predator is proportional to the rate of predation (food
intake).

Lotka-Volterra
model:

(N)
dN/dt = aN - bNP (prey population)

(P)
dP/dt = -cP + dPN (predator population)

a,
b, c and d > 0

Using
Euler method does not give exact results but it shows the cycle
approximation.

a =
growth rate of prey in the absence of predator

c =
death rate of predator in the absence of prey ,

b =
predator efficiency in causing prey population decline

bP
= death rate of prey due to predation

d =
prey efficiency in contributing to predator population growth

dN
= growth rate of predator due to feeding on prey

FILE
LV-EU: oleh Rudy C Tarumingkeng, PhD

JUNI
1996

INTERAKSI
DUA SISTEM, MODEL LOTKA-VOLTERRA

SOLUSI
DENGAN METODA EULER: DERET TAYLOR SAMPAI SUKU
KEDUA