Systems Modelling and Simulation - Prey predator model. The goal of this experiment is to model the population dynamics of animals both predator and prey when they are present in an environment.

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Systems Modelling and Simulation

Assignment No 2

Predator Prey Model

By

Vishal Vora (roll no 32)

Submitted in partial fulfilment of the course requirement to

Prof. Girja Sharan & Mr. Bhavesh Dharmani

                                   Predator Prey Model

Goal: 

The goal of this experiment is to model the population dynamics of animals both predator and prey when they are present in an environment.

Description:

  1. Initially at time t=0, the population of prey is some value say x0 and that of predator is y0
  2. Prey eats vegetarian food and predator eats prey
  3. If there are no predators, the population of preys will grow exponentially over time and will be growing at the rate of the difference of the birth and death rate.
  4. If there are predators, the population of prey will decrease to the extent they interact and the predator is successful in hunting the prey (Alpha)
  5. The population of the predator is dependent on the growth rate of the predator due to prey availability (Beta) and the death rate of the predator.

Assumptions:

  1. The forest is large and the preys are born and die continuously.
  2. There is no shortage of food.

At time t, the prey population is x.
After time t+Δt, the prey population is given by : x+ no of prey born in time Δt- no of natural prey deaths in time Δt.

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The rate of growth during interval Δt is :  (x +Δx-x)/(t+Δt-t)

Taking  lim         Δx/Δt= dx/dt.

             Δt0      

Thus we are assuming that the number of preys is large enough to support a continuous death and birth rates.

dx/dt = (birth rate- death rate)*x

 dx/dt= µx

dx/x = µdt

ln(x) = µt+ln(c)

ln(x/c) = µt

x = x0ceµt since at t=0, x=x0

Matlab Code:

t=0:10;

x0=20;

u= 0.4;

x= x0*exp(u*t)

plot(t,x)

However this is not a stable model and we need to ...

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