# Python代写 | FIT3139: Assignment 2

本次澳洲代写主要为python建模相关的assignment

Part 1

Background

This exercise uses the Lotka-Volterra model to explore the sustainability of an ecosystem with rabbits, foxes

and hunting. We start by exploring the eect of hunting rates rates in a deterministic model.

A stochastic extension further allow us to explore the sustainability of the ecosystem using a combination

of Gillespie and Montecarlo simulations.

Questions Part 1A [2 marks]

The system tracks the number of rabbits x, and foxes y, and the dynamics are given by:

_ x = g(x; y)

_ y = h(x; y)

In the absence of foxes and hunting, rabbits grow exponentially with a growth rate b and a death rate

d (b > d); the number of rabbits eaten by foxes is proportional to the product of the number of rabbits

present and the number of foxes present by a factor . Foxes decline exponentially in isolation, with a

birth and death rate b0

and d0

, respectively (d0

> b0

). A parameter is the proportional constant of foxes

surviving by eating rabbits { thus foxes in the presence of rabbits increase at a rate b0

+ x proportional

to the number of foxes. Rabbits are hunted at a rate f, where as foxes are twice as hard to hunt.

(a) Formulate g(x; y) and h(x; y) re ecting the assumptions above∗.

(b) Using your own RK2 numerical integrator, inspect the dynamics of this system for dierent hunting

rates f. Assume b = 0:8, d = 0:1, b0

= 0:1, d0

= 0:6, = 0:04, and = 0:01. The initial population

consist of 25 rabbits, and 15 foxes. You should study at least 3 dierent hunting rates, and present

the time-evolution of the system as well as a phase plot of the dynamics for each parameter set.

What should you submit for this question?

You will have to submit

• Your own implementation of RK2.

• For each of your chosen f rates, a time-evolution plot, a phase plot and an interpretation of the

dynamics.