Question

Pls help:)

Answer 1

I don't have any Idea, Sorry...!!

Answer 2

that's k. thnx:)

Answer 3

you have to make a lot of assumptions or maybe one already exists.

Answer 4

i am not sure of it. but is this one of the assumptions.
the two species of insect do not interfere with each apart from competing for food.

Answer 5

@hartnn @ganeshie8

Answer 6

system of linear ODEs right ?

Answer 7

i am learning this under mathematical modelling.

Answer 8

Okay, as long as this is ODEs i can attempt...

Answer 9

say \(\large x_1(t), ~x_2(t)\) represent the population of species as function of time

Answer 10

then the population growth cqan be modeled as :

\(\large x_1' = ax_1 + bx_2 + f(t)\)

\(\large x_2' = cx_1 + dx_2 + g(t)\)

Answer 11

population should decrease as food decreasing ??

Answer 12

i dont have much idea but it is what i think

Answer 13

yeah the constants a,b,c,d decide the fate of populations

Answer 14

@ajprincess does the above setup look familiar, or are you looking for something else ?

Answer 15

a,b,c,d need not be constants however, they could be functions of time as well

but for simplicity we can assume no natural disasters are allowed and they can be constants

Answer 16

sorry for replying late. it was because of slow connection. this is what i am looking for. usually we do it this way. first list out all the variables or factors involved and then the assumptions.finally we form the equation

Answer 17

i tink we cannot let f(t)=g(t) = 0 because it has to model the decreasing resources

Answer 18

are f(t) and g(t) functions of food?

Answer 19

yes they are food here,
and we can make them identical functions as the amount of food available is same, right ?

Answer 20

\(\large x_1' = ax_1 + bx_2 + f(t) \)

\(\large x_2' = cx_1 + dx_2 + f(t) \)

Answer 21

since they are competing for food,
b,c have to be negative and f(t) must be a decreasing function

Answer 22

a,d will be positive for obvious reasons
more population in present generation = more population next generation

Answer 23

ya

Answer 24

also give some initial conditions :
\(\large x_1(0) = y_1(0) = 100\)

both species start with a population of 100

Answer 25

what else you can we adjust ?
do you want to assign specific numeric values for a,b,c,d ?

to make the species \(x_1\) species slightly aggressive, you can choose below values :
a = 3, b=-1
c = -2, d= 2

Answer 26

if you want a single equation, you can turn that into system inot a second order equation

Answer 27

that may not work, try this instead :

\(\large x_1' = f(t)x_1 -x_2 \)
\(\large x_2' = -x_1 + f(t)x_2 \)

Answer 28

check this
http://www.eeb.cornell.edu/ellner/lte/chapter4.pdf

Answer 29

thnx a lot.:)