Question

hallo can somebody help for this problem?
Suppose that there exist two populations, one is a predator the other one the prey. The size of the predator population at time t is denoted by xt and the size of the prey population by yt. The gross growth rate of the predator population is a linearly increasing function of the prey population, namely
xt+1 / xt = a + byt
where both a and b are positive parameters and where a < 1. The prey population is assumed
to evolve according to
yt+1 = √yt / 1+ xt
What happens to the predator population in the long run if there is no prey, i.e., if yt = 0
holds for all t? What happens to the prey population in the long run if there are no predators, i.e.,ifxt =0 for all t?
(b) For which parameter constellations is the fixed point (x∗, y∗) locally asymptotically stable?

Answer 1

heeeeelp

Answer 2

can u type out using the equation

Answer 3

equation editor*

Answer 4

hi you can see it here http://homepage.univie.ac.at/Gerhard.Sorger/Dynamisch/HE_7.pdf

Answer 5

the pass is dynamic

Answer 6

if you can tell me all solution i will be very thankfull of you because i have a hube problems in matt

Answer 7

thank you anyway

Answer 8

I assume this is non-linear, you have to transfer into system of linear de's and then perturb the system (Jacobian).
At least that is the typical procedure, have you not been given methods to follow?

Answer 9

i do not know how to Transfer into into system of linear de

Answer 10

do you know where can i find an example solution of this problem because i am really bad i n math

Answer 11

Maybe if you try a search "Lotka-Volterra" equations, see if that takes you anywhere

Answer 12

aha ok thank you so much

Answer 13

Hope it helps....

Answer 14

i hope too thank you anyway that you spend your time for my problem

Answer 15

ur welcome.

Answer 16

hei people pls try to tell me how to make a solution

Answer 17

can somebody tell me how to find fixed points from my problem and how to make jacobian Matrix in my case?

Answer 18

Problem is this is easy to ask but a lot of work to answer........

Answer 19

yes this is true

Answer 20

but can you give me some advices and may be i will do it with myself

Answer 21

But it seems you understand the main points already:
Get equilibrium point of de's

Get Jacobian

Linearize in the neighborhood of the equibrium point.

Are u at university?

Answer 22

yes

Answer 23

I am surprised that they have not provided you with materials that goes step by step through this.

Answer 24

i have a problem with the fixed point i do not know how to find them

Answer 25

no no we have examples in the lectures but i really do not uderstand that type of problems, because of that i search help here

Answer 26

because i have to make my homewort to have a points before final exam

Answer 27

I will try and write somethinga bit later, OK?

Answer 28

ok thank you so much about everything