Predator-prey system

May 2019
Bulgaria, Sofia
[FONT=&quot]I have to solve the following task with predator-prey method.[/FONT]

[FONT=&quot]The dynamics of self-regulating "predator-prey" populations in the population is described by the model:[/FONT]
[FONT=&quot]dN1/dt = (a - bN2 - αN1); dN2/dt = (-c + mN1)N2 (1),[/FONT]
[FONT=&quot]where α is coefficient of internal victim struggle, [/FONT]
[FONT=&quot]and a>0,b>0,α>0,c>0,m>0[/FONT]
[FONT=&quot]With this change N1=k1x, N2=k2y,t=k3z (2) the system (1) can be reduced to: dx/dz=x(E - Ax - y); dy/dz=y(-1 + x) (3) [/FONT]
[FONT=&quot]And here is the questions:[/FONT]
[FONT=&quot]1)Find the coefficients ki of element (2), where i =1,3 (irrationals)[/FONT]
[FONT=&quot]2)Find the relationship/connection between params A and E from (3) and the params from (1)[/FONT]
[FONT=&quot]3)Find the equilibrium (specific points) of system (3)[/FONT]
[FONT=&quot]4)Examine the stability of the equilibrium position of (3)[/FONT]
[FONT=&quot]5)Build a Phase Portrait of (3)[/FONT]

[FONT=&quot]Thank you in advance! [/FONT]
Dec 2013
Since you have to solve it, and not us, perhaps you could tell us what you have managed so far.
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