sistema dinamico

[mariecurie]

devo risolvere questo problema sia in modo standard (punti fissi, varietà invarianti, stabilità... ) che rispondendo alle domande specifiche. Non lo traduco perché mi sembra banale. Scusate se non so usare Latex.


The interaction between two populations with densities N1 e N2 is modelled by

dN1/dt=rN1(1-N1/K)-aN1N2(1-exp[-bN1])

dN2/dt=-cN2+N2e(1-exp[-bN1])

where a, b, c, e, r, K are positive constants. What type of interaction exists between N1 e N2? What do the various terms imply ecologically?

Nondimensionalise the system by writing

u=N1/K

v=aN2/r

[tau]=rt

[alfa]=e/r

[delta]=d/r

[beta]=bK

Determine the nonnegative equilibria and note any parameter restrictions. Discuss the linear stability of the equilibria. Show that a nonzero N2-population can exist if [beta]>[beta subscript c]=-ln(1-[delta]/[alfa]). Briefly describe the bifurcation behaviour as [beta] increases with 0<[delta]/[alfa]<1.

[mariecurie]

nessuno lo sa risolvere?