Question

Perform a phase-plane analysis for the following system and compute its vector field: Nu = 0.2N2 (120X+20) N2 = 0.3N2 (60=N3 =W3)

Answer 1

Solution Given that N= 0.2N, (120 - N₂-2011 NIE 0.2 Mil 30 - N₂ = 0+3 N2 / 60-N1-N2 E L - 15 For caruilibrium Point Ni=OF Ny. is MC 120-N2-2N, ) = 0 = N2 (60-NE-Nel 2 NI2O ; QN, + N2 = 120 ... N2 =0) Ni+N2= 60 when Nizo if N2=0 then Coo) is cauilibrium a point if NitN2= 60 then Co160) Ý cauilibrium Poink' When 2NEN₂ = 120 if N2=0 then . N. 60 and : (60, 0) il can point. If NTN2=60 then N= 60). N2=0 so caruilibrium points are coo) (600) & 60,60) When N2=0 When N, O. - N2EO - Nied . No change in vertical direction No change in horizontal direction If ZNEN2 > 120 and Niso . If NX No to & Naza NICO. Niis decreasing N₂ 20, N2 it decreasing If anothe 4120 & N, JO If Nene 260 A N220 NJO IN, is increasing Naso, Nog in increasing If an, the 420 & Nico . If Nitra 260 & NILO Nico, Ni is decreasing N₂20 N2 is decreasing

When NHN2=60 N2=0 No this line no change in vertical direction : NE 0.7 Nine . When 2N, AN2=120 MED No change in horizontal direction on this line. N2 = -0-3 NY

We can draw below! . Nico oraya forusunda Nzzo ☆ MAN2580 QM+ N2bo .