Question

= • (Problem 4) Consider the following alternate predator-prey (Leslie) model: dF F(a – bF – cS) dt dS S S(-k +13). dt F Note that the prey model is the same as in the Lotka-Volterra model. However, the predators change in a different manner. Show that if there are many predators for each prey, then the predators cannot cope with the excessive competition for their prey and die off. On the other hand if there are many prey for each predator, then the predator will find them and increase. Do you have any objections to this model? Compare this model to the Lotka-Volterra model.

Answer 1

prey model is / Given alternative predator- df fla-bf-cs) dt 능위한 ds dt SI-K+S ) F let us assume X - = Fla-bF-C) at 10 Y = ds s(-K+DF) - Practanpa at Now, we have to find out equilibrium points, so df ds co, O w dt dt ie df → Farbf-cs) - co at Sa de =o, when f=0 (or) (a-be-cs) = 0 (ar) both are qeros ང dt rullra w a-b F- CS = 0 a-cs-SF a-cs O F= In the same way, ds at =0 when SCK+0F)-0, ie.-kt df=0 cord S-0. F =

At point (0,0), we get all the combinations for FE a-cs [150] b F = a- (lo) a-o a - b 811 F= a get one of the equilibrium point is (42,0) from equations ' and ② K a-CS yo b Kb = ad-cds cds = Moc: us - ad - kb ad-kb cd get on ther So, here we equilibrium points is, eft ada kb . Finally, ed we get equilibrium points are (0,0),19,0), 15), (adKb) ad_kby me