We wish to model a population of two fish species by a system ofdifferential eqns. x? = f(x,y), y? = g(x,y).
Provide a system of differential eqns. that describe thefollowing assumptions:
(a)(5) A predator-prey system in which prey can grow to no limits,but predators die out unless they find prey to eat.
(b)(5) Two species which individually would die out butcollaboration enhances survival of BOTH species.
(c)(5) A predator-prey system in which prey can grow with nolimits, but predators die out unless they find prey to eat. Inaddition the PREDATORS are being fished at a constant rate of 100per units of time.
(d) (5) A predator- prey system in which the prey species issubject to environmental limits to growth(if the population issmall it increases at a rate proportional to its size, but forpopulations > 1000 the rate becomes negative). The predatorspecies dies out unless they have prey to eat.
