Differential equationsGiven the system of differential equations in the picture:Show that (N,P)=(0,0) is an equilibrium point by evaluating the right-hand sides of the two system equations at these values and showing that both derivatives are equal to zero. Show complete solution. AN = rN (1 – ) – NP·R(N)dtdP-doP + eP. R(N)dtHere, N is the prey population, P is the predator population, K is the carryingcapacity, do is the death rate of predators, r is the response time of prey, e is anenhancement factor for the predator response, and R(N) = A/(N + B) is thepredator response (it defines saturation for prey-intake).Let K= 1.0, A = 3, B = 100, do = 0.8, and e = 100. The initial= 2000, r =conditions are N = 19 and P = 2 at t = 0.

The differential equation is dNdt=N1-N2000-3NPN+100 and dPdt=-0.8P-300PN+100 Set the derivative to…

Answered: Show that (N,P)=(0,0) is an equilibrium…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential equations

Given the system of differential equations in the picture:

Show that (N,P)=(0,0) is an equilibrium point by evaluating the right-hand sides of the two system equations at these values and showing that both derivatives are equal to zero. Show complete solution.

AN = rN (1 – ) – NP·R(N)
dt
dP
-doP + eP. R(N)
dt
Here, N is the prey population, P is the predator population, K is the carrying
capacity, do is the death rate of predators, r is the response time of prey, e is an
enhancement factor for the predator response, and R(N) = A/(N + B) is the
predator response (it defines saturation for prey-intake).
Let K
= 1.0, A = 3, B = 100, do = 0.8, and e = 100. The initial
= 2000, r =
conditions are N = 19 and P = 2 at t = 0.

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