4. Suppose that an insect population, r(t), is controlled by a natural predator population,y(t).a) Write down the Lotka-Volterra predator-prey model that can describe the inter-action of these populations.b) Find and graph the null-clines and the equilibria of your model. Sketch a vector-field in the phase plane.c) Suppose an insecticide is applied, but it is also toxic to the predators. Hence,the poison kills both predator and prey at rates proportional to their respectivepopulations. Modify your model from a) to take this into account, and write outthe new model governing the populations.d) Find the equilibria of the new model, and compare them to your results underb). How does the application of the insecticide change the equilibrium levels ofthe insects and their natural predator? What does this mean?

Since the sub parts are not specified so i am solving first three parts. (a) It is given that an…

Answered: 4. Suppose that an insect population,…

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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4. Consider the following linear predator-prey model with harvesting: dr dt dw dt = 6r2w - 1, = 2r+w-2, where r(t) is the population of rabbits and w(t) the population of wolves. Convert the system into vector form and use the method of Problem 3 to solve it.
16) (a) Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. (b) Use a computer to graph the path of the particle. a(t)=ti+e^tj+e^-tk, v(0)=k, r(0)=j+k
Hi. I need help with part (d) and (e) The bond behavior of reinforcing bars is an important determinant of strength and stability. The article "Experimental Study on the Bond Behavior of Reinforcing Bars Embedded in Concrete Subjected to Lateral Pressure"† reported the results of one experiment in which varying levels of lateral pressure were applied to 21 concrete cube specimens, each with an embedded 16 mm plain steel round bar, and the corresponding bond capacity was determined. Due to differing concrete cube strengths (fcu, in MPa), the applied lateral pressure was equivalent to a fixed proportion of the specimen's fcu (0, 0.1fcu, , 0.6fcu). Also, since bond strength can be heavily influenced by the specimen's fcu, bond capacity was expressed as the ratio of bond strength (MPa) to sqrt. of fcu . Pressure 0 0 0 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 Ratio 0.123 0.100 0.101 0.172 0.133 0.107 0.217 0.172 0.151 0.263 0.227 0.252 0.310 Pressure 0.4 0.4 0.5 0.5 0.5…
dê. ds Is bx(cxa) = (axc)xb? Justify your answer. dê. show that. dt (1) Ifx² x= -=vrên where v = ds dt (ii) (iii) If a-ȧ = 0, where à =(a) *0, what can be stated about a? dt (iv) Is (axb)xc in the plane formed by a and b. b and c, or a and c? Justify.
Solve the following initial value problem, 10y′′+2y = {cos(t) for 0</=t<5pi/6 and 10y''+2y={sin(t) for 5pi/6</=t with initil conditions y(0)=0 y'(0)=0
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