(1 point) Math 216 Homework webHW10, Problem 4 Consider the predator/prey model r' = y =...
(1 point) Math 216 Homework webHW10, Problem 8 Consider the spring model " – 182 +2:03 = 0, where the linear part of the spring is repulsive rather than attractive (for a normal spring it is attractive). Rewrite this as a system of first-order equations in 2 and y=r'. x' = y' = Write down your system when you have it correct, for use in the next three problems. Then find all critical points and enter them below, in order...
Math 216 Homework webHW10, Problem 5 Consider the predator/prey model r' = 73 - 22 - ry y = -5y + xy. Find the linearization of this system at the second of the critical points you found in problem 3. , where A = [)] = A ( 3 ) where A = Then solve this to find the eigenvalues of the linearized system (enter any complex numbers you may obtain by using "" for V-1. For real answers, enter...
Math 216 Homework webHW10, Problem 9 Consider the spring model *" – 1x + 1x2 = 0, we looked at in the previous problem. Linearize the first-order system that you obtained there at the second of the critical points you found. [")=[*] where A = Then solve this to find the eigenvalues of the linearized system (enter any complex numbers you may obtain by using "i" for V-1. For real answers, enter them in ascending order; for complex, enter the...
Can someone please help answer this question? Math 216 Homework webHW10, Problem 2 Find the solution to the linearization around zero of the system x' = 6x – 4y – x°, y' = 4x + 6y + 3xys with initial conditions x(0) = -0.4 and y(0) = -0.4. x = y =
Find all equilibrium points for the predator-prey model [x = - xy/2 y = -3y/4 + y/4 and describe the trajectories near those points. Have WolframAlpha or some other program to draw some trajectories. (Here x is the population of the prey (rabbits) and y is the population of the predators (foxes).)
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(t)-2y(t)l, y'(t) = y(t)12-y(t)--2(t)] (a) Find all critical points of this system, and at each determine whether or not the system is locally stable or unstable. (b) We proved in class, using the Bendixson-Dulac theorem, that this system has no periodic solution with trajectory in the first quadrant of the plane. Assuming this, use the Poincare-Bendixson theorem to prove that all trajectories (z(t),y(t)) of the system (2) with initial...
1. Consider the Lotka-Volterra model for the interaction between a predator population (wolves W(t)) and a prey population (moose M(t)), À = aM - bmw W = -cW+dMW with the four constants all positive. (a) Explain the meaning of the terms. (b) Non-dimensionalize the equations in the form dx/dt = *(1 - y) and dy/dt = xy(x - 1). (c) Find the fixed points, linearize, classify their stability and draw a phase diagram for various initial conditions (again, using a...
(1 point) Math 216 Homework webHW3, Problem 11 Find the solution of the system where primes indicate derivatives with respect to t, that satisfies the initial condition x(0) - -2, y(0) - 5((-1/5)-(5/(10sqrt(30))))en(sqrt(30)t)-5(1/5)-(5/(10sqrt(C X- ysqrt(30)((-1/5)-(5/(10sqrt(30))e (sqrt(30)t)+sqrt(30)(1/ Based on the general solution from which you obtained your particular solution, complete the following two statements: The critical point (0,0) is A. unstable B. asymptotically stable C. stable and is a A. saddle point B. node ° C. Spiral D. center
(1 point) Math 216 Homework webHW3, Problem 4 Consider the cascade of two tanks of brine shown in the figure below, with V-105 gallons and V2-209 gallons being the volumes of brine in the two tanks. Each tank also initially contains 52 lb of salt. The three flow rates indicated in the figure are each 5.1 gal/min, with pure water flowing into tank (Click on the picture to see a larger version.) (a) Find the amount x(t) of salt in...
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit in absence of species r? (c) Find all critical (equilibrium) points d) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point. (e)...