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Math 216 Homework webHW10, Problem 5 Consider the predator/prey model r' = 73 - 22 -...
Math 216 Homework webHW10, Problem 9 Consider the spring model *" – 1x + 1x2 =...
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...
Consider the spring model x″−8x+2x3=0, x ″ − 8 x + 2 x 3 = 0...
Consider the spring model
x″−8x+2x3=0, x ″ − 8 x + 2 x 3 = 0 , we looked at in the previous
problem. Linearize the first-order system that you obtained there
at the third of the critical points you found. [x′y′]=A[xy] [ x ′ y
′ ] = A [ x y ] , where
Consider the spring model x"-8x2x30, we looked at in the previous problem. Linearize the first-order system that you obtained there at the third of...
(1 point) Math 216 Homework webHW10, Problem 4 Consider the predator/prey model r' = y =...
(1 point) Math 216 Homework webHW10, Problem 4 Consider the predator/prey model r' = y = 60 - 22 - my -2y + xy. Find all critical points and enter them below, in order of increasing x coordinate. (x.y)= ( LD : (x,y)= :(X,Y)= (( For reference for the next three problems, write down your critical points after you've gotten them all right.
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...
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)...
(1 point) Math 216 Homework webHW3, Problem 11 Find the solution of the system where primes...
(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 webHW10, Problem 8 Consider the spring model " – 182 +2:03...
(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...
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(...
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...
The following problem can be interpreted as describing the interaction of two species with populations x...
The following problem can be interpreted as describing the interaction of two species with populations x and y. (A computer algebra system is recommended.) dx dy =y(3.5-y-s). (b) Find the critical points. (Order your answers from smallest to largest x, then from smallest to largest y.) G1 (x, ) 0,0 C2 (x, y)-(10. C3 (x, y) (11,0 (c) For each critical point find the corresponding linear system. (Let u =x-xo and v = y-yo where (Xo, yo) is the critical...
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)...
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...
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...
Consider the spring model
x″−8x+2x3=0, x ″ − 8 x + 2 x 3 = 0 , we looked at in the previous
problem. Linearize the first-order system that you obtained there
at the third of the critical points you found. [x′y′]=A[xy] [ x ′ y
′ ] = A [ x y ] , where
Consider the spring model x"-8x2x30, we looked at in the previous problem. Linearize the first-order system that you obtained there at the third of...
(1 point) Math 216 Homework webHW10, Problem 4 Consider the predator/prey model r' = y = 60 - 22 - my -2y + xy. Find all critical points and enter them below, in order of increasing x coordinate. (x.y)= ( LD : (x,y)= :(X,Y)= (( For reference for the next three problems, write down your critical points after you've gotten them all right.
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)...
(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 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...
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...
The following problem can be interpreted as describing the interaction of two species with populations x and y. (A computer algebra system is recommended.) dx dy =y(3.5-y-s). (b) Find the critical points. (Order your answers from smallest to largest x, then from smallest to largest y.) G1 (x, ) 0,0 C2 (x, y)-(10. C3 (x, y) (11,0 (c) For each critical point find the corresponding linear system. (Let u =x-xo and v = y-yo where (Xo, yo) is the critical...
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...
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