If a population with harvesting rate h is modeled by dx/dt = 9-x^2-h. Find the bifurcation...

If a population with harvesting rate h is modeled by dx/dt = 9-x^2-h. Find the bifurcation point for the equation.

Expert Solution

Colby Messinger answered 3 years ago

If a population with harvesting rate h is modeled by dx/do=9-x^2-h find the bifurcation point for...

If a population with harvesting rate h is modeled by dx/do=9-x^2-h find the bifurcation point for the equation.

Sec 2.2: Analyze the DE dx/dt = x(2-x) - h, where h is the rate of harvesting....

Sec 2.2: Analyze the DE dx/dt = x(2-x) - h, where h is the rate of harvesting. For each h>0, what are the critical points of the DE? Which of them are stable? What is the bifurcation point? Draw a bifurcation diagram indicating which equilibrium points are stable and which are unstable. (Use a phase line diagram to aid in your analysis.)

dx dt =ax+by dy dt =−x − y, 2. As the values of a and b...

dx dt =ax+by dy dt =−x − y, 2. As the values of a and b are changed so that the point (a,b) moves from one region to another, the type of the linear system changes, that is, a bifurcation occurs. Which of these bifurcations is important for the long-term behavior of solutions? Which of these bifurcations corresponds to a dramatic change in the phase plane or the x(t)and y(t)-graphs?

Find the general solution: dx/dt + x/(1+2t) = 5

Consider the non linear ODE: (dx/dt) = -y = f(x,y) (dy/dt) = x^2-x = g(x,y) (a)....

Consider the non linear ODE: (dx/dt) = -y = f(x,y) (dy/dt) = x^2-x = g(x,y) (a). Compute all critical points (b) Derive the Jacobian matrix (c). Find the Jacobians for each critical point (d). Find the eigenvalues for each Jacobian matrix (e). Find the linearized solutions in the neighborhood of each critical point (f) Classify each critical point and discuss their stability (g) Sketch the local solution trajectories in the neighborhood of each critical point

Equilibrium solutions of non linear ODEs dx/dt = cot(x) & dx/dt=sin(x) Using linear stability characterise the...

Equilibrium solutions of non linear ODEs dx/dt = cot(x) & dx/dt=sin(x) Using linear stability characterise the E.S.

Section 5.3: Find the equilibrium values of a general quadratic population model: dx/dt=a1x+b1x^2+c1xy dy/dt=a2y+b2y^2+c2xy Don’t forget...

Section 5.3: Find the equilibrium values of a general quadratic population model: dx/dt=a1x+b1x^2+c1xy dy/dt=a2y+b2y^2+c2xy Don’t forget to show this for all four cases: Case 1: ? = 0, ? = 0 Case 2: ? ≠ 0, ? = 0 Case 3: ? = 0, ? ≠ 0 Case 4: ? ≠ 0, ? ≠ 0 (Use Cramer’s Rule to set up the solution for this case.)

Find the general solution of the given system. dx dt = 6x + y dy dt...

Find the general solution of the given system. dx dt = 6x + y dy dt = −2x + 4y [x(t), y(t)]= _____________, _______________ (6c1+8c2)10sin(6t)+(6c2+8c1)10cos(6t), c1cos(6t)+c2sin(6t) ^above is the answer I got, which is incorrect.

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 =...

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 = 0 (a) Convert the equation into a first-order system in terms of x and v, where v = dx/dt. (b) Find all of the equilibrium points of the first-order system. (c) Make an accurate sketch of the direction field of the first-order system. (d) Make an accurate sketch of the phase portrait of the first-order system. (e) Briefly describe the behavior of the first-order...

Use a LaPlace transform to solve d^2x/dt^2+dx/dt+dy/dt=0 d^2y/dt^2+dy/dt-4dy/dt=0 x(0)=1,x'(0)=0 y(0)=-1,y'(0)=5

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