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.

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Colby Messinger answered 2 years ago

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

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...

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

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