sketch phase lines for: dy/dt = y(y+3)^3(y-2)^2(y-5) sketch bifurcation diagram for: dy/dt = y(y^2+ α) where...
In Exercises 1-6, locate the bifurcation values for the one-parameter family and draw the phase lines for values of the parameter slightly smaller than, slightly larger than, and at the bifurcation values. dy α-ly 6. dt
dy 2. Locate the bifurcation values for the one-parameter family: = a- and draw the phase lines for the parameter a slightly smaller than, slightly larger than, and at the bifurcation value. (15 points)
Bifurcation dy Consider the autonomous differential equation =y? - 2y + 8. We will begin by examining dt the equilibrium solutions of the equation for various values of the parameter 8 1. Find the equilibrium solutions of the equation for 8 = -4,-2, 0, 2, 4 and make a sketch of the phase line for each value. Determine the stability of each equilibria. 2. Use a computer or some other means to sketch some solution curves for each value of...
A bifurcation occurs where the number of equilibrium solutions changes as the parameter varies. As 8 increases, the number of equilibrium solutions changes from two to one and eventually there are none. 4. Solve the equation 0 = yd – 2y + Bfor y in terris of B. Describe how the number of solutions depends on B. 5. Sketch the bifurcation diagram, which shows the graph of y versus 8. It is traditional to show stable equilibria with solid lines...
Sketch the phase portrait for each linear system below Y. dt - (33) = (211) dY dt Y.
Consider the family of differential equations dy/dx=y^3+ky+k^2 Are there any equilibrium solutions when k=0? Draw bifurcation diagram Draw phase diagram for when k=1/2 Does limit exist when k=1/2 and y(0)=0
dy 3. (5 points): Consider the autonomous differential equation dt is given below. Draw the phase line and classify the equilibria. f(y) where the graph of f(y) Y 1 -0.5 0.5 1 y
#19 all parts Problems 17 through 19 deal with competitive systems much like those in Examples 1 and 2 except that some coefficients depend on a parameter a. In each of these problems, assume that x, y, and a are always nonnegative. In each of Problems 17 through 19: (a) Sketch the nullclines in the first quadrant, as in Figure 9.4.5. For different ranges of a your sketch may resemble different parts of Figure 9.4.5 (b) Find the critical points...
[SBDu] Which of the following differential equations with real parameter u matches the bifurcation diagram in the figure below? Thin blue lines indicate unstable states, thick red lines indicate stable states. 20 -15 -10 -5 ο μ 5 10 15 : Ο α' = (2 – α) (( – 1)? – (μ – 3)) Ο α' = (x – 2) ((α + 1)? – (μ – 3)) Ο α' = (x – 2) (α - 1)? – (μ – 3))...
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt = 3xy − y 3a (5 pts): Find the steady states of the system. 3b (15 pts): Linearize the model about each of the fixed points and determine the type of stability. 3b (15 pts): Draw the phase portrait for this system, including nullclines, flow trajectories, and all fixed points. Problem 2 (25 pts): Two-dimensional linear ODEs For the following linear systems, identify the...