Problem 3: For each of the following difference equations, find all equilibrium points and investigate their...
For each of the following equations you should locate all equilibrium points and investigate their stability properties for different values of the parameter u ER. You should then draw a summary/bifurcation diagram, with arrows, indicating the qualitative behaviour of the non-equilibrium solutions for all values of y, including at the bifurcation point u = u*. Note any bifurcations that occur and determine which of the following terms can be used to describe the nature of the bifurcations you find: transcritical,...
Find all equilibrium solutions of the system of ordinary
differential equations d
(6 points) Find all equilibrium solutions of the system of ordinary differential equations ry - 2x dir dt dy dt = my - r - 2y + 2,
Question # 3 Two systems are defined by the following difference equations, for each system find the impulse response, determine whether the filter is FIR or IR and draw the block diagram of each system. a) y(n)x(n) + 0.5x(n 1) 0.8x(n - 2) b) y(n)- x(n) + 0.5y(n -1)
Problem 3 (Stewart & Day 7.2.9) For each of autonomous differential equations below, find all equilibria and determine the values of a for which each equilibrium is locally stable. Assume that a #0 for all equations. (a) y = 1+ ay. (b) y = 1- e-ay. (c) y' = aecos(y).
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
dt dt (a) Find all the critical points, and investigate their (linear) stability, as the param eters β and δ are varied. [3 marks] (b) For this part, set 0. Show that the v axis is invariant. Find the phase flow on this invariant axis. 1 marks
dt dt
(a) Find all the critical points, and investigate their (linear) stability, as the param eters β and δ are varied. [3 marks] (b) For this part, set 0. Show that the...
PROBLEM 01 Use the equations of equilibrium to find the external reactions at Points A and C. Next solve for the internal forces in individual truss members using the "method of joints". Show the component (x & y) forces for each member on the provided worksheet. Look for "zero force" members to simplify the problem. Once component forces are solved for diagonal members, use the Pythagorean Theorem to calculate the overall axial tension or compression force for each member. Complete...
Find the equilibrium points in the dynamics of the following system. Analyse the stability of each equilibrium point. 3x – x2 – 2xY ý = 2y – y² – xy Summarise your results in the form of a table, with fixed points horizontally and A vertically (where A is the corresponding matrix).
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system. 185 Exercises (b) Describe the phase portrait for the nonlinear system (c) Does the linearized system accurately describe the local bchavior near the equilibrium points? We were unable to transcribe this image
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system....
3. For each of the following markets, find the equilibrium price and quantity. (3 points each) a. ls= 60-5P es = 5P-10 b. ls= 240-6P es= 4P-120