3. Consider the dynamic system dx Determine the fixed points and their nature and draw a bifurcation diagram 3. Consider the dynamic system dx Determine the fixed points and their nature and dra...
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
3. [10 points] - Draw an equivalent block diagram for the system of the two differential equations 3. [10 points] - Draw an equivalent block diagram for the system of the two differential equations dt2dt d+ 11 3. [10 points] - Draw an equivalent block diagram for the system of the two differential equations dt2dt d+ 11
Consider the system * =y j= +1. Find the fixed points and the linearisation of the system at each. Identify the type and sketch a local phase portrait (i.e. a sketch of the orbits just around the fixed points) at each fixed point. Show that the system has a time reversal symmetry. Draw a sketch showing isoclines and the directions of orbits in all parts of phase space. Use this information, together with the symmetry, to show there exists a...
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to find the linear approximation at each of the critical points. Determine the type and the stability. . Briefly describe the overall behavior of r and y Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to...
3) Given the systemxx2-x,y'-2y, find all fixed points. For each fixed point linearize the system near the fixed point, shift the fixed point to the origin, determine the eigenvalues of the linearized system, and determine whether the fixed point is a source, sink, saddle, stable orbit, or spiral. Attach a phase plane diagram to verify the behavior you found. 3) Given the systemxx2-x,y'-2y, find all fixed points. For each fixed point linearize the system near the fixed point, shift the...
1. Consider the family of differential equations dy/dx = y^3 + ky + k^3 . Please Help me with it, thanks so much 1. Consider the family of differential equations de set = y2 + ky + k3. (a) Are there any equilibrium solutions when k = 0? If so, what are they? (b) Draw the bifurcation diagram. That is, sketch a graph of the critical values as a function of the parameter k. Clearly label the axes. (You may...
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...
Consider the nondimensional differential equation du where u is an unknown parameter (constant) (a) Determine the equilibrium solutions in terms of μ. (b) Draw the bifurcation diagram and clearly identify the bifurcation point. (c) Classify the stability of the branches in your bifurcation diagram using the process in class where we assumed u(t)uilibrium +u(t) where uequilibrium is the constant(s) you determined in (a) Repeat the steps in exercise (2) for the nondimensional differential equation given by du_2 dt where u...
1 Consider the system shown as below. Draw a Bode diagram of the open-loop transfer function G(s). Determine the phase margin, gain-crossover frequency, gain margin and phase-crossover frequency, (Sketch the bode diagram by hand) 2 Consider the system shown as below. Use MATLAB to draw a bode diagram of the open-loop transfer function G(s). Show the gain-crossover frequency and phase-crossover frequency in the Bode diagram and determine the phase margin and gain margin. 3. Consider the system shown as below. Design a...
Determine the internal moments OF EACH SUPPORT, then draw the moment diagram. Assume A is fixed. EI is constant. USE MOMENT DISTRIBUTION METHOD ONLY. 10-7 Determine the moments at each support, then draw the moment diagram. Assume A is fixed. El is constant. 12 k 4 k/ft Use both slope deflection equations and moment distribution method