1. Consider the dynamical system i = x(y – 1) ý = -y(x + a) + b, where a, b > 0 are parameters. (a) Show that a bifurcation occurs when b = a. Identify the type of bifurcation.

Q: Exercise 3. A WSS process X(t) with autocorrelation function Rx(+) = e-+2/(207) is passed through an…

A: We have to find the values with the help of Hilbert transformation.

Q: A. y" + 2y' + y = 0 B. y" + 2y' + 2y = 0 C. y" + 4y = 0 D. y" – 3y' + 2y = 0 Table 1: A-D are…

A: We find the solution of the given homogeneous differential equation after solving characteristic…

Q: -5 2 3. Let A = -6 Classify the equilibrium point of the system x' Ax based on the position of (T.…

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Q: 3. Transform the DE: (12-7t+6)y" + 3y²+ 5ty = sec(t); y(4) =1, y'(4) = 3 into a system of two first…

A: To transform the given second-order differential equation into a system of two first-order…

Q: Exercise 3. A WSS process X(t) with autocorrelation function Rx(+) = e-2/(207) is passed through an…

A: The objective of this question is to find the cross-spectral density Sxy(w), the cross-correlation…

Q: Consider a point particle with position vector r = (x, y, z) in Cartesian coordinates, moving with a…

A: The objective of the question is to find the position of a particle as a function of time, given its…

Q: Consider a dynamical system: dx dt = y + 2xy dy = x + x² - y² dt Select the only true statement:…

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Q: Which of the following functions (y1, y2) is a Lyapunov function for the dynamical system y₁ = - Y₁…

A: Which of the following function Vy1 , y2 is the Lyapunov function for the dynamic system? y1˙=-y1y22…

Q: a'(t) = x · (1 – 2²), y/(t) = –y³ %3D |

A: The given system is, x'(t)=x.(1-x2),  y'(t)=-y3 We have to find the Nullclines and Equilibria for…

Q: Find all the second order partial derivatives of the given function. 10) f(x, y) = (x2 + y2)7

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Q: Consider the function y²x² y² + x² 0 if (x, y) = (0,0) if (x, y) = (0,0) Compute the partial…

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Q: 2) Consider the following system: - ax (1-)– Bxy (): x' - Вху K. y =ry (1-) µx. Find the equilibria…

A: 2) Consider the following system: x'=αx1-xk-βxyy'=γy1-yμx Find the equilibria and analyze their…

Q: Consider the system of linear ODES The system of equation written as y' (t) = Ay(t), where y(t) =…

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Q: II) Consider the following three equations ry-2w=0 y-2w² <-2 <<=0 5 <=0 1. Determine the total…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: . Show that it is possible to solve u and v from: xyu + xy2uv2 = 2  and  x2yvu4 + yu3v2 = 2, in…

A: Given: xyu + xy2uv2 = 2  and  x2yvu4 + yu3v2 = 2 To show that we can solve for u &amp; v in terms of…

Q: Determine minimal conditions on the real constant ? so that (0, 0) is a center for the linear system…

A: Consider the given linear system, x'=-μx+yy'=-x+μy we know that if x'=ax+by and y'=cx+dy then…

Q: a) Which of the following systems of ODEs is autonomous and dynamical? || III, where 1:y₁ = e…

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