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- 6. Consider the dynamical system dx - = x (x² − 4x) - dt where X a parameter. Determine the fixed points and their nature (i.e. stable or unstable) and draw the bifurcation diagram.8. Find and classify the equilibrium points of the following equations: (9 +x – 3y)x (-8+4x – y)y Discuss the stability of each equilibrium point.2. Linearize the following equation about the equilibrium point (xo, Yo, Zo, uo) * = a X 1+ y² + c y = yu z = xy + u Where z is the output, u is the input and a and care constant.
- 1. Consider the discrete model 2n+1= -Xn- Find the equilibrium points and determine their stability.Find the equilibrium points of d = y²(6 - y)² and classify each one as stable, unstable, or dt semistable. Stable equilibria occur at y = Unstable equilibria occur at y = Semistable equilibria occur at y = (If there is more than one equilibrium of a certain type, enter a comma-separated list. If there are no equilibria, enter "none".) On paper, sketch several solutions to the differential equation.(3) The approximate enrollment, in millions between the years 2009 and 2018 is provided by a linear model Y3D0.2309x+18.35 Where x-0 corresponds to 2009, x=1 to 2010, and so on, and y is in millions of students. Use the model determine projected enrollment for the year 2014. 近