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1 a explain the dierence between an autoregressive and a moving-average processb why are ar and ma processes referred
1 using symbolic dynamics describe the itineraries of all points that eventually land on 0 how many such points are
1 describe the bifurcations that the function fx ax x3 undergoes when a 1 and a -1 2 a in the cantor
1 a for the function fx ax what is the type of the fixed point at 0 this type will depend upon a b at which
1 a find all fixed points for the function fx x2 b what is the fate of all other orbits for this
a consider the duffing oscillator equation with no forcing y v v y - y3 what are the equilibrium points for this
a a model due to beddington and may for the competitive behavior of whales and krill a small type of shrimp is x
a consider a simpler version of the competing species model where we do not include overcrowdingx x - xy y y -
1 give an example of a nonlinear system that has an equilibrium point for which the linearized system has a zero
a find all equilibrium points for the system x x2 y y xb compute the jacobian matrix at each
1 using nullclines determine the phase plane for the following system x x1 - x y x - y22 a consider the
a find the x- and y-nullclines for the system x y y 2xb sketch the regions where the
1 find the steady-state solution of the forced mass-spring system with spring constant 2 damping constant 1 and forcing
a solve the periodically forced first-order equation y y sint b what happens to all solutions of this
1 consider the mass-spring systems with spring constant 1 and damping constant b for which values of b is this system
1 find the general solution of the mass-spring system with spring constant 2 and damping constant 22 if we
1 use the product rule to compute the derivative of e2tcos3t2 use eulers formula to expand e2t 3it3
a find the general solution of the mass-spring system with spring constant 6 and damping constant 5 b
1 write the second-order differential equation for the mass-spring system with mass 1 spring constant 2 and damping
1 a sketch the direction field for the following system of differential equations x y y
1 a sketch the direction field for the system below x x yamp39 yb what happens to solutions of this
1 a for the differential equation y y find the solution satisfyingy0 1 b then use eulers method
1 what is the equation of the tangent line to the graph of y t2 at the point t 12 consider the
first lets try some refreshers from algebra in the t-y plane a what is the slope of the straight line in the
1 for the unlimited population model with y gt 1 check that solutions assume the form discussed in the lecture2