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1. Discuss lyapunov function theory and how it can be used to prove global assmptotic stability of solutions.(Give an example form natural and engineering sciences.)
--- Draw level sets of Lyapunov function.
2. Discuss Perron-Frobenius theorem and how it can be used to prove global stability of solutions(Give an example) .
3. Discuss the stability of solutions of non-autonomous system dx/dt=f(x,t).
4. Discuss bifurcation theory, and show how to (theoretically) characterise varies, bifurcation types apriori (saddle node, pitchfork, hopf, transcritical). Show to charactrise super and sub-critical pitchfork and hopf.(Give an example of each)
1) transcritical.
2)pitchfork(super and sub-critical)
3)Hopf(super and sub-critical)
4)saddle-node
The expected monetary value method The expected pay off as profit associated with a described combination of act and event is acquired by multiplying the pay off for that act a
What is the square root of 36? To search the square root (√) you ask yourself, "What number multiplied through itself gives me 36?" 6 .6 = 36; thus, 6 is the square root of 36.
y"-3y''-4y=2sinx
a) Determine the distance traveled among t = 0 and t =∏/2 by a particle P(x, y) whose position at time t is given by Also check your result geometrically. (5) b) D
If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
Dividing Mixed Numbers Dividing mixed numbers is a 3-step process: 1. Convert the mixed numbers to improper fractions. 2. Divide the fractions 3. Convert the result ba
Ask question #Minimum 100 words what is the hypotunus of a right bangled triangle a=5@ b=25 find c accwhepted#
I need to graph rational numbers on the number line Point A-.60, point B-1/4, point C-.4,point D-7/8
integrate sin(x) dx
What is Faltings Theorem? Explain Faltings Theorem
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