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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
9:59 p.m. to 10:45 p.m
Define sample space
WHATS HALVE OF 21
limits
Ashley's car insurance costs her $115 per month. How much does it cost her per year? Multiply $115 by 12 because there are 12 months in a year; $115 × $12 = $1,380 per year.
3 3/7 + 2 8/9 * 4=
Q. Find a common factor of the numerator and denominator? Ans. There's only one key step to simplifying (or reducing) fractions: find a common factor of the numerator and
what is equizilent to 2/5
Prove that one of every three consecutive integers is divisible by 3. Ans: n,n+1,n+2 be three consecutive positive integers We know that n is of the form 3q, 3q +1, 3q +
A circular print is being matted in a square frame. If the frame is 18 in by 18 in, and the radius of the print is 7 in, what is the area of the matting? (π = 3.14) a. 477.86 in
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