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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
Let be the set of all divisors of n. Construct a Hasse diagram for D15, D20,D30. Check whether it is a lattice Or Complement lattice.
What are the ingredients of a Mathematical Model? What is a model?
) Show that the following argument is valid: (~p ? q) => r s ? ~q ~t p => t (~p ? r) => ~s ------------------------ ? ~q 2) Show that the following argum
i can not figer out my homework it says "USE THE MAKE AN ORGANIZED LIST STRATEGY,Medeline bikes 4 laps around her neighborhood 2 times a week.How many laps does she bike in 8 weeks
why
Forecast Errors Differences among actual results and predictions may arise from many reasons. They may arise from random influences, usual sampling errors, option of the wrong
Consider the Van der Pol oscillator x′′- µ(1 - x 2 )x′ + x = 0 (a) Write this equation as a system of first order equations (b) Taking µ = 2, use MatLab's routine ode45 to
you are in charge of making punch for an upcoming dance. the punch recipe makes 5 cups of punch by making 3 cups of cranberry juice with 2 cups of apple juice. What is the ratio of
Two circles touching internally at O. OXY, OAB straight lines, the latter passing through the centres. Prove that OX : OY = OA : OB. Given : Two circles touching internally a
The function A(t) = 5(0.7)^t was used to define the amount A in milliliters of a drug in the bloodstream t hours after the drug was ingested. Determine algebraically the time it wi
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