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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
Characteristics of Time Series Time series has the given characteristics. a) A long term trend (T) -tendency of the whole series to fall and rise. b) Seasonal variati
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
Find the number of zeros of the polynomial from the graph given. (Ans:1)
what is the difference between North America''s part of the total population and Africa''s part
Determine the property of Partial ordered relation Question: Partial ordered relation is transitive, reflexive and Answer: antisymmetric
We require to check the derivative thus let's use v = 60. Plugging it in (2) provides the slope of the tangent line as -1.96, or negative. Thus, for all values of v > 50 we will ha
Series Solutions to Differential Equations Here now that we know how to illustrate function as power series we can now talk about at least some applications of series. There ar
Calculate the area and circumference of a circle: Calculate the area and circumference of a circle with a 3" radius. Solution: A = πr2
|a.x|=1 where x = i-2j+2k then calculate a
my question involves frequencies less than five and i cannot aggregate the data, what do i use instead of the chi-square test?
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