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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 angles between three non-zero and non coplanar vectors a,b and c are α between b and c and β between c and a and γ between a and b. The vector u and v are defined by u=(aX
A Solid toy in the form of a hemisphere surmounted by the right circular cone of height 2cm and diameter of the base 4 cm .If a right circular cylinder circumscribes the
uses of vector in daly life
The Invisible Effort : Although the development of children is a process, what is noticed and given recognition to is the end-product. We usually speak of children having achieve
How does finding the unit rate help make smart decisions?
Find out the next number in the subsequent pattern. 320, 160, 80, 40, . . . Each number is divided by 2 to find out the next number; 40 ÷ 2 = 20. Twenty is the next number.
Example of Rounding Off: Example: Round off the subsequent number to two decimal places. 6.238 Solution: Step 1: 8 is the number to the right of t
Normally, sets are given in the various ways A) ROASTER FORM OR TABULAR FORM In that form, we describe all the member of the set within braces (curly brackets) and differen
If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. [Ans: 3/2 , 3/√ 3/2 or 3/2, -3√ 3/2] Ans: OA = OB = AB OA 2 = OB 2 = AB 2
A mortgage lender seeks to maximize the expected value of its portfolio. The portfolio, of course, is the sum of all of the mortgages in it, so no generality is lost by examining t
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