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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
Derivatives The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is
Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means
If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0
miaty and yesenia have a group of base ten blocks.Misty has six more than yesnia. Yesenia''s blocks repersent 17 together they have 22 blocks,and the total of blocks repersent 85.
To help Himalya herbal launch a successful marketing campaign in the UK
The distance from the earth to the moon is approximately 240,000 miles. What is this distance expressed in scientific notation? To convert to scienti?c notation, place a decima
Decision-Making Under Conditions of Uncertainty With decision making under uncertainty, the decision maker is aware of different possible states of nature, but has insufficient
can anyone explain me the concept of quadratic equation?
Use Newton's Method to find out an approximation to the solution to cos x = x which lies in the interval [0,2]. Determine the approximation to six decimal places. Solution
Fermat's Theorem : If f ( x ) contain a relative extrema at x = c & f ′ (c ) exists then x = c is a critical point of f ( x ) . Actually, it will be a critical point such that f
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