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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
how do u do it
The Addition Rule: Mutually Exclusive Events P(A or B or C) = P(A) + P(B) + P(C) This can be represented by the Venn diagram as follows:
25/5(2+3)
Four-year-old Mariamma was reciting number names - some of them in order, and others randomly. The child's aunt, sitting nearby, asked her, "Can you write 'two'?" She said she coul
what is commercial mathematics profit and loss
a shopkeeper buys two cameras at the same price . he sells one camera at a profit of 18% and the other at a price of 10% less than the selling price of the first camera. find his p
(3x+2)^2 d^2y/dx^2+3(3x+2)dy/dx-36y=3x^2+4x+1
1. A drainage system overflows into a river causing pollution when the rainfall falling in an hour exceeds 50 mm. During any given year, the maximum hourly rainfall follows an expo
i dont understand it can you help
Q. How to calculate Mode? The mode of a data set is the value that is repeated most often in the data set. It has the highest frequency. There can be one, more than one, or n
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