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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
Give the Examples in Real World of Proportions? Proportions can be used in cooking. For example, the following is a set of ingredients for a pasta called "Spaghetti All' Amatri
I have 6 cups of patatos that I have to share with 13 friends write that as the nearest hundredth
Truth Criteria : Consider the following statements: i) Peahens (i.e., female peacocks) lay eggs around September. ii) Water boils at 100°C. iii) 5 divides 15 without lea
(-85) from (-21) and explain me
with t =[a b c] construct a matrix A = 1 1 1 a b c a^2 b^2 c^2 a^3 b^3 c^3 using vector operations
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
interestind topic in operation research for doing project for msc mathematics
Components of the Vector We should indicate that vectors are not restricted to two dimensional (2D) or three dimensional space (3D). Vectors can exist generally n-dimensional s
How to construct a histogram into an ogive
The Definition of the Limit In this section we will look at the precise, mathematical definition of three types of limits we'll be looking at the precise definition of limits
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