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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
2 1/3
If you have 60% alcohol and wish to dilute with water to make 12 liters 40% alcohol, How many liters of water should you add?
Determine if the subsequent series is convergent or divergent. Solution As the cosine term in the denominator doesn't get too large we can suppose that the series term
Give an example to illustrate how language incompetence can interfere with a child's ability to perform a task. While setting up a classification activity, a teacher gave the ch
a child prepares a poster to save energy on a square sheet whose each side measures 50 cm . At each corner she draws a quadrant of radius 5 cm and the centre of a circle of diamete
Consider a discrete-time system that is characterized by the following difference equation: Y(n) = x(n)cos? 0 n, where ? 0 is constant value, x(n)are the discrete-time input
using a pair of compasses a ruler and a pencil. construct a triangle CDE in which DE=10cm, DC+8cm and CDE= 45 degrees. construct CF perpendicular to DE such that F lies on DE using
How do i divide 200 by 4
Vectors This is a quite short section. We will be taking a concise look at vectors and a few of their properties. We will require some of this material in the other section a
a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit
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