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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
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A reliability system consists of 15 independent components. The probability that a component works is 0.9 for each. The system works if at least 11 of the components work. Fi
Describe Multiplication and Division Equations? Multiplication Equations : To solve multiplication equations, divide both sides of the equation by the number being multiplie
condition for linearly independent
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Interpretation A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that there is a causal relationship that is
we know that A^m/A^m=1 so A^(m-m)=1 so A^0=1.....
The longer base of a trapezoid is 3 times the shorter base. The nonparallel sides are congruent. The nonparallel side is 5 cm more that the shorter base. The perimeter of the trape
Solve 8 cos 2 (1 - x ) + 13 cos(1 - x )- 5 = 0 . Solution Now, as specified prior to starting the instance this quadratic does not factor. Though, that doesn't mean all i
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