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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
If PA and PB are tangents to a circle from an outside point P, such that PA=10cm and ∠APB=60 o . Find the length of chord AB.
Definition of a Function Now we need to move into the second topic of this chapter. Before we do that however we must look a quick definition taken care of.
Testing The Difference Between Two Sample Means (Large Samples) A large sample is defined as one which have 30 or more items as n≥30 whereas n is the sample size In a busine
E1) From your experience, and what you have studied so far, by which age would-you expect an average child to be ready to acquire the following concepts? i) Simple classificatio
100+5000
We are here going to begin looking at nonlinear first order differential equations. The first type of nonlinear first order differential equations which we will see is separable di
what is 10+5..
The numbers used to measure quantities such as length, area, volume, body temperature, GNP, growth rate etc. are called real numbers. Another definition of real numbers us
Determine a particular solution for the subsequent differential equation. y′′ - 4 y′ -12 y = 3e5t + sin(2t) + te4t Solution This example is the purpose that we've been u
do you have a decimal place value chart
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