Archive for the ‘Chaos’ Category

Chaos Lecture 7 and 8

January 11, 2009

What is state? It is all the information you need about the system in order to predict its behavior an instant later.

What is nonlinear? When causes produce disproportianate effects.

A linear system shows no bifurcations i.e. changes in its qualitative long-term behavior.

In a linear system, the whole is exactly equal to the sum of the parts. (superposition) You can break a problem into parts, do each one separately, and combine back to get the right answer. eg -bank account, separate principal and interest to calculate new interest.

That doesn’t happen in nonlinear system. Whenever parts of a system compete or cooperate and don’t just add up, you have nonlinearity. eg- insect population model. If you listen to two favorite songs, you don’t get double the pleasure, because of non-linearity of actions in your head. You are not supposed to take two drugs at the same time if they have interactions. Or they can work synergistically, where effect of 3 drugs given simultaneously is more than if each were given separately.