Chaos Lecture 7 and 8

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.

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