What is the relationship between linearity and nonlinearity?

Wha.....?

What do you mean by relationship?

I'm having trouble articulating my question without seeming like a dummy.

By nonlinearity I mean chaotic dynamics. I am wondering if some systems are completely linear…no chaos whatesoever. I can't imagine there are any but, if not, how do you integrate the two types of behavior into a description of one system. 50% order, 50% disorder?

I don’t know what I’m talking about, but I'm hoping someone that does will respond. :o

A linear relationship between two variables, x and y is of the form:

y = mx + c

where c is a constant (which may be zero).

A non-linear relationship is anything else. Examples:

y = x²
y = sin x
y = log(x+17)
xy + 27 = 0