- #1

the7joker7

- 113

- 0

## Homework Statement

Basically, the problem involves a linear system dx/dt = ax + by and dy/dt = -x - y, with a and b being parameters that can take on any real value. Basically, you go through this system for several values of a and b (I did -12 to 12) to find the state at various points. That is, whether or not the point is a saddle, source, sink, perodic, or whatever else. I've found all of that. The only thing I haven't found yet is which sources and sinks are spirals. I know that it's a spiral if a complex number is involved. I've been told two different ways to find this.

## The Attempt at a Solution

A: Graph the trace of the system (a + d)*x and the determinant (ad - bc) and the area inside the parabola has the spirals. I'm having a hard time doing this on the graphing tools I've found on the internet.

B: Using the quadratic x^2 - (trace*x) + determinant = 0, find what values of the trace and determinant make is such that x = sqrt(negative number). This equation simplifies to x = sqrt(trace*x - determinant). An x on both sides, so that complicates things...

What would be the easiest way to go about this?