after getting fixed points of this system :
$x_{t+1} = a\cdot x_t\cdot(1-x_t)$
i want to analyze the stability of the system for a = 0.9 , a = 2.1 and a = 3,58.
given :
from the bifurcation diagram, i can deduce for a = 2.1 we have 1 stable state and 3.58 we have chaotic behaivor. And from wikipedia i know that a < 1 ...
the population will eventually die, independent of the initial population.
I don't understand the criteria for stability in this equation .
Can someone explain this ?
edit : for the record. i have the solutions, but i want to understand !