Theory and Modern Applications
Table 3 Existence of equilibria and period-two solutions for \(a=0\), \(f>0\)
From: Global dynamic scenarios for competitive maps in the plane
C, d | f, E | Equilibria | Period-two solutions |
|---|---|---|---|
C ≤ d | f>E | \(\bar {x}_{0}=0\) | one |
C ≥ d | f<E | \(\bar {x}_{0}=0\) | none |
C ≠ d | f = E | \(\bar {x}_{0}=0\) | none |
C<d | f<E | \(\bar {x}_{0}=0\), \(\bar {x}_{+}>0\) | none |
C>d | f>E | \(\bar {x}_{0}=0\), \(\bar {x}_{+}>0\) | one |
C = d | f = E | Any x̄ ≥ 0 is a fixed point. | none |