Theory and Modern Applications
Table 1 Existence of equilibria and period-two solutions for \(a>0\), \(f>0\), \(C>0\)
From: Global dynamic scenarios for competitive maps in the plane
| Â | C, d | f, E | Equilibria | Period-two solutions | |
|---|---|---|---|---|---|
C>0 | C ≤ d | f = E | \(\bar {x}_{0}=0\) | none | |
f>E | \(\bar {x}_{0}=0\) | one | |||
C>d | f = E | \(\bar {x}_{0}=0\), \(\bar {x}_{+}>0\) | none | ||
arbitrary | f<E | \(\bar {x}_{0}=0\), \(\bar {x}_{+}>0\) | none | ||
C>d | f>E | R<0 | \(\bar {x}_{0}=0\) | one | |
R = 0 | \(\bar {x}_{0}=0\), \(\bar {x}_{\pm}>0\) | one | |||
R>0 | \(\bar {x}_{0}=0\), \(\bar {x}_{-}>0\), \(\bar {x}_{+}>0\) | one | |||