I am interested in the following standard dynamical system: $N_{t+1}=N_t exp[r(1-N_t/K)]$.
In R.May's 1974 science paper (pp.645, Table1, Biological populations with non overlapping generations),he states that chaotic behaviour (cycles of arbitrary period, or aperiodic behaviour, depending on initial condition.) occurs if r>2.692.
However in the same paper (pp.646), he also says that if r>3.102, then it can be shown that the dynamical system above has cycles of period 3.
I do not see any point of stating the second result since May has already shown that this dynamical system generates a cycle of period 3 (or cycles of any period) if r>2.692.
Anybody has any thought?