Figure 13.10 Population cycles in models containing delayed density dependence. (a) In population models where the product of rτ is a low value (rτ < 0.37), the population approaches the carrying capacity without any oscillations. (b) When the product of rτ is an intermediate value (0.37 < rτ < 1.57), the population will exhibit damped oscillations. (c) When the product is a high value (rτ > 1.57), the population will oscillate over time as a stable limit cycle.