Consumption driven population dynamics (CDPD): Further explorations

► 'CDPD response' generates all consumption functional response types. ► Introduction of past consumption in single peaks produces observed peak shapes. ► Stochasticity at two time scales replicates Seasonal oscillations with fidelity. ► CDPD shows persistent aperiodic oscillations at Rp close to instability threshold. ► CDPD discloses a simple mechanism for this aperiodic oscillation.