In pape "Weak trophic interactions and the balance of nature" by McCann, Hastings and Huxel (Nature, 1998). The authors state that weak links might be “the glue that binds natural communities together”, because they help to dampen oscillations between consumers and resources. This helps to maintain population densities further away from zero, which decreases the statistical chance that a population will become extinct and consequently stabilizes complex, multi-trophic food webs.
Here we implemented the differential equation and analyzed trajectories in phase plane, finding (un)stable point and bifurcation situation.
The simplest example of an omnivorous system is a 3-species food chain (figure), where the top predator P not only feeds on the intermediate consumer C, but also on the basal resource R. By increasing the strength of the omnivorous link, then it will decreases the strength of the link between the top predator P and the intermediate consumer C. The parameter Ω therefore describes a trade-off between feeding on the consumer versus feeding on the resource.