A General Model of Population Dynamics Accounting for Multiple Kinds of Interaction

Figure 5

Phase space and trajectories for two populations involved in a predator-prey interaction. We show here a special case where the coexistence spiral solution diverges and become unstable. When that happens, a limit cycle appears. To the left, we have a case with a smaller predation, i.e., than to the right, where . In both cases, , which means that both populations benefit the same from population , but the predatory effects of on are stronger on the right. For greater cooperation values, the intermediate solution might even disappear, as it is shown on the right. The green, blue, and yellow dots in the phase space mark the initial conditions of the simulations located below. Here, .

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