Laurie Henry, Venturino Ezio
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa.
Dipartimento di Matematica Giuseppe Peano, via Carlo Alberto 10, Università di Torino, 10123 Torino, Italy. - Member of the INdAM research group GNCS.
Theor Biol Forum. 2018 Jan 1;111(1-2):27-47. doi: 10.19272/201811402003.
We construct a mathematical model considering the populations of multiple predators and one prey, with herd defense by the prey modelled by modifying the law of mass action with a single parameter. This modification introduces a novel bifurcation in the case where all the predators are specialists. When some predators may be generalists, the analysis is more complicated and we consider only the case of two predators of which one or two may be generalists. In this case, novel steady states occur via saddlenode bifurcation, and in some cases the coexistence steady state exhibits Hopf bifurcation to a stable limit cycle. We show that the phenomenon of finite time extinction of prey also occurs in this context. Finally, we extend the analysis from constant herding effect to a model where predator pressure increases the strength of herding.
我们构建了一个数学模型，该模型考虑了多种捕食者和一种猎物的种群数量，并通过用一个参数修改质量作用定律来模拟猎物的群体防御。这种修改在所有捕食者都是 specialists 的情况下引入了一种新的分岔。当一些捕食者可能是 generalists 时，分析会更加复杂，我们仅考虑两种捕食者的情况，其中一种或两种可能是 generalists。在这种情况下，通过鞍结分岔会出现新的稳态，并且在某些情况下，共存稳态会表现出霍普夫分岔到一个稳定的极限环。我们表明，猎物的有限时间灭绝现象在这种情况下也会发生。最后，我们将分析从恒定的群体效应扩展到一个捕食者压力增加群体强度的模型。
