Population dynamics has been modelled using differential equations almost since Malthus times, more than two centuries ago. Basic ingredients of population dynamics models are typically a growth rate, a saturation term in the form of Verhulst's logistic brake, and a functional response accounting for interspecific interactions. However intraspecific interactions are not usually included in the equations. The simplest models use linear terms to represent a simple picture of the nature, meanwhile to represent more complex landscapes, it is necessary to include more terms with higher order or analytically more complex. The problem to use a simpler or more complex model depends on many factors: mathematical, ecological, or computational. To address it, here we discuss a new model based on a previous logistic-mutualistic model. We have generalised the interspecific terms (for antagonistic and competitive relationships) and we have also included new polynomial terms to explain any intraspecific interaction. We show that by adding simple intraspecific terms, new free-equilibrium solutions appear driving a much richer dynamics. These new solutions could represent more realistic ecological landscapes by including a new high order term.

中文翻译：

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考虑多种相互作用的种群动力学通用模型

几乎从马尔萨斯时代开始，即两个多世纪前，就已经使用微分方程对人口动态进行了建模。人口动力学模型的基本要素通常是增长率，Verhulst逻辑制动形式的饱和项以及考虑种间相互作用的功能响应。然而，种内相互作用通常不包括在等式中。最简单的模型使用线性项表示自然的简单图片，同时表示更复杂的景观，有必要包括更多具有更高阶或分析上更复杂的项。使用更简单或更复杂的模型的问题取决于许多因素：数学的，生态的或计算的。为了解决这个问题，我们在此讨论基于先前的逻辑互模型的新模型。我们已经概括了种间术语（用于对抗和竞争关系），并且还包括了新的多项式术语来解释任何种内相互作用。我们表明，通过添加简单的种内术语，新的自由平衡解决方案似乎可以驱动更丰富的动态。这些新的解决方案可以通过包含一个新的高阶术语来代表更现实的生态景观。