论文标题
与成对相关相互作用的大型Lotka-Volterra系统中的平衡
Equilibrium in a large Lotka-Volterra system with pairwise correlated interactions
论文作者
论文摘要
在相互作用系数形成大型随机矩阵的情况下，我们研究了耦合微分方程的大型Lokta-Volterra系统的平衡。在这种随机矩阵遵循椭圆模型的情况下，我们研究了A（compontionWise）正平衡的存在，并描述了矩阵归一化的相位过渡。如果没有积极平衡，我们为存在稳定平衡的模型参数提供了条件（具有稳定的平衡（具有消失的组件）和态度的启发式，以构成组合数的数字数量。 Lotka-Volterra系统在数学生物学/理论生态学中很重要。
We study the equilibria of a large Lokta-Volterra system of coupled differential equations in the case where the interaction coefficients form a large random matrix. In the case where this random matrix follows an elliptic model , we study the existence of a (componentwise) positive equilibrium and describe a phase transition for the matrix normalization.If there is no positive equilibrium, we provide conditions on the model parameters for the existence of a stable equilibrium (with vanishing components) and state heuristics to compute the number of positive components of the equilibrium. Lotka-Volterra systems are important in mathematical biology/ theoretical ecology.
