The classification of the dynamical behavior of 3-dimensional type K monotone Lotka-Volterra systems
The authors consider \(K\)-monotone Kolmogorov systems \(x_i'= x_i f_i(x)\) in \(\mathbb{R}^n\) ordered by a cone of the type \(K= \{(x_i): x_1,\dots, x_k\geq 0\), \(x_{k+1},\dots, x_n\leq 0\}\), where \(f\in C^1(\mathbb{R}^n_+, \mathbb{R}^n)\) is assumed to be such that solutions depend increasing on the initial value. The authors investigate attracting Lipschitz manifolds and hyperbolic equilibria of such systems. In particular, three-dimensional systems are studied, and the results are applied to classify three-dimensional \(K\)-monotone Lotka-Volterra systems.
scientific article; zbMATH DE number 1836613
scientific article