Dynamics of the attractor in the Lotka-Volterra equations (Q1268086)

The paper is a comprehensive analysis of Lotka-Volterra systems \[ \dot x_j= \varepsilon_j x_j+ \sum^n_{k= 1} a_{jk} x_jx_k,\quad j= 1,\dots, n. \] All basic cases (cooperative/competitive, conservative, dissipative) are considered separately. The most interesting result concerns the existence of a global attractor whose dynamics is Hamiltonian. Periodic solutions are analyzed as well as their stability. Other problems considered are nonintegrability in the sense of Arnold-Liouville and strong hyperbolicity of periodic orbits.