Bifurcation analysis of the Zhukovskii–Volterra system via bi-Hamiltonian approach

The main goal of this paper consists of bifurcation analysis of classical integrable Zhukovskii–Volterra system. We use the fact that the ZV system is bi-Hamiltonian and apply new techniques [1] for analysis of singularities of bi-Hamiltonian systems, which can be formulated as follows: the structure of singularities of a bi-Hamiltonian system is determined by that of the corresponding compatible Poisson brackets.