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We investigate global stability and dynamics of large ecological networks byclassical methods of the dynamical system theory, including Hamiltonianmethods, and averaging. Our analysis exploits the network topologicalstructure, namely, existence of strongly connected nodes (hubs) in thenetworks. We reveal new relations between topology, interaction structure andnetwork dynamics. We describe mechanisms of catastrophic phenomena leading tosharp changes of dynamics and investigate how these phenomena depend onecological interaction structure. We show that a Hamiltonian structure ofinteraction leads to stability and large biodiversity.

New perspectives: stability and complex dynamics of food webs via Hamiltonian methods