Abstract
We present a method of finding the second independent integral of the three-dimensional Lotka–Volterra equations with a known first integral. The method is based on the elaboration of three-dimensional Poisson structures and is called the Hamiltonian structure (HS) method. As examples we study the Lotka–Volterra (LV) equations. An exactly integrable case of two-dimensional LV equations is obtained. Many new non-chaotic cases of three-dimensional LV equations are found.
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