We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.
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Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C 1, C 2, C 3, C 4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.
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