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We construct a family of integrable deformations of the Bogoyavlenskij-Itohsystems and construct a Lax operator with spectral parameter for it. Ourapproach is based on the construction of a family of compatible Poissonstructures for the undeformed system, whose Casimirs are shown to yield agenerating function for the integrals in involution of the deformed systems. Weshow how these deformations are related to the Veselov-Shabat systems.

Integrable deformations of the Bogoyavlenskij-Itoh Lotka-Volterra systems