Existence of periodic solutions for the Lotka–Volterra type systems

In this paper we prove the existence of nonstationary periodic solutions of delay Lotka–Volterra equations. In the proofs we use the S1-degree due to Dylawerski et al. [G. Dylawerski, K. Geba, J. Jodel, W. Marzantowicz, An S1-equivariant degree and the Fuller index, Ann. Polon. Math. 63 (1991) 243–280].