Abstract:

By means of Nussbaum degree theory, a sufficient condition is established for the existence of positive periodic solutions of a neutral delay competition model with diffusion and stock

x′₁(t)=x₁(t)[a₁(t)-b₁(t)x₁(t)-c₁(t)y(t) ]+D₁(t)[x₂(t)-x₁(t)]+S₁(t),
x′₂(t)=x₂(t)[a₂(t)-b₂(t)x₂(t)]+D₂(t)[x₁(t)-x₂(t) ]+S₂(t),

y′(t)=y(t)[a₃(t)-b₃(t)y(t)-α(t)y(t-τ₁(t))-β(t) ∫⁰_τ k(s)y(t+s)ds
-γ(t)y’(t-τ₂(t))-c₃(t)x₁(t)].

Key words: Nussbaum degree, Positive periodic solution, Neutral delay competition model, Diffusion, Stock