Existence of positive periodic solutions of a neutral delay competition model with diffusion and stock. (Chinese. English summary) Zbl 1174.34070
Summary: By means of the Nussbaum degree theory, a sufficient condition is established for the existence of positive periodic solutions of the neutral delay competition model with diffusion and stock
\(x'_1(t)=x_1(t)[a_1(t)-b_1(t)x_1(t)-c_1(t)y(t)]+D_1(t)[x_2(t)-x_1(t)]+S_1(t),\)
\(x'_2(t)=x_2(t)[a_2(t)-b_2(t)x_2(t)]+D_2(t)[x_1(t)-x_2(t)]+S_2(t),\)
\(y'(t)=y(t)[a_3(t)-b_3(t)y(t)-\alpha(t)y(t-\tau_1(t))-\beta (t)\int^0_{-\tau} k(s)y(t+s)\, \text{d}s -\gamma(t)y'(t-\tau_2(t))-c_3(t)x_1(t)]\).
\(x'_1(t)=x_1(t)[a_1(t)-b_1(t)x_1(t)-c_1(t)y(t)]+D_1(t)[x_2(t)-x_1(t)]+S_1(t),\)
\(x'_2(t)=x_2(t)[a_2(t)-b_2(t)x_2(t)]+D_2(t)[x_1(t)-x_2(t)]+S_2(t),\)
\(y'(t)=y(t)[a_3(t)-b_3(t)y(t)-\alpha(t)y(t-\tau_1(t))-\beta (t)\int^0_{-\tau} k(s)y(t+s)\, \text{d}s -\gamma(t)y'(t-\tau_2(t))-c_3(t)x_1(t)]\).
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
| 92D25 | Population dynamics (general) |
| 34K20 | Stability theory of functional-differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
