Periodic solutions of nonautonomous stage-structured cooperative system
The purpose of this note is to study the stage-structured nonautonomous cooperative system of species \[ \begin{gathered} \dot x_1(t)= \alpha(t)x_2(t)- r_1(t)x_1(t)- x_1(t)- \eta_1(t)x^2_1(t),\\ \dot x_2(t)= \beta(t)x_1(t)- r_2(t)x_2(t) - \eta_2(t)x^2_2(t)+ b(t)x_2(t)y(t),\\ \dot y(t)= y(t) [R(t)- a(t)y(t)+ c(t)x_2(t)],\end{gathered}\tag{\(*\)} \] where \(\alpha(t)\), \(\beta(t)\), \(r_i(t)\), \(\eta_i(t)\), \(i= 1,2\), \(a(t)\), \(b(t)\), \(c(t)\) and \(R(t)\) are positive periodic continuous functions with period \(\omega> 0\). The authors prove the existence of a positive \(\omega\)-periodic solution of system \((*)\). The method used is based on the continuation theorem of coincidence degree theory.
scientific article; zbMATH DE number 2142338