On a generalized yorke condition for scalar delayed population models

• Autor(a) principal: Faria, Teresa
• Data de Publicação: 2005
• Outros Autores: Liz, Eduardo, Oliveira, José J., Trofimchuk, Sergei
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/1822/3909
• topic: Delay population model; Global attractivity; Yorke condition; 3/2-condition; Delayed population model; Science & Technology

For a scalar delayed differential equation $\dot x(t)=f(t,x_t)$, we give sufficient conditions for the global attractivity of its zero solution. Some technical assumptions are imposed to insure boundedness of solutions and attractivity of non-oscillatory solutions. For controlling the behaviour of oscillatory solutions, we require a very general condition of Yorke type, together with a 3/2-condition. The results are particularly interesting when applied to scalar differential equations with delays which have served as models in populations dynamics, and can be written in the general form $\dot x(t)=(1+x(t))F(t,x_t)$. Applications to several models are presented, improving known results in the literature.