Boundedness of Solutions in Neutral Delay Predator-Prey and Competition Systems

Abstract

In this paper, we establish conditions under which solutions of

$$ \left\{ \begin{gathered} \dot{x}\left( t \right) = rx\left( t \right)\left[ {1 - \int_{0}^{{{{\tau }_{1}}}} {x\left( {t - s} \right)d\mu \left( s \right) - \rho \dot{x}} \left( {t - {{\tau }_{2}}} \right) - y\left( {t - {{\tau }_{3}}} \right)g\left( {x\left( t \right)} \right)} \right], \hfill \\ y\left( t \right) = y\left( t \right)\left[ {a + bx\left( {t - {{\tau }_{4}}} \right)g\left( {x\left( {t - {{\tau }_{4}}} \right)} \right) - cy\left( {t - {{\tau }_{5}}} \right)} \right], \hfill \\ \end{gathered} \right. $$

((2.1))

will be bounded. This partially answers the open questions proposed by this author in his recent works on neutral predator-prey and competition systems.