Persistence, stability and level crossings in an integrodifferential system (Q1328186)

The paper deals with a model of two competitive species when their ``per capita'' growth rates are affine functionals of the past. First the authors provide some sufficient conditions guaranteeing the uniform persistency or non-persistency of the (autonomous and the nonautonomous version of the) system. Section 3 of the paper contains some convergence characteristics of the solutions, while in section 4 the existence and global attractivity of a periodic solution is discussed. The case of the monotonic convergence to the periodic solution is discussed separately by investigating the so called ``level crossing''. A special example with reducible kernels is discussed in Section 5.