Oscillations and stability due to juvenile competitive effects on adult fertility

The case of juvenile versus adult competitive effects on adult fertility in an agedependent population dynamics model introduced by Cushing and Li [1] is considered. It is shown that stronger juvenile competition stabilises the model, while low sensitivity of adult fertility to juvenile cohort sizes leads to destabilisation and oscillatory solutions. As a special case, there is included a form of Gurtin-MacCamyʹs equation for which no Hopf bifurcations are possible. We have tried to maintain a certain balance between analytical and numerical methods of investigation. The paper contains, therefore, a considerable amount of numerically computed illustrations.