Canard solutions and travelling waves in the spruce budworm population model

The spruce budworm and forest population models are investigated both in the form of ODE’s and in the form of PDE’s. In the former, the canard solutions were detected. In the latter, the canard travelling waves were discovered. We investigate mainly the curvilinear waves and we suggest an approach which gives us the possibility to overcome the difficulties arising due to different diffusion coefficients.