In this paper, the complex dynamics of the cross-linking reaction of the polymer composite model, are analyzed and studied. This model is described by five-dimensional nonlinear ordinary differential equations with three real parameters. The nature of the response of collagen with cross-linking chemicals is detailed in this model, and it is very essential not only in leather technology but also in the nutritional business. We present a thorough analysis of their invariant algebraic hypersurfaces of this model. The flow on invariant sets for the model is investigated. Using the invariant algebraic hypersurfaces, we verify the non-existence of periodic solutions and investigate their dynamics in these invariant sets. It is established that the five-dimensional model, depending on the parameters, is completely integrable with four independent first integrals.
