A Hybrid Non-Local Model of Ontogenetic Growth Revealed a Phase Transition and Two Bifurcations

The problem this study deals with is the dynamics of growth of animals. In the study, some features of the growth of pigs were modelled. The research concerns the growth dynamics during a period of growth close to a bifurcation point. In the point, two bifurcations of the growth trajectory take place. The period of growth entails the weight in which an animal's growth stops when individual maximum weight is reached. In the study, methods of applied mathematics were used. The growth of animals was modelled by a hybrid and continuum methods as a dynamic system. In the hybrid model, time was considered as a discrete variable. In the study the factors, which control trajectories and the dynamics of growth were revealed. There are three results in this study. The first result suggests that in animals, the current weight M can be described by derivative of the average consumed feed. The second result gives the equation of the weight balance in an integral form. Third result implies that in ontogeny, growth of pigs has to be modelled as a dynamic system. The system has two bifurcations; one of the trajectory of the weight gain, and other of the trajectory of the growth invariant K. As a result, new growth trajectories emerge. In some instances, the findings can be translated to man in others they apply to animals.