On a Dynamic System of Five Interacting Species in a Natural Environment with Holling’s Type I Functional Responses for Some and Holling’s Type Ii Functio Nal Responses for Others

We propose and analyse a prey-predator model with five interacting species in a natural environment. We assume that there exists ecosystems which can group together in a given place a number of species interacting with each other through different types of interaction. In our model we assume that in such environment it can exist many type of interaction between species which live there. In our model, we use a mixed functional response. Both Holling’s Type I and Type II functional responses are considered. We carry out a mathematical analysis of the proposed model followed by a numerical analysis. Our aim is to examine the dynamics of different populations in an interaction where the super predator has a diverse food source in a multi-species ecosystem and through the study of this model, to highlight the impact of species diversity and interaction diversity on the dynamics of species living in an environment favorable to these types of interactions. The mathematical analysis first concerns the existence, boundedness, local and global stability of the solutions using the Routh-Hurwitz’ criterion and the Lyapunov’s principle. In addition, we look for conditions under which solutions persist or die out. Finally, numerical simulations are carried out to support the theoretical results. The research will contribute to a better understanding and prediction of the evolution of populations living in areas that bring together several species with multiple interactions.