The Connection Matrix analysis of a Prey-Predator system with a Strong Allee effect and multiple interior equilibria

We consider a Gause-type prey-predator system incorporating a strong allee effect for the prey population. For the existence of multiple interior equilibria we consider Holling-type predator functional response and the density dependent death rate for the predator. With the help of the Conley connection matrix theory we study the dynamics of the system in presence of one, two and three interior equilibria. It is found that (i) the saddle-saddle connections exist in presence of single and multiple interior equilibria connecting interior flows to the boundary and (ii) the system admits a set of degree-2 (i.e, a 2-discs of) connecting orbits from interior equlibrium to the origin. Thus permanence or robust permanence of the system is not possible.