Narrow Results

In this paper, a two-patch model with additive Allee effect, nonlinear dispersal and commensalism is proposed and studied. The stability of equilibria and the existence of saddle-node bifurcation, transcritical bifurcation are discussed. Through qualitative analysis of the model, we know that the persistence and the extinction of population are influenced by the Allee effect, dispersal and commensalism. Combining with numerical simulation, the study shows that the total population density will increase when the Allee effect constant $a$ increases or $m$ decreases. In addition to suppress the Allee effect, nonlinear dispersal and commensalism are crucial to the survival of the species in the two patches.

In a previous paper we showed that emergence of mutualism is made possible by selective recognition processes which allow the host to discriminate true symbionts from commensalists. In hydra/algae associations, algae are first ingested in the apex of digestive cells and then migrate to their basis. Both processes are selective.We extend here the previous differential model to a compartmental model and study the role of the two selection processes.

We analyze the global stability of the coexisting equilibria for several models of commensalism, first by devising a procedure to modify several Lyapunov functionals which were introduced earlier for corresponding models of mutualism, further confirming their usefulness. It is seen that commensalism promotes global stability, in connection with higher-order self-limiting terms which prevent unboundedness. We then use the theory of asymptotically autonomous systems to prove global stability results for models of commensalism which are subject to Allee effects, finding that commensalisms of appropriate strength can overcome the influence of strong Allee effects.

Business can be a for-profit, not-for-profit or hybrid organization. But all these businesses focus on the satisfaction of their stakeholders. Although many businesses adopt a limited perspective of their stakeholders, focusing primarily on the interests of their investors, customers and, in some cases, their employees, it is a fact that the long-term sustainability of any business will depend on its contributions to the society. The long-term objective of all businesses is to serve and support the society and contribute to the socioeconomic development of their people. Therefore, this chapter presents a comprehensive review of the relationship between business and society, with special reference to the three main types of businesses: commercial businesses, social enterprises and non-governmental organizations. As in the case of biological systems, the relationship between business and society may be characterized predominantly by one of the three types of symbiotic relationships: mutualism, commensalism and parasitism. However, the successful co-existence of business and society, in the long run, would depend on the degree of mutualism in their relationship.