Interaction and coexistence with self-regulating species

Based on Lotka-Volterra (LV) system with spatial diffusion we study a self-regulating species, whose interactions can change with the other's population size. These interactions can be divided into four types described by the interaction portrait. The activity of self-regulation in population also depends on the opposite species, when the opposite species is strong competitive, the self-regulating species cannot adjust its population actively until the roles reverse. Furthermore the way of coexistence with self-regulating system, including competition-coexistence and parasitism-coexistence is discussed; it suggests that proper competition is better to acquire larger total population than a single sacrifice as a host. Moreover both self-regulation and spatial diffusion may be opportunities to switch the final surviving species, but self-regulation can result into stable situation and promote the diversity, in accordance with Darwin's theory of evolution.