| Abstract: | Multi species communities coexist in the natural environment while simple theoretical models typically result in one or few species taking over. Some environmental fluctuations are known to open multiple temporal niches thereby increasing the number of species that can stably coexist. However, little is known about the effects of very fast environmental fluctuations and whether they can increase stability of communities within the same temporal niche. We analyze the stability of three mathematical models of species interaction and test whether introduction of fast external oscillations can increase the diversity of coexisting species. We find that oscillations introduce new effective interactions which stabilize unstable equilibrium points in the system. The stability in one of these systems is analogous to the dynamic stabilization of the Kapitza's pendulum. |
