  Based on a multi-agent model, we investigate how target waves emerge from a
population dynamics with cyclical interactions among three species. We show
that the periodically injecting source in a small central area can generate
target waves in a two-dimensional lattice system. By detecting the temporal
period of species' concentration at the central area, three modes of target
waves can be distinguished. Those different modes result from the competition
between local and global oscillations induced by cyclical interactions: Mode A
corresponds to a synchronization of local and global oscillations, Mode B
results from an intermittent synchronization, and Mode C corresponds to the
case when the frequency of the local oscillation is much higher than that of
the global oscillation. This work provides insights into pattern formation in
biologic and ecologic systems that are totally different from the extensively
studied diffusion systems driven by chemical reactions.

Biological Physics;Data Analysis, Statistics and Probability;Populations and Evolution