The influence of coupling on chaotic maps modelling bursting cells

Bursting behavior is ubiquitous in physical and biological systems, specially in neural cells where it plays an important role in information processing. This activity refers to a complex oscillation characterized by a slow alternation between spiking behavior and quiescence. In this paper, the interesting phenomena which transpire when two cells are coupled together, is studied in terms of symbolic dynamics. More specifically, we characterize the topological entropy of a map used to examine the role of coupling on identical bursters. The strength of coupling leads to the introduction of a second topological invariant that allows us to distinguish isentropic dynamics. We illustrate the significant effect of the strength parameter on the topological invariants with several numerical results.