Abstract
We study curious features appearing in three systems of two coupled rings of cells with Z3 × Z5 exact symmetry, and Z3 and Z5 interior symmetries. This study was motivated by previous work by Antoneli et al. [2008, 2010], on two rings of cells coupled through a "buffer" cell, with Z3 × Z5 and D3 × D5 exact and interior symmetry groups. There, quasi-periodic behavior was found through a sequence of Hopf bifurcations, and relaxation oscillation phenomena appearing further away from the third Hopf point seemed to be necessary for a curious dynamic feature to occur. In this paper, we analyze the dynamical behavior of three distinct networks of two coupled rings of cells, with no "buffer" cell, and find an analogous bifurcation scenario to explain the appearance of quasi-periodic motion in these systems and the curious exotic feature. We compute the relevant states numerically.
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