Luis Israel Pabón

Sequential switching is a dynamical mechanism in which different units transiently dominate in a reproducible order without convergence to a single permanent winner. Such behavior is often linked to saddle-type structures and is commonly generated through directed or explicitly asymmetric interactions. Here, we investigate whether recurrent sequential dominance can arise in a minimal discrete-time network with symmetric coupling. We study a three-unit network of non-chaotic Rulkov maps coupled through symmetric state-difference interactions. Although the coupling does not impose a preferred activation order, small intrinsic offsets in the excitability parameters break the degeneracy among the units and select reproducible switching sequences. We identify regimes displaying this behavior using simple criteria based on amplitude, exclusivity, recurrence, and order consistency. The dynamics are illustrated through representative trajectories and supported by local stability analysis near dominance configurations, which is consistent with saddle-type organization. Perturbation tests further show that sequential switching can reappear after transient forcing or persist under selected sustained drives. These results provide a concise dynamical characterization of sequential switching in a minimal symmetrically coupled non-chaotic Rulkov network.

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