We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin–Huxley type [Wojcik et al., PLoS One 9, e92918 (2014)]. The computational reduction to return maps for the phase-lags between neurons reveals a rich multiplicity of rhythmic patterns in such circuits. We perform a detailed bifurcation analysis to show how such rhythms can emerge, disappear, and gain or lose stability, as the parameters of the individual cells and the synapses are varied.
We propose a minimalistic model called the 2θ-burster due to two slow phase characteristics of endogenous bursters, which when coupled in 3-cell neural circuits generate a multiplicity of stable rhythmic outcomes. This model offers the benefits of simplicity for designing larger neural networks along with an acute reduction in the computation cost. We developed a dynamical system framework for explaining the existence and robustness of phase-locked states in activity patterns produced by small rhythmic neural circuits. Several 3-cell configurations, from multifunctional to monostable, are considered to demonstrate the versatility of the proposed approach, allowing the network dynamics to be reduced to the examination of 2D Poincaré return maps for the phase lags between three constituent 2θ-bursters.
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