Dynamics and bifurcations in multistable 3-cell neural networks
J. Collens, K. Pusuluri, A. Kelley, D. Knapper, T. Xing, S. Basodi, D. Alacam, A. L. Shilnikov
Abstract
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.
Topics & Concepts
MultistabilityBifurcationBiological applications of bifurcation theoryArtificial neural networkComputer scienceDynamics (music)GeneralityControl theory (sociology)MathematicsBifurcation theoryBiological neural networkTopology (electrical circuits)Statistical physicsNeural systemRhythmNonlinear systemDynamical systems theoryCentral pattern generatorComplex dynamicsLimit cycleNonlinear dynamical systemsReduction (mathematics)BistabilityPhysicsSaddle-node bifurcationElectronic circuitNeuroscienceMultiplicity (mathematics)Pitchfork bifurcationNeural dynamics and brain functionNeural Networks Stability and SynchronizationAdvanced Memory and Neural Computing