K. Pusuluri | Search arXiv

arXiv2020

Dynamics and bifurcations in multistable 3-cell neural networks

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 . 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.

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arXiv2020

Homoclinic puzzles and chaos in a nonlinear laser model

We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. In a symbiotic approach combining the traditional parameter continuation methods using MatCont and a newly developed technique called the Deterministic Chaos Prospector (DCP) utilizing symbolic dynamics on fast parallel computing hardware with graphics processing units (GPUs), we exhibit how specific codimension-two bifurcations originate and pattern regions of chaotic and simple dynamics in this classical model. We show detailed computational reconstructions of key bifurcation structures such as Bykov T-point spirals and inclination flips in 2D parameter space, as well as the spatial organization and 3D embedding of bifurcation surfaces, parametric saddles, and isolated closed curves (isolas).

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