Chaotic Dynamics in Neural Systems

Pusuluri, Krishna; Ju, Huiwen; Shilnikov, Andrey

doi:10.1007/978-3-642-27737-5_738-1

Cited by 5 publications

(5 citation statements)

References 99 publications

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“…We performed detailed computational reconstruction and visualization of the three dimensional embedding of bifurcation surfaces, parametric saddles and isolas. The knowledge and the methodology created in this study should further advance new ideas and approaches for a better understanding of cross-disciplinary nonlinear phenomena at large, while the generality of our modeling approaches are also applicable to other biological, medical, and engineering systems [32].…”

Section: Discussionmentioning

confidence: 99%

“…Our motivation is to extend the existing theory of homoclinic bifurcations of low-codimensions [1,5,19,20,21,22,3,23,24,25,26,27,28] and to make it accessible and practical for the nonlinear dynamics community. Recently, we have advanced an approach called the "Deterministic Chaos Prospector" (DCP) that utilizes symbolic representations of simple and chaotic dynamics [29,30,31,32], based on our earlier works [18,33]. This allows for fast and effective identification of bifurcation structures underlying and governing deterministic chaos in various systems.…”

Section: Introductionmentioning

confidence: 99%

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(INVITED) Homoclinic puzzles and chaos in a nonlinear laser model

Pusuluri

Meijer²,

Shilnikov

2021

Communications in Nonlinear Science and Numerical Simulation

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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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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

(INVITED) Homoclinic puzzles and chaos in a nonlinear laser model

Pusuluri

Meijer²,

Shilnikov

2021

Communications in Nonlinear Science and Numerical Simulation

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“…4 reveal the sequence of bifurcations that stable rhythms undergo near the borderlines. Such bifurcation diagrams have proven useful for studying the dynamics of small CPG-circuits and other nonlinear systems [44][45][46][47][48] . In addition to the fully symmetric motif in Fig.…”

Section: Methodsmentioning

confidence: 99%

Dynamics and bifurcations in multistable 3-cell neural networks

Collens,

Pusuluri,

Kelly

et al. 2020

Preprint

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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 type1 . 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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“…An extensive modern overview of mathematical theory on slow-fast ODE systems is given by Kuehn (2015). In particular, slow-fast systems have become a big research topic in mathematical neuroscience, see for example Rubin and Terman (2002); Izhikevich (2007); Ermentrout and Terman (2010); Pusuluri et al (2020). Another notable application of SPT is for control science, where the classical text is Kokotovic et al (1999).…”

Section: Singular Perturbation Theorymentioning

confidence: 99%

Dimensions of Timescales in Neuromorphic Computing Systems

Jaeger,

Doorakkers,

Lawrence

et al. 2021

Preprint

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This article is a public deliverable of the EU project Memory technologies with multi-scale time constants for neuromorphicarchitectures (MeMScales, memscales.eu/, Call ICT-06-2019 Unconventional Nanoelectronics, project number 871371). This arXiv version is a verbatim copy of the deliverable report, with administrative information stripped. It collects a wide and varied assortment of phenomena, models, research themes and algorithmic techniques that are connected with timescale phenomena in the fields of computational neuroscience, mathematics, machine learning and computer science, with a bias toward aspects that are relevant for neuromorphic engineering. It turns out that this theme is very rich indeed and spreads out in many directions which defy a unified treatment. We collected several dozens of sub-themes, each of which has been investigated in specialized settings (in the neurosciences, mathematics, computer science and machine learning) and has been documented in its own body of literature. The more we dived into this diversity, the more it became clear that our first effort to compose a survey must remain sketchy and partial. We conclude with a list of insights distilled from this survey which give general guidelines for the design of future neuromorphic systems.

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Chaotic Dynamics in Neural Systems

Cited by 5 publications

References 99 publications

(INVITED) Homoclinic puzzles and chaos in a nonlinear laser model

(INVITED) Homoclinic puzzles and chaos in a nonlinear laser model

Dynamics and bifurcations in multistable 3-cell neural networks

Dimensions of Timescales in Neuromorphic Computing Systems

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