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  1. Article ; Online: Leonid Shilnikov and mathematical theory of dynamical chaos.

    Gonchenko, Sergey / Kazakov, Alexey / Turaev, Dmitry / Shilnikov, Andrey L

    Chaos (Woodbury, N.Y.)

    2022  Volume 32, Issue 1, Page(s) 10402

    Language English
    Publishing date 2022-02-01
    Publishing country United States
    Document type Editorial
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0080836
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article ; Online: Measuring chaos in the Lorenz and Rössler models: Fidelity tests for reservoir computing.

    Scully, James J / Neiman, Alexander B / Shilnikov, Andrey L

    Chaos (Woodbury, N.Y.)

    2021  Volume 31, Issue 9, Page(s) 93121

    Abstract: This study focuses on the qualitative and quantitative characterization of chaotic systems with the use of a symbolic description. We consider two famous systems, Lorenz and Rössler models with their iconic attractors, and demonstrate that with ... ...

    Abstract This study focuses on the qualitative and quantitative characterization of chaotic systems with the use of a symbolic description. We consider two famous systems, Lorenz and Rössler models with their iconic attractors, and demonstrate that with adequately chosen symbolic partition, three measures of complexity, such as the Shannon source entropy, the Lempel-Ziv complexity, and the Markov transition matrix, work remarkably well for characterizing the degree of chaoticity and precise detecting stability windows in the parameter space. The second message of this study is to showcase the utility of symbolic dynamics with the introduction of a fidelity test for reservoir computing for simulating the properties of the chaos in both models' replicas. The results of these measures are validated by the comparison approach based on one-dimensional return maps and the complexity measures.
    MeSH term(s) Entropy ; Nonlinear Dynamics
    Language English
    Publishing date 2021-09-23
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0065044
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Article ; Online: Ordered intricacy of Shilnikov saddle-focus homoclinics in symmetric systems.

    Xing, Tingli / Pusuluri, Krishna / Shilnikov, Andrey L

    Chaos (Woodbury, N.Y.)

    2021  Volume 31, Issue 7, Page(s) 73143

    Abstract: Using the technique of Poincaré return maps, we disclose an intricate order of subsequent homoclinic bifurcations near the primary figure-8 connection of the Shilnikov saddle-focus in systems with reflection symmetry. We also reveal admissible shapes of ... ...

    Abstract Using the technique of Poincaré return maps, we disclose an intricate order of subsequent homoclinic bifurcations near the primary figure-8 connection of the Shilnikov saddle-focus in systems with reflection symmetry. We also reveal admissible shapes of the corresponding bifurcation curves in a parameter space. Their scalability ratio and organization are proven to be universal for such homoclinic bifurcations of higher orders. Two applications with similar dynamics due to the Shilnikov saddle-foci are used to illustrate the theory: a smooth adaptation of the Chua circuit and a 3D normal form.
    Language English
    Publishing date 2021-08-03
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0054776
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  4. Book ; Online: 2$\theta$-burster for rhythm-generating circuits

    Kelley, Aaron / Shilnikov, Andrey L.

    2020  

    Abstract: We propose and demonstrate the use of a minimal 2$\theta$ model for endogenous bursters coupled in 3-cell neural circuits. This 2$\theta$ model offers the benefit of simplicity of designing larger neural networks along with an acute reduction on the ... ...

    Abstract We propose and demonstrate the use of a minimal 2$\theta$ model for endogenous bursters coupled in 3-cell neural circuits. This 2$\theta$ model offers the benefit of simplicity of designing larger neural networks along with an acute reduction on the computation cost.
    Keywords Quantitative Biology - Neurons and Cognition
    Publishing date 2020-07-29
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Book ; Online: Poincare return maps in neural dynamics

    Kolomiets, Marina L. / Shilnikov, Andrey L.

    three examples

    2020  

    Abstract: Understanding of the onset and generic mechanisms of transitions between distinct patterns of activity in realistic models of individual neurons and neural networks presents a fundamental challenge for the theory of applied dynamical systems. We use ... ...

    Abstract Understanding of the onset and generic mechanisms of transitions between distinct patterns of activity in realistic models of individual neurons and neural networks presents a fundamental challenge for the theory of applied dynamical systems. We use three examples of slow-fast neural systems to demonstrate a suite of new computational tools to study diverse neuronal systems.
    Keywords Quantitative Biology - Neurons and Cognition ; Nonlinear Sciences - Chaotic Dynamics
    Publishing date 2020-07-08
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Article ; Online: Noise-activated barrier crossing in multiattractor dissipative neural networks.

    Taylor, Joseph D / Chauhan, Ashok S / Taylor, John T / Shilnikov, Andrey L / Nogaret, Alain

    Physical review. E

    2022  Volume 105, Issue 6-1, Page(s) 64203

    Abstract: Noise-activated transitions between coexisting attractors are investigated in a chaotic spiking network. At low noise level, attractor hopping consists of discrete bifurcation events that conserve the memory of initial conditions. When the escape ... ...

    Abstract Noise-activated transitions between coexisting attractors are investigated in a chaotic spiking network. At low noise level, attractor hopping consists of discrete bifurcation events that conserve the memory of initial conditions. When the escape probability becomes comparable to the intrabasin hopping probability, the lifetime of attractors is given by a detailed balance where the less coherent attractors act as a sink for the more coherent ones. In this regime, the escape probability follows an activation law allowing us to assign pseudoactivation energies to limit cycle attractors. These pseudoenergies introduce a useful metric for evaluating the resilience of biological rhythms to perturbations.
    Language English
    Publishing date 2022-07-19
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.105.064203
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  7. Article ; Online: Bursting dynamics in the normal and failing hearts.

    Bondarenko, Vladimir E / Shilnikov, Andrey L

    Scientific reports

    2017  Volume 7, Issue 1, Page(s) 5927

    Abstract: A failing heart differs from healthy hearts by an array of symptomatic characteristics, including impaired ... ...

    Abstract A failing heart differs from healthy hearts by an array of symptomatic characteristics, including impaired Ca
    MeSH term(s) Action Potentials/physiology ; Animals ; Calcium Signaling ; Computer Simulation ; Heart Failure/physiopathology ; Markov Chains ; Mice ; Models, Cardiovascular ; Time Factors
    Language English
    Publishing date 2017-07-19
    Publishing country England
    Document type Journal Article ; Research Support, Non-U.S. Gov't ; Research Support, U.S. Gov't, Non-P.H.S.
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/s41598-017-05198-z
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  8. Book ; Online: Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits

    Scully, James / Bourahmah, Jassem / Bloom, David / Shilnikov, Andrey L

    2022  

    Abstract: The purpose of this paper is trifold -- to serve as an instructive resource and a reference catalog for biologically plausible modeling with i) conductance-based models, coupled with ii) strength-varying slow synapse models, culminating in iii) two ... ...

    Abstract The purpose of this paper is trifold -- to serve as an instructive resource and a reference catalog for biologically plausible modeling with i) conductance-based models, coupled with ii) strength-varying slow synapse models, culminating in iii) two canonical pair-wise rhythm-generating networks. We document the properties of basic network components: cell models and synaptic models, which are prerequisites for proper network assembly. Using the slow-fast decomposition we present a detailed analysis of the cellular dynamics including a discussion of the most relevant bifurcations. Several approaches to model synaptic coupling are also discussed, and a new logistic model of slow synapses is introduced. Finally, we describe and examine two types of bicellular rhythm-generating networks: i) half-center oscillators ii) excitatory-inhibitory pairs and elucidate a key principle -- the network hysteresis underlying the stable onset of emergent slow bursting in these neural building blocks. These two cell networks are a basis for more complicated neural circuits of rhythmogensis and feature in our models of swim central pattern generators.
    Keywords Quantitative Biology - Neurons and Cognition ; Mathematics - Dynamical Systems ; Nonlinear Sciences - Adaptation and Self-Organizing Systems ; Nonlinear Sciences - Chaotic Dynamics
    Subject code 612
    Publishing date 2022-10-31
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Article ; Online: Design Principles for Central Pattern Generators With Preset Rhythms.

    Lodi, Matteo / Shilnikov, Andrey L / Storace, Marco

    IEEE transactions on neural networks and learning systems

    2019  Volume 31, Issue 9, Page(s) 3658–3669

    Abstract: This article is concerned with the design of synthetic central pattern generators (CPGs). Biological CPGs are neural circuits that determine a variety of rhythmic activities, including locomotion, in animals. A synthetic CPG is a network of dynamical ... ...

    Abstract This article is concerned with the design of synthetic central pattern generators (CPGs). Biological CPGs are neural circuits that determine a variety of rhythmic activities, including locomotion, in animals. A synthetic CPG is a network of dynamical elements (here called cells) properly coupled by various synapses to emulate rhythms produced by a biological CPG. We focus on CPGs for locomotion of quadrupeds and present our design approach, based on the principles of nonlinear dynamics, bifurcation theory, and parameter optimization. This approach lets us design the synthetic CPG with a set of desired rhythms and switch between them as the parameter representing the control actions from the brain is varied. The developed four-cell CPG can produce four distinct gaits: walk, trot, gallop, and bound, similar to the mouse locomotion. The robustness and adaptability of the network design principles are verified using different cell and synapse models.
    Language English
    Publishing date 2019-11-08
    Publishing country United States
    Document type Journal Article ; Research Support, U.S. Gov't, Non-P.H.S. ; Research Support, Non-U.S. Gov't
    ISSN 2162-2388
    ISSN (online) 2162-2388
    DOI 10.1109/TNNLS.2019.2945637
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  10. Article ; Online: The Art of Grid Fields: Geometry of Neuronal Time.

    Shilnikov, Andrey L / Maurer, Andrew Porter

    Frontiers in neural circuits

    2016  Volume 10, Page(s) 12

    Abstract: The discovery of grid cells in the entorhinal cortex has both elucidated our understanding of spatial representations in the brain, and germinated a large number of theoretical models regarding the mechanisms of these cells' striking spatial firing ... ...

    Abstract The discovery of grid cells in the entorhinal cortex has both elucidated our understanding of spatial representations in the brain, and germinated a large number of theoretical models regarding the mechanisms of these cells' striking spatial firing characteristics. These models cross multiple neurobiological levels that include intrinsic membrane resonance, dendritic integration, after hyperpolarization characteristics and attractor dynamics. Despite the breadth of the models, to our knowledge, parallels can be drawn between grid fields and other temporal dynamics observed in nature, much of which was described by Art Winfree and colleagues long before the initial description of grid fields. Using theoretical and mathematical investigations of oscillators, in a wide array of mediums far from the neurobiology of grid cells, Art Winfree has provided a substantial amount of research with significant and profound similarities. These theories provide specific inferences into the biological mechanisms and extraordinary resemblances across phenomenon. Therefore, this manuscript provides a novel interpretation on the phenomenon of grid fields, from the perspective of coupled oscillators, postulating that grid fields are the spatial representation of phase resetting curves in the brain. In contrast to prior models of gird cells, the current manuscript provides a sketch by which a small network of neurons, each with oscillatory components can operate to form grid cells, perhaps providing a unique hybrid between the competing attractor neural network and oscillatory interference models. The intention of this new interpretation of the data is to encourage novel testable hypotheses.
    MeSH term(s) Action Potentials/physiology ; Animals ; Computer Simulation ; Entorhinal Cortex/cytology ; Humans ; Models, Neurological ; Nerve Net/physiology ; Neurons/physiology ; Periodicity ; Space Perception ; Time Factors ; Time Perception
    Language English
    Publishing date 2016-03-08
    Publishing country Switzerland
    Document type Journal Article ; Research Support, N.I.H., Extramural ; Research Support, Non-U.S. Gov't ; Research Support, U.S. Gov't, Non-P.H.S.
    ZDB-ID 2452968-0
    ISSN 1662-5110 ; 1662-5110
    ISSN (online) 1662-5110
    ISSN 1662-5110
    DOI 10.3389/fncir.2016.00012
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