Network attractors and nonlinear dynamics of neural computation

[1]  L. Young,et al.  Chaotic heteroclinic networks as models of switching behavior in biological systems. , 2022, Chaos.

[2]  H. Meyer-Ortmanns,et al.  Heteroclinic units acting as pacemakers: entrained dynamics for cognitive processes , 2021, Journal of Physics: Complexity.

[3]  M. Timme,et al.  Decoding complex state space trajectories for neural computing. , 2021, Chaos.

[4]  M. Timme,et al.  Bio-inspired computing by nonlinear network dynamics—a brief introduction , 2021, Journal of Physics: Complexity.

[5]  P. Ashwin,et al.  Excitable networks for finite state computation with continuous time recurrent neural networks , 2020, Biological Cybernetics.

[6]  M. Rabinovich,et al.  Sequential dynamics of complex networks in mind: Consciousness and creativity , 2020 .

[7]  K. Kaneko,et al.  Short term memory by transient oscillatory dynamics in recurrent neural networks , 2020, 2010.15308.

[8]  M. Rabinovich,et al.  Nonlinear dynamics of creative thinking. Multimodal processes and the interaction of heteroclinic structures , 2020, Physics-Uspekhi.

[9]  M. Rabinovich,et al.  Non-linear dynamics of creative thinking , 2020 .

[10]  Matthew D Egbert,et al.  Where Computation and Dynamics Meet: Heteroclinic Network-Based Controllers in Evolutionary Robotics , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[11]  Julia Steinberg,et al.  Associative memory of structured knowledge , 2020, bioRxiv.

[12]  Pantelis R. Vlachas,et al.  Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics , 2019, Neural Networks.

[13]  I. Labouriau,et al.  Asymptotic stability of robust heteroclinic networks , 2019, Nonlinearity.

[14]  C. Postlethwaite,et al.  A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock–Paper–Scissors , 2019, Nonlinearity.

[15]  Peter Ashwin,et al.  Noisy network attractor models for transitions between EEG microstates , 2019, The Journal of Mathematical Neuroscience.

[16]  Murray Shanahan,et al.  Activity in perceptual classification networks as a basis for human subjective time perception , 2019, Nature Communications.

[17]  Christian Bick,et al.  Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks , 2018, Journal of Nonlinear Science.

[18]  A. Guillamón,et al.  Quasiperiodic perturbations of heteroclinic attractor networks. , 2018, Chaos.

[19]  Pablo Varona,et al.  Discrete Sequential Information Coding: Heteroclinic Cognitive Dynamics , 2018, Front. Comput. Neurosci..

[20]  Lorenzo Livi,et al.  Interpreting Recurrent Neural Networks Behaviour via Excitable Network Attractors , 2018, Cognitive Computation.

[21]  Peter Ashwin,et al.  From coupled networks of systems to networks of states in phase space , 2018 .

[22]  Peter Ashwin,et al.  Sensitive Finite-State Computations Using a Distributed Network With a Noisy Network Attractor , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Peter beim Graben,et al.  Sequences by Metastable Attractors: Interweaving Dynamical Systems and Experimental Data , 2017, Front. Appl. Math. Stat..

[24]  Christian Bick,et al.  Heteroclinic switching between chimeras. , 2017, Physical review. E.

[25]  Hillel J. Chiel,et al.  Robustness, flexibility, and sensitivity in a multifunctional motor control model , 2016, Biological Cybernetics.

[26]  Panos E. Trahanias,et al.  A reservoir computing model of episodic memory , 2016, 2016 International Joint Conference on Neural Networks (IJCNN).

[27]  Liliana Garrido-da-Silva,et al.  Stability of quasi-simple heteroclinic cycles , 2016, 1606.02592.

[28]  Claire M. Postlethwaite,et al.  Quantifying Noisy Attractors: From Heteroclinic to Excitable Networks , 2016, SIAM J. Appl. Dyn. Syst..

[29]  Stephen Coombes,et al.  Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience , 2015, The Journal of Mathematical Neuroscience.

[30]  Claire M. Postlethwaite,et al.  Designing Heteroclinic and Excitable Networks in Phase Space Using Two Populations of Coupled Cells , 2015, J. Nonlinear Sci..

[31]  Ichiro Tsuda,et al.  Chaotic itinerancy and its roles in cognitive neurodynamics , 2015, Current Opinion in Neurobiology.

[32]  M. J. Field,et al.  Heteroclinic Networks in Homogeneous and Heterogeneous Identical Cell Systems , 2015, Journal of Nonlinear Science.

[33]  M. Kramer,et al.  Beyond the Connectome: The Dynome , 2014, Neuron.

[34]  Pablo Varona,et al.  Chunking dynamics: heteroclinics in mind , 2014, Front. Comput. Neurosci..

[35]  Roger D. Quinn,et al.  Stable Heteroclinic Channels for Slip Control of a Peristaltic Crawling Robot , 2013, Living Machines.

[36]  Han Yuan,et al.  Spatiotemporal dynamics of the brain at rest — Exploring EEG microstates as electrophysiological signatures of BOLD resting state networks , 2012, NeuroImage.

[37]  Thomas Nowotny,et al.  Criteria for robustness of heteroclinic cycles in neural microcircuits , 2011, Journal of mathematical neuroscience.

[38]  D. Ville,et al.  BOLD correlates of EEG topography reveal rapid resting-state network dynamics , 2010, NeuroImage.

[39]  Yuri Bakhtin.  Small noise limit for diffusions near heteroclinic networks , 2010 .

[40]  R. Huerta,et al.  Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model. , 2008, Chaos.

[41]  A. Selverston,et al.  Dynamical principles in neuroscience , 2006 .

[42]  Dario Floreano,et al.  Exploring the T-Maze: Evolving Learning-Like Robot Behaviors Using CTRNNs , 2003, EvoWorkshops.

[43]  D. Armbruster,et al.  Noisy heteroclinic networks , 2003 .

[44]  Dietrich Lehmann,et al.  Millisecond by Millisecond, Year by Year: Normative EEG Microstates and Developmental Stages , 2002, NeuroImage.

[45]  Marco Giunti,et al.  Computation, Dynamics, and Cognition , 2001 .

[46]  M. I. Rabinovich,et al.  Dynamical coding of sensory information with competitive networks , 2000, Journal of Physiology-Paris.

[47]  杉内 友理子.  平衡神経系の Systems Neuroscience , 2000 .

[48]  Walter J. Freeman,et al.  Neurodynamics: An Exploration in Mesoscopic Brain Dynamics , 2000, Perspectives in Neural Computing.

[49]  R. Beer.  Dynamical approaches to cognitive science , 2000, Trends in Cognitive Sciences.

[50]  T. Gelder,et al.  The dynamical hypothesis in cognitive science , 1998, Behavioral and Brain Sciences.

[51]  Kunihiko Kaneko,et al.  On the strength of attractors in a high-dimensional system: Milnor attractor network, robust global attraction, and noise-induced selection , 1998, chao-dyn/9802016.

[52]  M. Krupa.  Robust heteroclinic cycles , 1997 .

[53]  Randall D. Beer,et al.  On the Dynamics of Small Continuous-Time Recurrent Neural Networks , 1995, Adapt. Behav..

[54]  Vivien Kirk,et al.  A competition between heteroclinic cycles , 1994 .

[55]  Ken-ichi Funahashi,et al.  Approximation of dynamical systems by continuous time recurrent neural networks , 1993, Neural Networks.

[56]  D. Amit.  Modelling Brain Function: The World of Attractor Neural Networks , 1989 .

[57]  Hermann Haken,et al.  Synergetics: an overview , 1989 .

[58]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[59]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[60]  T. Ohira,et al.  Random Perturbations , 2021, Mathematics as a Laboratory Tool.

[61]  Kyriacos Nikiforou,et al.  The dynamics of continuous-time recurrent neural networks and their relevance to episodic memory , 2019 .

[62]  Pablo Varona,et al.  Transient Brain Dynamics , 2012 .

[63]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.