Data resampling: An approach for improving characterization of complex dynamics from noisy interspike intervals

Extracting dynamics from point processes produced by different models describing spiking phenomena depends on several factors affecting the quality of reconstruction of nonuniformly sampled dynamic...

[1]  A. Sherman.  Anti-phase, asymmetric and aperiodic oscillations in excitable cells--I. Coupled bursters. , 1994, Bulletin of mathematical biology.

[2]  Sauer,et al.  Reconstruction of dynamical systems from interspike intervals. , 1994, Physical review letters.

[3]  H. Kantz.  A robust method to estimate the maximal Lyapunov exponent of a time series , 1994 .

[4]  J. Kurths,et al.  Determining the largest Lyapunov exponent of chaotic dynamics from sequences of interspike intervals contaminated by noise , 2017 .

[5]  Vadim S. Anishchenko,et al.  Reconstruction of dynamical and geometrical properties of chaotic attractors from threshold-crossing interspike intervals , 1998 .

[6]  Sriram Ganeshan,et al.  Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System. , 2016, Physical review letters.

[7]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[8]  Quantifying chaotic dynamics from integrate-and-fire processes. , 2015, Chaos.

[9]  J B Gao,et al.  Distinguishing chaos from noise by scale-dependent Lyapunov exponent. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  T. Sauer,et al.  Reconstructing chaotic dynamics through spike filters , 1999 .

[11]  H. Kantz,et al.  Embedding of sequences of time intervals , 1997 .

[12]  Sawada,et al.  Measurement of the Lyapunov spectrum from a chaotic time series. , 1985, Physical review letters.

[13]  J Kurths,et al.  Characterization of the chaos-hyperchaos transition based on return times. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Antonio Politi,et al.  Universal scaling of Lyapunov-exponent fluctuations in space-time chaos. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Tim Sauer,et al.  Chaotic Stochastic Resonance: Noise-Enhanced Reconstruction of Attractors , 1997 .

[16]  E Mosekilde,et al.  Chaotic dynamics from interspike intervals. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Dmitry E. Postnov,et al.  CHAOTIC HIERARCHY IN HIGH DIMENSIONS , 2000 .

[18]  Holger Kantz,et al.  The problem of spurious Lyapunov exponents in time series analysis and its solution by covariant Lyapunov vectors , 2013 .

[19]  D. Broomhead,et al.  Embedding theorems for non-uniformly sampled dynamical systems , 2007 .

[20]  Mingzhou Ding,et al.  DETERMINISTIC POINT PROCESSES GENERATED BY THRESHOLD CROSSINGS : DYNAMICS RECONSTRUCTION AND CHAOS CONTROL , 1997 .

[21]  André Longtin,et al.  Interspike interval attractors from chaotically driven neuron models , 1997 .

[22]  Ulrich Parlitz,et al.  Identification of True and Spurious Lyapunov Exponents from Time Series , 1992 .

[23]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[24]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory , 1980 .

[25]  Julien Clinton Sprott,et al.  Recent new examples of hidden attractors , 2015 .

[26]  O. N. Pavlova,et al.  Improving the quality of extracting dynamics from interspike intervals via a resampling approach , 2018, Commun. Nonlinear Sci. Numer. Simul..

[27]  J. Rinzel,et al.  INTEGRATE-AND-FIRE MODELS OF NERVE MEMBRANE RESPONSE TO OSCILLATORY INPUT. , 1981 .

[28]  Lei Yang,et al.  Detecting chaos in heavy-noise environments. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  E Mosekilde,et al.  Extracting dynamics from threshold-crossing interspike intervals: possibilities and limitations. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  L. Glass,et al.  A simple model for phase locking of biological oscillators , 1979, Journal of mathematical biology.

[31]  Jing Hu,et al.  Facilitating Joint Chaos and Fractal Analysis of Biosignals through Nonlinear Adaptive Filtering , 2011, PloS one.

[32]  P. Alstrøm,et al.  Phase-locking structure of “integrate-and-fire” models with threshold modulation , 1988 .

[33]  H. Abarbanel,et al.  LYAPUNOV EXPONENTS IN CHAOTIC SYSTEMS: THEIR IMPORTANCE AND THEIR EVALUATION USING OBSERVED DATA , 1991 .