Is there chaos in the brain? II. Experimental evidence and related models.

Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in high-dimensional dynamical systems with and without a noise term has motivated a new interpretation of this dynamic neural activity, cast in terms of the high-dimensional transitory dynamics among "exotic" attractors. This interpretation is quite different from the conventional one, cast in terms of simple behavior on low-dimensional attractors. Skarda and Freeman (1987) presented evidence in support of the conclusion that animals cannot memorize odor without chaotic activity of neuron populations. Following their work, we study the role of chaotic dynamics in biological information processing, perception, and memory. We propose a new coding scheme of information in chaos-driven contracting systems we refer to as Cantor coding. Since these systems are found in the hippocampal formation and also in the olfactory system, the proposed coding scheme should be of biological significance. Based on these intensive studies, a hypothesis regarding the formation of episodic memory is given.

/pdf/toward-an-interpretation-of-dynamic-neural-activity-in-terms-dzzzc11nnw.pdf

Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems

Discrimination of sleep stages: a comparison between spectral and nonlinear EEG measures

The Hodgkin--Huxley model was developed to characterize the action potential of a squid axon It has served as an archetype for compartmental models of the electrophysiology of biological membranes Thus the dynamics of the Hodgkin--Huxley model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods that can be applied to more complex models This note demonstrates previously unobserved dynamics in the Hodgkin--Huxley model, namely, the existence of chaotic solutions in the model with its original parameters The solutions are found by displaying rectangles in a cross-section whose images under the return map produce a Smale horseshoe The chaotic solutions are highly unstable, but they are significant as they lie in the basin boundary that establishes the threshold of the system

https://epubs.siam.org/doi/pdf/10.1137/S1111111101394040

Chaos in the Hodgkin--Huxley Model

Long-counting-time pulse-number distributions (PNDs) were measured from a broad variety of cat primary auditory fibers using different tone and noise stimuli, counting times T, and number of samples N/sub T/. Whereas short-counting-time PNDs (T approximately 50 ms) manifest the presence of spike pairs (an enhancement of even- over odd-count probabilities), the irregular shapes of the long-counting-time PNDs (T>or approximately=0.1 s) reveal that the underlying sequence of action potentials consists of spike clusters when viewed on a longer time scale. For all units measured, the count variance-to-mean ratio (Fano factor) F(T) varied little over some 90 dB change in the stimulus level. On the other hand, F(T) increased substantially as T and/or N/sub T/ were increased, corresponding to the capture of larger and larger spike clusters in the counting time. A relationship is developed between the Fano-time function F(T) and the normalized coincidence rate function, g ( tau ) versus delay time tau . The behavior of the PNDs and the scale invariance implicit in fractional-power-law relationships suggest that the neural events on all primary auditory fibers exhibit fractal behavior for sufficiently large times (sufficiently low frequencies). >

Fractal character of the auditory neural spike train

12. Chaotic oscillations and bifurcations in squid giant axons

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

K. Aihara

Author Tools

Chat about Author

Papers

12. Chaotic oscillations and bifurcations in squid giant axons