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Main Author: HAVINAL, VINAY KUMAR
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Published: Zenodo 2026
Online Access:https://doi.org/10.5281/zenodo.20020077
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author HAVINAL, VINAY KUMAR
author_facet HAVINAL, VINAY KUMAR
contents <p>The Collatz conjecture — one of the most celebrated unsolved problems in mathematics —asserts that iterative application of a simple branching rule on any positive integer eventually converges to 1. In this paper, we propose a novel theoretical framework that maps the structural dynamics of the Collatz sequence onto the phases of neuronal signal transmission, with particular focus on the convergence to resting membrane potential (−70mV). We demonstrate that the odd-step rule (3n+1) is mathematically analogous to Na⁺-mediated depolarization, the even-step rule (n/2) mirrors K⁺-driven re polarization, and the Collatz stopping time provides a computable upper bound estimate for neuronal refractory period duration. This cross-disciplinary framework connects number theory, discrete dynamical systems, and computational neuroscience, opening a new avenue for modeling neuronal convergence behavior using integer sequence theory</p>
format Recurso digital
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institution Zenodo
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publishDate 2026
publisher Zenodo
record_format zenodo
spellingShingle Collatz Stopping Time as a Mathematical Model for Neuronal Refractory Period Duration: A Discrete Dynamical Systems Approach
HAVINAL, VINAY KUMAR
<p>The Collatz conjecture — one of the most celebrated unsolved problems in mathematics —asserts that iterative application of a simple branching rule on any positive integer eventually converges to 1. In this paper, we propose a novel theoretical framework that maps the structural dynamics of the Collatz sequence onto the phases of neuronal signal transmission, with particular focus on the convergence to resting membrane potential (−70mV). We demonstrate that the odd-step rule (3n+1) is mathematically analogous to Na⁺-mediated depolarization, the even-step rule (n/2) mirrors K⁺-driven re polarization, and the Collatz stopping time provides a computable upper bound estimate for neuronal refractory period duration. This cross-disciplinary framework connects number theory, discrete dynamical systems, and computational neuroscience, opening a new avenue for modeling neuronal convergence behavior using integer sequence theory</p>
title Collatz Stopping Time as a Mathematical Model for Neuronal Refractory Period Duration: A Discrete Dynamical Systems Approach
url https://doi.org/10.5281/zenodo.20020077