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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.20020077 |
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| _version_ | 1866901337607766016 |
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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 |
| id | zenodo_https___doi_org_10_5281_zenodo_20020077 |
| institution | Zenodo |
| language | |
| 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 |