PreprintArticleVersion 1Preserved in Portico This version is not peer-reviewed
Are Some Voltage State Orbits, Computed in a Discrete-Time Hopfield Neural Network, Which Correspond to Bifurcation Values, Fractals? Exists These Orbits in Reality or They Exists Just in Theory i.e.Has These Orbits a Real Couterpart?
Version 1
: Received: 20 September 2024 / Approved: 20 September 2024 / Online: 23 September 2024 (02:26:57 CEST)
How to cite:
Cojocaru, A. V.; Balint, S. Are Some Voltage State Orbits, Computed in a Discrete-Time Hopfield Neural Network, Which Correspond to Bifurcation Values, Fractals? Exists These Orbits in Reality or They Exists Just in Theory i.e.Has These Orbits a Real Couterpart?. Preprints2024, 2024091623. https://doi.org/10.20944/preprints202409.1623.v1
Cojocaru, A. V.; Balint, S. Are Some Voltage State Orbits, Computed in a Discrete-Time Hopfield Neural Network, Which Correspond to Bifurcation Values, Fractals? Exists These Orbits in Reality or They Exists Just in Theory i.e.Has These Orbits a Real Couterpart?. Preprints 2024, 2024091623. https://doi.org/10.20944/preprints202409.1623.v1
Cojocaru, A. V.; Balint, S. Are Some Voltage State Orbits, Computed in a Discrete-Time Hopfield Neural Network, Which Correspond to Bifurcation Values, Fractals? Exists These Orbits in Reality or They Exists Just in Theory i.e.Has These Orbits a Real Couterpart?. Preprints2024, 2024091623. https://doi.org/10.20944/preprints202409.1623.v1
APA Style
Cojocaru, A. V., & Balint, S. (2024). Are Some Voltage State Orbits, Computed in a Discrete-Time Hopfield Neural Network, Which Correspond to Bifurcation Values, Fractals? Exists These Orbits in Reality or They Exists Just in Theory i.e.Has These Orbits a Real Couterpart?. Preprints. https://doi.org/10.20944/preprints202409.1623.v1
Chicago/Turabian Style
Cojocaru, A. V. and Stefan Balint. 2024 "Are Some Voltage State Orbits, Computed in a Discrete-Time Hopfield Neural Network, Which Correspond to Bifurcation Values, Fractals? Exists These Orbits in Reality or They Exists Just in Theory i.e.Has These Orbits a Real Couterpart?" Preprints. https://doi.org/10.20944/preprints202409.1623.v1
Abstract
In case of a discrete-time Hopfield neural network of two neurons with two delays and no self- connections at 23 bifurcation values 23 voltage trajectories appear.Among the 23 voltage trajectories 14 voltage trajectory are not what we call orbits in classic sense. The geometrical aspect of these trajectories suggest that they are fractals. Our conjecture is that the 14 trajectories in discussion are fractals having real couterpart. In case of a discrete-time Hopfield neural network of five neuron with delay and ring architecture at 9 bifurcation values 9 voltage trajectories appear.Among the 9 voltage trajectories we find 5 voltage trajectory which are not what we call orbits in classic sense.The geometrical aspect of these trajectories suggest that they are fractals.Our conjecture is that the 5 trajectories in discussion are fractals having real couterpart.. In case of a discrete-time Hopfield neural network of two neurons with a single delay and self- connections the computed trajectories are what we call orbits in classic sense. In case of a discrete-time Hopfield neural network of two neurons with two delays and self- connections the computed trajectories are what we call orbits in classic sense.
Keywords
fractals; discrete- timeHopfield neural networks; two neurons with delay and no self-connection; five neurons with delay and ring architecture
Subject
Biology and Life Sciences, Behavioral Sciences
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
