Year: 2025
Type: article
Abstract: Imaginary coquaternions cℍ can be represented by matrices of negative feedback N^-, positive feedback P^+ and reciprocal links R^± . Added environmental element E^± endows biologic systems with the structure of cℍ module. Although cℍ representation links base patterns with geometric structure of pseudo-Euclidean R_2^4 space, unknown physiologic aspects of relationships between base elements may add new functional features to the structure of a functional module. Another question is whether achieving and remaining in the equilibrium state provides stability of a biologic system. Considering the property of a biologic system to return deviated conditions to the equilibrium, the system of ordinary differential equations describing behavior of a mechanical pendulum was modified and used as a basic tool to find the answers. The obtained results show that in evolving systems the regulatory patterns are organized in a sequence NPRN of base elements allowing the system to perform the high amount of the consuming energy functions. In order to keep dissipating energy at the same level the system bifurcates and finalizes its regulatory cycle in R^± by splitting P^+ after which the next cycle may begin. Obtained flows are continuous pathways not interfering with equilibrium states, thus providing a homeostasis mechanism with nonequilibrium dynamics. Functional transformations reflect changes in the geometry and metric index of coquaternion. Related coquaternion dynamics shows transformation of hyperbolic hyperboloid to the closed surface, which is the fusion of the portions of hyperbolic hyperboloid and two spheres.
Source: AppliedMath
Author: Garri Davydyan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W4407226044