Download This Paperm-Stability, Asymptotic Behavior And Properties Of A Class Of Covariant Nonlinear Multi-Agent Systems.
9 Pages Posted: 11 May 2020 Last revised: 20 Mar 2024
Date Written: Revised 2023
Abstract
The equation x^a+y^b+z^c=m in real numbers represents a group of Nonlinear Multi-Agent Systems, is an ill-posed problem and can be used in physical sciences and social sciences. This article introduces some Equivalence-Conditions, Existence-Conditions and properties of x^a+y^b+z^c=m in real numbers, and also defines “m-Stability”, a new measure of Stability of nonlinear equations. This article also introduces simple Java codes (the “Hyena-Attack Algorithm”) that can be used to verify Theorem-1 herein, and for finding feasible solutions for (x,y,z,a,b,c, m) in the Equation [(x^a+y^b+z^c)=m, for Integers in the interval: (-10^1677721600000000000000000000000000000) < x,y,z, a,b,c, m< 10^1677721600000000000000000000000000000 (and even larger positive-integers and smaller negative-integers depending on available computing power).
Keywords: Nonlinearity; Stability; Existence-Conditions; Equivalence-Conditions; Dynamical Systems; AI/ML; Ill-posed Problems; Asymptotic Behavior.
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