Dynamic stability of a class of fractional‐order nonlinear systems via fixed point theory

Abstract

In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in. However, the case of the fractional-order belonging to (0, 1 2 ) has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective.

Image Processing Based on Fuzzy Mathematics Theory

“…If the noise resistance of the algorithm is improved, the actual edge area will be weakened, resulting in edge missing detection. In both cases, the detected edge will deviate from the actual edge, resulting in unreasonable segmentation results [3][4][5].…”

Finite‐time stability of reaction–diffusion genetic regulatory networks with nondifferential time‐varying mixed delays

“…The results obtained from the analysis of GRNs are used to help understand their dynamic behaviors, which offers insights into how biological systems differentiate and evolve [2][3][4]. In recent years, quantities of results have been published on dynamic behaviors of GRNs [5][6][7][8], among which the stability problem of GRNs has become one of the most fundamental research topics.…”