Dynamic Exploration and Control of Bifurcation in a Fractional-Order Lengyel-Epstein Model Owing Time Delay

Abstract

Delayed differential equation plays a vital role in revealing the dynamics of chemical reaction law. In this work, we propose a novel fractional-order Lengyel-Epstein model owing time delay. By regarding the delay as parameter and investigating the distribution of roots of the associated characteristic equation of the formulated fractional-order delayed Lengyel-Epstein model, we set up a new delay-dependent criterion on stability and bifurcation of the involved fractional-order delayed Lengyel-Epstein model. Making use of nonlinear delayed feedback controller, we can effectually control the stability domain and the time of bifurcation phenomenon of the formulated fractional-order delayed Lengyel-Epstein model. Taking advantage of hybrid controller, we are able to adjust the stability domain and the time of bifurcation phenomenon of the established fractional-order delayed Lengyel-Epstein model. The study shows that delay is a vital factor which affects the stability and bifurcation behavior of the addressed fractional-order delayed Lengyel-Epstein model. In order to illustrate the rationality of the acquired theoretical outcomes, we execute Matlab simulations to check this fact. The gained outcomes in this work are absolutely innovative and possess enormous theoretical significance in adjusting concentrations of different chemical substance.