Hopf Bifurcation of the Oregonator Oscillator with Distributed Delay

Article Hopf Bifurcation of the Oregonator Oscillator with Distributed Delay Yu Wang 1,* and Luca Guerrini 2 1 School of Mathematics, Southeast University, Nanjing 210096, China 2 Department of Management, Polytechnic University of Marche, 60121 Ancona, Italy * Correspondence: [email protected] Received: 2 June 2024; Revised: 10 July 2024; Accepted: 30 July 2024; Published: 19 August 2024 Abstract: This paper investigates the bifurcation problem of the Oregonator oscillator with distributed time delay, and two cases are considered, namely weak and strong kernels. First, theoretical approaches are provided to analyze the stability properties of the equilibrium in these systems using the chain trick method. Near the positive equilibrium point, the Routh-Hurwitz criteria are employed to establish precise conditions for stability and Hopf bifurcation and determine the bifurcation direction. Additionally, this paper explores the implications of inffnite memory within a distributed delay to gain insights into the dynamic behavior. Moreover, extensive numerical simulations are conducted to support our theoretical analysis. The main simulations illustrate the bifurcation waveform and phase diagrams and reveal complex dynamic behavior, including stable and unstable oscillations.