Experimental detection of Hopf bifurcation in two-dimensional dynamical systems. (June 2021)

• Record Type: Journal Article
• Authors: Jiménez–Ramírez, O.; Cruz–Domínguez, E.J.; Quiroz–Juárez, M.A.; Aragón, J.L.; Vázquez–Medina, R.
• Is Part Of: Chaos, solitons & fractals. Volume 6(2021)
• Publication Date: 2021-06
• Subjects: Hopf bifurcation -- stability -- nonlinear systems -- analog electronic circuit; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Solitons; Fractals; Chaotic behavior in systems; Periodicals; Electronic journals; 003.7
• DOI: 10.1016/j.csfx.2021.100058
• Languages: English
• ISSNs: 2590-0544

Abstract

Highlights: We propose a tool to detect Hopf bifurcations (HB) in a two-parameters space Hopf bifurcations are detected in nonlinear systems using an electronic circuit. We electronically implement the kinetics of a reaction-diffusion model. Dynamical evolution of the system is explored in a fast, easy and accessible way. We show the quantitative agreement between analytical and experimental HBs. Abstract: In this work, we propose a strategy based on an analog active network to detect Hopf bifurcations in two–dimensional dynamical systems described by ordinary differential equations. With the proposed strategy, two parameters of the nonlinear system are established in the analog active network by using external controllable voltage levels in order to explore the dynamical evolution of the system in a fast, easy, and accessible way, making our approach a powerful tool to detect Hopf bifurcations in a two-dimensional space. To demonstrate the proposed strategy's potential and functionality, we electronically implement the kinetics of a reaction-diffusion model proposed by Barrio et al. in 1999 [1], called BVAM model. Hopf bifurcations are detected by following the changes in the system, going from stationary to periodic solutions when varying the control parameters. Local linear stability analysis is performed to show the quantitative agreement between analytical and experimental bifurcations. We additionally found that global effects are detected by the experimental approach, which cannot be predicted from a local analysis. The proposed strategy opens the way to use analog active networks to detect bifurcations in dynamical systems experimentally.