Dynamical investigation and FPGA implementation of a new Heartbeat model based on the Barrio-Varea-Aragon-Maini oscillator

Abstract

This paper is devoted to the investigation of the nonlinear dynamics of a heartbeat model. The model is based on three coupled nonlinear autonomous oscillators representing the three automatism centres of the physical heart; each of these automatism centres is represented by an autonomous Barrio-Varea-Aragon-Maini (BVAM) oscillator model. Our study includes theoretical and experimental investigations. The theoretical part consists of the analysis of fixed point(s), bifurcations, Hamiltonian energy, hysteretic behaviour and coexisting attractors. The experimental investigation includes the discretization of the mathematical model followed by its synthesis and implementation under the Vivado 2017.4 platform and its simulation and its physical implementation on the Nexys-4 Artix-7 xc7a-100T FPGA trainer board. Two R-2R network digital-to-analog converters are built to visualise the practical results on a digital storage oscilloscope; a perfect correlation is observed between the theoretical, numerical and experimental results.