Dynamical properties of the improved FK3V heart cell model

Abstract

The main aim of this paper is to study the evolution of the transmembrane potential on the cardiac cell under different rates and amplitudes of stimulation. For modeling this potential, the modification of the Fenton‐Karma model was applied. It is a phenomenological model with 3 degrees of freedom that corresponds to nondimensional transmembrane potential and gating variables for regulation of inward and outward ion currents that can better reproduce the shape of the transmembrane potential than the original Fenton‐Karma model. The model was newly forced by stimulus with the shape of the half‐sine period. As the main goal of the paper is to show that this model is showing regular as well as irregular motion; periodic and chaotic patterns are detected using bifurcation diagrams, the Fourier spectra, Poincaré sections, and 0‐1 test for chaos.

Detection of embedded dynamics in the Györgyi-Field model

“…The results return values close to either 0 or 1, with 0 corresponding to regular dynamics and 1 to chaotic dynamics. With its easy implementation, evaluation, and wide range of application, using this tool for detecting chaos is becoming more popular in different fields [35][36][37][38] .…”

A fractional-order difference Cournot duopoly game with long memory

“…Figure 2: Firm 1's output bifurcation (blue) and K (red) of system (5.18) with varying ν ∈ (0, 1).The criterion of the 0-1 chaos test[100][101][102][103][104][105][106][107][108][109][110] shows that bounded trajectories in the (p, s)−plane or K ≈ 0 mean system (3.13) is regular, and Brownian-like trajectories in the (p, s)−plane or K ≈ 1 indicate system (3.13) is chaotic. So, system (3.13) is chaotic when ν < 0.4, i.e., when K ≈ 1.…”