Complex oscillations in the delayed Fitzhugh-Nagumo equation
The paper considers the bifurcations in the FitzHugh-Nagumo system with delayed feedback \[ \begin{aligned} x'(t) & = x(t)-\frac{1}{3}x^{3}(t)+y(t)+J(x(t)-x(t-\tau)),\\ y'(t) & = \varepsilon(a-x(t)),\end{aligned} \] where \(J,a\), and \(\varepsilon\ll 1\) are parameters. A detailed analytical study of the bifurcations of steady states is presented. This includes families of Hopf bifurcations for various values of parameters and time-delay \(\tau\) as well as Bogdanov-Takens condimension-2 bifurcation. Additionally, a numerical bifurcation analysis is given that conjectures a variety of complex oscillations in the system such as regular bursting, chaotic bursting or torus canards.
scientific article; zbMATH DE number 6547871
scientific article