On the dynamics of an electronic circuit in moderate dimensions

We consider the cyclic system of differential equations \begin{equation}\label{syst} {\dot x}_n = - x_n + \alpha \sigma(x_{n-1}) + \beta \sigma(x_{n+1}),\quad n = 1,2,\dots,N \end{equation} with parameters in $$ {\cal R} = \left\{ (\alpha,\beta) \in {\mathbb R}^2 | \alpha > 0 \mbox{ and } \beta \in (0,\alpha] \right\} $$ and the saturated, piecewise linear sigmoid nonlinearity \begin{equation}\label{sigmoid}%{nonlin} \sigma(x) = \frac{1}{2}(|x+1| - |x-1|) \mbox{ for each } x \in {\mathbb R} \end{equation} modeling a Chua--Yang ring of $N$ electrical oscillators with two--sided nearest neighbor couplings.
Comments on periodic and heteroclinic orbits are made. Numerical aspects are not trivial, too. Equilibrium patterns are discussed by using generalized Fibonacci--Lucas polynomials.
This is ongoing joint work with Mikl\'os Koller