Dynamics of a Chua-Yang ring network in 8D

A circle of eight identical Chua-Yang oscillators with two-parameter nearest-neighbor coupling is investigated. The dynamics governed by the standard piecewise linear saturated activation function as well as the dynamics governed by tangent hyperbolic as a smooth activation function are considered and compared. In both cases, essential dynamics is restricted to an invariant 2D topological sphere containing all equilibria except the origin. The dynamics on these 2D spheres are the same and also the underlying bifurcation scenarios (two degenerate versus five regular bifurcations) are closely related. Numerical findings obtained by MATCONT, TC-HAT, and GEFRI packages are explained by a posteriori mathematical arguments.