Mixed-Mode Oscillations in a Modified Chua’s Circuit

We consider a singularly perturbed system of differential equations of the form εu′=g(u,v,λ), v′=f(u,v,λ), where (u,v)∈R3, 0<ε≪1, and λ is a set of parameters. Such a system describes a modified Chua’s circuit with mixed-mode oscillations (MMOs). MMOs consist of a series of small-amplitude oscillations (canard solutions) and large-amplitude relaxations. In the paper we provide a series of both numerical and analytical analyses of the singularly perturbed system for the modified Chua’s circuit with nonlinear f and g. In particular, we analyze the occurrence of the Farey sequence$\it L^{s}$, where $\it L$ and $\it s$ are the numbers of large and small oscillations, respectively.