No abstract

We consider a singularly perturbed system of differential equations of the form u = g (u, v, λ), v = f (u, v, λ), where (u, v) ∈ R 3 , 0 < 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 L s , where L and s are the numbers of large and small oscillations, respectively.

No abstract

Two dual memristive circuits are presented, the steady-state responses of which are periodic sequences of mixed-mode oscillations (MMOs) of type L 1 S1 L 2 S2 …L n sn where L k and s k are integers for k = 1, 2, …n. The L k and s k are the numbers of large-and small-amplitude oscillations, or LAOs and SAOs, respectively. This new feature of memristive circuits is illustrated through several MMO responses, all with the pinched hysteresis characteristics for both LAOs and SAOs. The mode-locking phenomenon for MMOs is also discussed. The MMO sequences depend on initial conditions and parameters of the circuits.

No abstract