Synthesis of memristive one-port circuits with piecewise-smooth characteristics

A generalized approach for the implementation of memristive two-terminal circuits with piesewise-smooth characteristics is proposed on the example of a multifunctional circuit based on a transistor switch. Two versions of the circuit are taken into consideration: an experimental model of the piecewise-smooth memristor (Chua's memristor) and a piecewise-smooth memristive capacitor. Physical experiments are combined with numerical modelling of the discussed circuit models. Thus, it is demonstrated that the considered circuit is a flexible solution for synthesis of a wide range of memristive systems with tuneable characteristics.Comment: 3 pages, 3 figure

Homogenized Models with Memory Effect for Heterogeneous Periodic Media

The homogenization of initial boundary value problems for heat conduction equations with asymptotically degenerate rapidly oscillating periodic coefficients are considered. Such problems model thermal processes in heterogeneous periodic media. Homogenized problems (whose solutions determine approximate asymptotics for solutions of the original problems) are presented. Estimates for the accuracy of the asymptotics and relevant convergence theorem are discussed. The homogenized problems have the form of initial boundary value problems for integro-differential equations in convolutions. The presence of convolutions in models for media is called the memory effect. Statements about the solvability and regularity for the problems and the homogenized problems are proved. These results are optimal even in the case of zero convolutions, when the homogenized problems coincide with the classical heat conduction problems

Stochastic control of spiking activity bump expansion: monotonic and resonant phenomena

We consider spatially localized spiking activity patterns, so-called bumps, in ensembles of bistable spiking oscillators. The bistability consists in the coexistence of self-sustained spiking dynamics and quiescent steady-state regime. We show numerically that the processes of growth or contraction of such patterns can be controlled by varying the intensity of multiplicative noise. In particular, the effect of the noise is monotonic in an ensemble of the coupled Hindmarsh-Rose oscillators. On the other hand, in another model proposed by V. Semenov et al. in 2016 (see Ref. [V. Semenov et al., Phys. Rev. E 93, 052210 (2016)]), a resonant noise effect is observed. In that model, stabilization of the activity bump expansion is achieved at an appropriate noise level, and the noise effect reverses with a further increase in noise intensity. Moreover, we show the constructive role of nonlocal coupling which allows to save domains and fronts being totally destroyed due to the action of noise in the case of local coupling.Comment: 5 pages, 3 figure