Delayed-feedback chimera states: Forced multiclusters and stochastic resonance

A nonlinear oscillator model with negative time-delayed feedback is studied numeri- cally under external deterministic and stochastic forcing. It is found that in the unforced system complex partial synchronization patterns like chimera states as well as salt-and-pepper like soli- tary states arise on the route from regular dynamics to spatio-temporal chaos. The control of the dynamics by external periodic forcing is demonstrated by numerical simulations. It is shown that one-cluster and multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. If a stochastic component is superimposed to the determin- istic external forcing, chimera states can be induced in a way similar to stochastic resonance, they appear, therefore, in regimes where they do not exist without noise.Comment: 6 pages of paper with references + tex style file + 5 figure

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

Euler potentials for the MHD Kamchatnov-Hopf soliton solution

In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invariant of the mapping of a 3D sphere into a 2D sphere; it can have arbitrary helicity depending on control parameters. It is shown how to define Euler potentials globally. The singular curve of the Euler potential plays the key role in computing helicity. With the introduction of Euler potentials, the helicity can be calculated as an integral over the surface bounded by this singular curve. A special programme for visualization is worked out. Helicity coordinates are introduced which can be useful for numerical simulations where helicity control is needed.Comment: 15 pages, 12 figure