# synchronization

## Coherence resonance and synchronization of stochastic self-sustained oscillations in the FitzHugh–Nagumo system

In present paper the phenomena of coherence resonance, mutual and external synchronization of noise-induced stochastic oscillations in FitzHugh–Nagumo system are studied by means of numerical and natural experiments. The properties of attractor in the system as well as energy exchange processes are analyzed. Self-sustained character of stochastic oscillations in non-autonomous FitzHugh–Nagumo system justified.

## Dynamics of a network of interacting phase oscillators with dynamic couplings

We investigate dynamical states formed in a network of coupled phase oscillators in which strength of interactions between oscillators evolve dynamically depending on their relative phases. The feature of the system is co-evolution of coupling weights and states of elements. It is ascertained that depending on the parameters the network exhibit several types of behavior: globally synchronized state, two-cluster and multi-cluster states, various synchronized states with a fixed phase relationship between oscillators and desynchronized state.

## Synchronous oscillations of two populations of different species linked via interspecific interference competition

A model for competition of two different species is considered. It is assumed that each consumer specializes on one resource only. The resource uptake rates are held constant.The basic feature of the model is that the dynamics of the resource is much slower than that of the consumer.The two consumers are coupled through direct reciprocal inhibition. Besides, self-limitation of the consumers due to overcrowding is also taken into account. The resources are noninteractive.

## Amazing robert adler. Adler’s tube, Adler’s equation, and more

The article is devoted to Robert Adler, the man who combined activities as theoretical physicist, an experimental physicist and engineer-inventor, the owner of more than 200 patents. Brief biographical information about this remarkable man is presented, and a more detailed presentation of the results of his two famous studies is given, known as Adler’s gated-beam tube and Adler’s equation. For those who are interested in the Adler’s contribution to acoustoelectronics, it is important to read the article Kent J., Fakeuchi M., Laux G.

## The dynamics of two nonlinearly coupled oscillators

In this paper the dynamics of two elastically coupled pendulums is studied. The pendulums oscillate under the influence of external rotational moments, their masses are considered to be equal. The current work is motivated by multiple applications in physics and biology that the model has. Due to the fact that most of the previous studies focused on similar systems of higher order, we believe that the current research can serve as a basis for understanding the functioning of more complex oscillatory ensembles.

## About influence of the changed harmonics on dynamics of self-oscillations in discrete time

The effect arising in discrete time at interaction of self-oscillations with higher harmonics of the main frequency is described. It is shown that it is similar to effect of capture of the frequency (synchronization) of self-oscillations by an external harmonic signal. As the discrete oscillator formally is autonomous system, the effect is classified as self-capture of frequency or self-synchronization. Self-capture is analysed by method of slow-changing amplitudes.

## Rotational dynamics in the system of two coupled pendulums

We consider dynamics in a pair of nonlinearly coupled pendulums. With existence of dissipation and constant torque such system can demonstrate in-phase periodical rotation in addition to the stable state. We have shown in numerical simulations that such in- phase rotation becomes unstable at certain values of coupling strength. In the limit of small dissipation we have created an asymptotic theory that explains instability of the in-phase cycle. Found analytical equations for coupling strength values corresponding to the boundaries of the instability area.

## Multistability in an ensemble of phase oscillators with long-distance couplings

The work is devoted to investigation of multistability of running waves in a ring of periodic oscillators with diffusive non-local couplings. It analyzes the influence of long-range couplings and their change with distance on the stability of spatially-periodic regimes with different wave numbers. The research are carried out by numerical (computer) experiments. The system under study is an ensemble of identical phase oscillators.

## Synchronization of beats in phase-locked loops

Dynamics of two phase-locked loops (PLL) with first order low-pass filters coupled via additional phase discriminator is studied. Mathematical models of the partial systems are pendulum-like type. Thus, mathematical model of the whole system consists of four ordinary differential equations. Phase space of the model is a cylindrical with two cyclic variables. In a case of low-inertial control loops the model transforms into dynamical system with toroidal phase space. The observed model has a great variety of dynamical modes both regular and chaotic.

## Synchronization in kuramoto–sakaguchi ensembles with competing influence of common noise and global coupling

We study the effects of synchronization and desynchronization in ensembles of phase oscillators with the global Kuramoto–Sakaguchi coupling under common noise driving. Since the mechanisms of synchronization by coupling and by common noise are essentially different, their interplay is of interest. In the thermodynamic limit of large number of oscillators, employing the Ott–Antonsen approach, we derive stochastic equations for the order parameters and consider their dynamics for two cases: (i) identical oscillators and (ii) small natural frequency mismatch.