Experimental switching between coexisting attractors in the yoke-bell-clapper system.

This paper presents experimental switching between two attractors in the swinging bell. In the considered yoke-bell-clapper system, two coexisting solutions appear. In the first one, we observe a single impact between the bell and the clapper per one period of motion, and in the second solution, no impacts occur-no sound is produced.

Review of sample-based methods used in an analysis of multistable dynamical systems.

Sample-based methods are a useful tool in analyzing the global behavior of multi-stable systems originating from various branches of science. Classical methods, such as bifurcation diagrams, Lyapunov exponents, and basins of attraction, often fail to analyze complex systems with many coexisting attractors. Thus, we have to apply a different strategy to understand the dynamics of such systems.

Dynamical response of a rocking rigid block.

This paper investigates the complex dynamical behavior of a rigid block structure under harmonic ground excitation, thereby mimicking, for instance, the oscillation of the system under seismic excitation or containers placed on a ship under periodic acting of sea waves. The equations of motion are derived, assuming a large frictional coefficient at the interface between the block and the ground, in such a way that sliding cannot occur. In addition, the mathematical model assumes a loss of kinetic energy when an impact with the ground takes place.

Time dependent stability margin in multistable systems.

We propose a novel technique to analyze multistable, non-linear dynamical systems. It enables one to characterize the evolution of a time-dependent stability margin along stable periodic orbits. By that, we are able to indicate the moments along the trajectory when the stability surplus is minimal, and even relatively small perturbation can lead to a tipping point.

Erratum: Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method.

A correction to this article has been published and is linked from the HTML version of this paper. The error has been fixed in the paper.

Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method.

In this paper we show the first broad experimental confirmation of the basin stability approach. The basin stability is one of the sample-based approach methods for analysis of the complex, multidimensional dynamical systems. We show that investigated method is a reliable tool for the analysis of dynamical systems and we prove that it has a significant advantages which make it appropriate for many applications in which classical analysis methods are difficult to apply.

Experimental multistable states for small network of coupled pendula.

Chimera states are dynamical patterns emerging in populations of coupled identical oscillators where different groups of oscillators exhibit coexisting synchronous and incoherent behaviors despite homogeneous coupling. Although these states are typically observed in the large ensembles of oscillators, recently it has been shown that so-called weak chimera states may occur in the systems with small numbers of oscillators. Here, we show that similar multistable states demonstrating partial frequency synchronization, can be observed in simple experiments with identical mechanical oscillators, namely pendula.

Experimental observation of three-frequency quasiperiodic solution in a ring of unidirectionally coupled oscillators.

The subject of the experimental research supported with numerical simulations presented in this paper is an analog electrical circuit representing the ring of unidirectionally coupled single-well Duffing oscillators. The research is concentrated on the existence of the stable three-frequency quasiperiodic attractor in this system. It is shown that such solution can be robustly stable in a wide range of parameters of the system under consideration in spite of a parameter mismatch which is unavoidable during experiment.

Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems.

We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with several next neighbors. We derive an amplitude equation of Ginzburg-Landau type, which describes the destabilization of a uniform stationary state and close-by solutions in the limit of a large number of nodes.

Detection, characterization and biological activities of [bisphospho-thr3,9]ODN, an endogenous molecular form of ODN released by astrocytes.

Astrocytes synthesize and release endozepines, a family of regulatory neuropeptides, including diazepam-binding inhibitor (DBI) and its processing fragments such as the octadecaneuropeptide (ODN). At the molecular level, ODN interacts with two types of receptors, i.e.

Synchronization extends the life time of the desired behavior of globally coupled systems.

Synchronization occurs widely in natural and technological world, but it has not been widely used to extend the life time of the desirable behavior of the coupled systems. Here we consider the globally coupled system consisting of n units and show that the initial synchronous state extends the lifetime of desired behavior of the coupled system in the case when the excitation of one or few units is suddenly (breakdown of energy supply) or gradually (as the effect of aging and fatigue) switched off. We give evidence that for the properly chosen coupling the energy transfer from the excited units allows unexcited units to operate in the desired manner.

Variability of spatio-temporal patterns in non-homogeneous rings of spiking neurons.

We show that a ring of unidirectionally delay-coupled spiking neurons may possess a multitude of stable spiking patterns and provide a constructive algorithm for generating a desired spiking pattern. More specifically, for a given time-periodic pattern, in which each neuron fires once within the pattern period at a predefined time moment, we provide the coupling delays and/or coupling strengths leading to this particular pattern. The considered homogeneous networks demonstrate a great multistability of various travelling time- and space-periodic waves which can propagate either along the direction of coupling or in opposite direction.

Why two clocks synchronize: energy balance of the synchronized clocks.

We consider the synchronization of two clocks which are accurate (show the same time) but have pendulums with different masses. We show that such clocks hanging on the same beam beside the complete (in-phase) and antiphase synchronizations perform the third type of synchronization in which the difference of the pendulums' displacements is a periodic function of time. We identify this period to be a few times larger than the period of pendulums' oscillations in the case when the beam is at rest.

Periodic patterns in a ring of delay-coupled oscillators.

We describe the appearance and stability of spatiotemporal periodic patterns (rotating waves) in unidirectional rings of coupled oscillators with delayed couplings. We show how delays in the coupling lead to the splitting of each rotating wave into several new ones. The appearance of rotating waves is mediated by the Hopf bifurcations of the symmetric equilibrium.

Routes to complex dynamics in a ring of unidirectionally coupled systems.

We study the dynamics of a ring of unidirectionally coupled autonomous Duffing oscillators. Starting from a situation where the individual oscillator without coupling has only trivial equilibrium dynamics, the coupling induces complicated transitions to periodic, quasiperiodic, chaotic, and hyperchaotic behavior. We study these transitions in detail for small and large numbers of oscillators.

Delay and periodicity.

Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic solutions. In particular, we show that delay systems generically have families of periodic solutions, which are reappearing for infinitely many delay times.

Experimental observation of ragged synchronizability.

Synchronization thresholds of an array of nondiagonally coupled oscillators are investigated. We present experimental results which show the existence of ragged synchronizability, i.e.

Comment on "synchronization in a ring of four mutually coupled van der Pol oscillators: theory and experiment".

We have verified some results of Nana and Woafo [Phys. Rev. E 74, 046213 (2006)] in the area of the complete synchronization.

Ragged synchronizability of coupled oscillators.

We discuss synchronization thresholds in an array of nondiagonally coupled oscillators. We argue that nondiagonal coupling can cause the appearance or disappearance of desynchronous windows in the coupling parameter space. Such a phenomenon is independent of the motion character (periodic or chaotic) of the isolated node system.