Synchronization transitions and sensitivity to asymmetry in the bimodal Kuramoto systems with Cauchy noise.

We analyze the synchronization dynamics of the thermodynamically large systems of globally coupled phase oscillators under Cauchy noise forcings with a bimodal distribution of frequencies and asymmetry between two distribution components. The systems with the Cauchy noise admit the application of the Ott-Antonsen ansatz, which has allowed us to study analytically synchronization transitions both in the symmetric and asymmetric cases. The dynamics and the transitions between various synchronous and asynchronous regimes are shown to be very sensitive to the asymmetry degree, whereas the scenario of the symmetry breaking is universal and does not depend on the particular way to introduce asymmetry, be it the unequal populations of modes in a bimodal distribution, the phase delay of the Kuramoto-Sakaguchi model, the different values of the coupling constants, or the unequal noise levels in two modes. In particular, we found that even small asymmetry may stabilize the stationary partially synchronized state, and this may happen even for an arbitrarily large frequency difference between two distribution modes (oscillator subgroups). This effect also results in the new type of bistability between two stationary partially synchronized states: one with a large level of global synchronization and synchronization parity between two subgroups and another with lower synchronization where the one subgroup is dominant, having a higher internal (subgroup) synchronization level and enforcing its oscillation frequency on the second subgroup. For the four asymmetry types, the critical values of asymmetry parameters were found analytically above which the bistability between incoherent and partially synchronized states is no longer possible.

Effect of Mechanical Stretching of the Right Atrium of Isolated Rat Heart on Dispersion of Repolarization before Fibrillation.

The multi-electrode mapping method was used to analyze electrical activity of isolated rat heart under conditions of standard perfusion, pharmacological stimulation of fibrillation, and mechanical stretching of the right atrium both under normal conditions and before cardiac fibrillation. It was shown that stretching of the right atrium prevented the increase of repolarization dispersion and latency of the electrical signal in the myocardium that were observed before cardiac fibrillation.

Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control.

We report the emergence of coexisting synchronous and asynchronous subpopulations of oscillators in one dimensional arrays of identical oscillators by applying a self-feedback control. When a self-feedback is applied to a subpopulation of the array, similar to chimera states, it splits into two/more sub-subpopulations coexisting in coherent and incoherent states for a range of self-feedback strength. By tuning the coupling between the nearest neighbors and the amount of self-feedback in the perturbed subpopulation, the size of the coherent and the incoherent sub-subpopulations in the array can be controlled, although the exact size of them is unpredictable. We present numerical evidence using the Landau-Stuart system and the Kuramoto-Sakaguchi phase model.

Transient and periodic spatiotemporal structures in a reaction-diffusion-mechanics system.

We study transient spatiotemporal structures induced by a weak space-time localized stimulus in an excitable contractile fiber within a two-component globally coupled reaction-diffusion model. The model which we develop allows us to analyze various regimes of excitation spreading and determine origin of the induced structures for various contraction types (defined by the fiber fixation) and global coupling strengths. One of the most notable effects we observed is the after-excitation effect. It leads to emergence of multiple excitation pulses excited by a single external stimulus and can result in long-lasting transient activity and appearance of new oscillatory attractor regimes, including the ones with multiple phase clusters.

Multistability of synchronous regimes in rotator ensembles.

We study collective dynamics in rotator ensembles and focus on the multistability of synchronous regimes in a chain of coupled rotators. We provide a detailed analysis of the number of coexisting regimes and estimate in particular, the synchronization boundary for different types of individual frequency distribution. The number of wave-based regimes coexisting for the same parameters and its dependence on the chain length are estimated. We give an analytical estimation for the synchronization frequency of the in-phase regime for a uniform individual frequency distribution.

Disorder fosters chimera in an array of motile particles.

We consider an array of nonlocally coupled oscillators on a ring, which for equally spaced units possesses a Kuramoto-Battogtokh chimera regime and a synchronous state. We demonstrate that disorder in oscillators positions leads to a transition from the synchronous to the chimera state. For a static (quenched) disorder we find that the probability of synchrony survival depends on the number of particles, from nearly zero at small populations to one in the thermodynamic limit. Furthermore, we demonstrate how the synchrony gets destroyed for randomly (ballistically or diffusively) moving oscillators. We show that, depending on the number of oscillators, there are different scalings of the transition time with this number and the velocity of the units.

Adaptive functional systems: learning with chaos.

We propose a new model of adaptive behavior that combines a winnerless competition principle and chaos to learn new functional systems. The model consists of a complex network of nonlinear dynamical elements producing sequences of goal-directed actions. Each element describes dynamics and activity of the functional system which is supposed to be a distributed set of interacting physiological elements such as nerve or muscle that cooperates to obtain certain goal at the level of the whole organism. During "normal" behavior, the dynamics of the system follows heteroclinic channels, but in the novel situation chaotic search is activated and a new channel leading to the target state is gradually created simulating the process of learning. The model was tested in single and multigoal environments and had demonstrated a good potential for generation of new adaptations.

Influence of passive elements on the dynamics of oscillatory ensembles of cardiac cells.

In this paper we focus on the influence of passive elements on the collective dynamics of oscillatory ensembles. Two major effects considered are (i) the influence of passive elements on the synchronization properties of ensembles of coupled nonidentical oscillators and (ii) the influence of passive elements on the wave dynamics of such systems. For the first effect, it is demonstrated that the introduction of passive elements may lead to both an increase or decrease in the global synchronization threshold. For the second effect, it is also demonstrated that the steady state of the passive element is a key parameter which defines how this passive element affects the wave dynamics of the oscillatory ensemble. It was shown that for different values of this parameter, one can observe increase or decrease in wave propagation velocity and increase or decrease in synchronization frequency in oscillatory ensembles with the growth of influence of passive elements. The results are obtained for the models of cardiac cells dynamics as well as for the Bonhoeffer-Van der Pol model and are compared with data of real biological experiments.

Numerical studies of slow rhythms emergence in neural microcircuits: bifurcations and stability.

There is a growing body of evidence that slow brain rhythms are generated by simple inhibitory neural networks. Sequential switching of tonic spiking activity is a widespread phenomenon underlying such rhythms. A realistic generative model explaining such reproducible switching is a dynamical system that employs a closed stable heteroclinic channel (SHC) in its phase space. Despite strong evidence on the existence of SHC, the conditions on its emergence in a spiking network are unclear. In this paper, we analyze a minimal, reciprocally connected circuit of three spiking units and explore all possible dynamical regimes and transitions between them. We show that the SHC arises due to a Neimark-Sacker bifurcation of an unstable cycle.

Variety of synchronous regimes in neuronal ensembles.

We consider a Hodgkin-Huxley-type model of oscillatory activity in neurons of the snail Helix pomatia. This model has a distinctive feature: It demonstrates multistability in oscillatory and silent modes that is typical for the thalamocortical neurons. A single neuron cell can demonstrate a variety of oscillatory activity: Regular and chaotic spiking and bursting behavior. We study collective phenomena in small and large arrays of nonidentical cells coupled by models of electrical and chemical synapses. Two single elements coupled by electrical coupling show different types of synchronous behavior, in particular in-phase and antiphase synchronous regimes. In an ensemble of three inhibitory synaptically coupled elements, the phenomenon of sequential synchronous dynamics is observed. We study the synchronization phenomena in the chain of nonidentical neurons at different oscillatory behavior coupled with electrical and chemical synapses. Various regimes of phase synchronization are observed: (i) Synchronous regular and chaotic spiking; (ii) synchronous regular and chaotic bursting; and (iii) synchronous regular and chaotic bursting with different numbers of spikes inside the bursts. We detect and study the effect of collective synchronous burst generation due to the cluster formation and the oscillatory death.

Synchronization phenomena in mixed media of passive, excitable, and oscillatory cells.

We study collective phenomena in highly heterogeneous cardiac cell culture and its models. A cardiac culture is a mixture of passive (fibroblasts), oscillatory (pacemakers), and excitable (myocytes) cells. There is also heterogeneity within each type of cell as well. Results of in vitro experiments are modelled by Luo-Rudy and FitzHugh-Nagumo systems. For oscillatory and excitable media, we focus on the transitions from fully incoherent behavior to partially coherent behavior and then to global synchronization as the coupling strength is increased. These regimes are characterized qualitatively by spatiotemporal diagrams and quantitatively by profiles of dependence of individual frequencies on coupling. We find that synchronization clusters are determined by concentric and spiral waves. These waves arising due to the heterogeneity of medium push covered cells to oscillate in synchrony. We are also interested in the influence of passive and excitable elements on the oscillatory characteristics of low- and high-dimensional ensembles of cardiac cells. The mixture of initially silent excitable and passive cells shows the transitions to oscillatory behavior. In the media of oscillatory and passive or excitable cells, the effect of oscillation death is observed.

Marginal chimera state at cross-frequency locking of pulse-coupled neural networks.

We consider two coupled populations of leaky integrate-and-fire neurons. Depending on the coupling strength, mean fields generated by these populations can have incommensurate frequencies or become frequency locked. In the observed 2:1 locking state of the mean fields, individual neurons in one population are asynchronous with the mean fields, while in another population they have the same frequency as the mean field. These synchronous neurons form a chimera state, where part of them build a fully synchronized cluster, while other remain scattered. We explain this chimera as a marginal one, caused by a self-organized neutral dynamics of the effective circle map.

Suppressing arrhythmias in cardiac models using overdrive pacing and calcium channel blockers.

Recent findings indicate that ventricular fibrillation might arise from spiral wave chaos. Our objective in this computational study was to investigate wave interactions in excitable media and to explore the feasibility of using overdrive pacing to suppress spiral wave chaos. This work is based on the finding that in excitable media, propagating waves with the highest excitation frequency eventually overtake all other waves. We analyzed the effects of low-amplitude, high-frequency pacing in one-dimensional and two-dimensional networks of coupled, excitable cells governed by the Luo-Rudy model. In the one-dimensional cardiac model, we found narrow high-frequency regions of 1:1 synchronization between the input stimulus and the system's response. The frequencies in this region were higher than the intrinsic spiral wave frequency of cardiac tissue. When we paced the two-dimensional cardiac model with frequencies from this region, we found that spiral wave chaos could, in some cases, be suppressed. When we coupled the overdrive pacing with calcium channel blockers, we found that spiral wave chaos could be suppressed in all cases. These findings suggest that low-amplitude, high-frequency overdrive pacing, in combination with calcium channel inhibitors (e.g., class II or class IV antiarrhythmic drugs), may be useful for eliminating fibrillation. (c) 2002 American Institute of Physics.

[Methodological bases for designing multipurpose laboratories]. / O metodologicheskikh osnovakh proektirovaniia komplektnykh laboratorii.

A well-grounded selection of the necessary minimum of measuring facilities is of paramount importance in projecting multipurpose laboratories. These facilities should ensure the required accuracy of analyses to be carried out, and measurements covering the whole dynamic range of the values variations. It was suggested to organise new multipurpose laboratories in accordance with technical and economical reasoning and with the calculated generalized index which shows a compliance of technical characteristics of the measuring equipment chosen with the methodical demands.

Interaction-based transition from passivity to excitability.

In this paper we study the process of transition from passive to excitable behavior due to interaction between nonlinear dynamical systems. We show that under certain conditions a passive unit may demonstrate qualitatively new excitable dynamics. We study the properties of an excitable medium constructed on the basis of the proposed transition. The effects are demonstrated with the realistic Luo-Rudy model. Application to the cardiac dynamics and functioning is discussed. The qualitative analytic and numerical description is also given for the phenomenological FitzHugh-Nagumo system.

Heteroclinic contours in oscillatory ensembles.

In this work, we study the onset of sequential activity in ensembles of neuronlike oscillators with inhibitorylike coupling between them. The winnerless competition (WLC) principle is a dynamical concept underlying sequential activity generation. According to the WLC principle, stable heteroclinic sequences in the phase space of a network model represent sequential metastable dynamics. We show that stable heteroclinic sequences and stable heteroclinic channels, connecting saddle limit cycles, can appear in oscillatory models of neural activity. We find the key bifurcations which lead to the occurrence of sequential activity as well as heteroclinic sequences and channels.

Distant synchronization through a passive medium.

This paper deals with the phenomenon of synchronization of oscillatory ensembles interacting distantly through the passive medium. Main characteristics of such a kind of synchronization are studied. The results of this work can be applied to describe the synchronization of cardiac oscillatory cells separated by the passive fibroblasts. In this work the phenomenological models (Bonhoeffer-Van der Pol) of cardiac cells as well as biologically relevant (Luo-Rudy, Sachse) models are used. We also propose equivalent model of distant synchronization and derive on its basis an analytical scaling of the frequency of synchronous oscillations.

Cluster synchronization and spatio-temporal dynamics in networks of oscillatory and excitable Luo-Rudy cells.

We study collective phenomena in nonhomogeneous cardiac cell culture models, including one- and two-dimensional lattices of oscillatory cells and mixtures of oscillatory and excitable cells. Individual cell dynamics is described by a modified Luo-Rudy model with depolarizing current. We focus on the transition from incoherent behavior to global synchronization via cluster synchronization regimes as coupling strength is increased. These regimes are characterized qualitatively by space-time plots and quantitatively by profiles of local frequencies and distributions of cluster sizes in dependence upon coupling strength. We describe spatio-temporal patterns arising during this transition, including pacemakers, spiral waves, and complicated irregular activity.

Using weak impulses to suppress traveling waves in excitable media.

Here we propose mechanisms for suppressing non-steady-state motions--propagating pulses, spiral waves, spiral-wave chaos--in excitable media. Our approach is based on two points: (1) excitable media are multistable; and (2) traveling waves in excitable media can be separated into fast and slow motions, which can be considered independently. We show that weak impulses can be used to change the values of the slow variable at the front and back of a traveling wave, which leads to wave front and wave back velocities that are different from each other. This effect can destabilize the traveling wave, resulting in a transition to the rest state.

Coherence resonance in excitable and oscillatory systems: the essential role of slow and fast dynamics.

Stochastic noise of an appropriate amplitude can maximize the coherence of the dynamics of certain types of excitable systems via a phenomenon known as coherence resonance (CR). In this paper we demonstrate, using a simple excitable system, the mechanism underlying the generation of CR. Using analytical expressions for the spectral density of the system's dynamics, we show that CR relies on the coexistence of fast and slow motions. We also show that the same mechanism of CR holds in the oscillatory regime, and we examine how CR depends on both the excitability of the system and the nonuniformity of the motion.