Timing control by redundant inhibitory neuronal circuits.

Rhythms and timing control of sequential activity in the brain is fundamental to cognition and behavior. Although experimental and theoretical studies support the understanding that neuronal circuits are intrinsically capable of generating different time intervals, the dynamical origin of the phenomenon of functionally dependent timing control is still unclear. Here, we consider a new mechanism that is related to the multi-neuronal cooperative dynamics in inhibitory brain motifs consisting of a few clusters. It is shown that redundancy and diversity of neurons within each cluster enhances the sensitivity of the timing control with the level of neuronal excitation of the whole network. The generality of the mechanism is shown to work on two different neuronal models: a conductance-based model and a map-based model.

Effect of synaptic connectivity on long-range synchronization of fast cortical oscillations.

Cortical gamma oscillations in the 20- to 80-Hz range are associated with attentiveness and sensory perception and have strong connections to both cognitive processing and temporal binding of sensory stimuli. These gamma oscillations become synchronized within a few milliseconds over distances spanning a few millimeters in spite of synaptic delays. In this study using in vivo recordings and large-scale cortical network models, we reveal a critical role played by the network geometry in achieving precise long-range synchronization in the gamma frequency band. Our results indicate that the presence of many independent synaptic pathways in a two-dimensional network facilitate precise phase synchronization of fast gamma band oscillations with nearly zero phase delays between remote network sites. These findings predict a common mechanism of precise oscillatory synchronization in neuronal networks.

Synchronization and beam forming in an array of repulsively coupled oscillators.

We study the dynamics of an array of Stuart-Landau oscillators with repulsive coupling. Autonomous network with global repulsive coupling settles on one from a continuum of synchronized regimes characterized by zero mean field. Driving this array by an external oscillatory signal produces a nonzero mean field that follows the driving signal even when the oscillators are not locked to the external signal. At sufficiently large amplitude the external signal synchronizes the oscillators and locks the phases of the array oscillations. Application of this system as a beam-forming element of a phase array antenna is considered. The phase dynamics of the oscillator array synchronization is used to reshape the phases of signals received from the phase array antenna and improve its beam pattern characteristics.

Spread spectrum communication system with chaotic frequency modulation.

A new spread spectrum communication system utilizing chaotic frequency modulation of sinusoidal signals is discussed. A single phase lock loop (PLL) system in the receiver is used both to synchronize the local chaotic oscillator and to recover the information signal. We study the dynamics of the synchronization process, stability of the PLL system, and evaluate the bit-error-rate performance of this chaos-based communication system.

Repulsive synchronization in an array of phase oscillators.

We study the dynamics of a repulsively coupled array of phase oscillators. For an array of globally coupled identical oscillators, repulsive coupling results in a family of synchronized regimes characterized by zero mean field. If the number of oscillators is sufficiently large, phase locking among oscillators is destroyed, independently of the coupling strength, when the oscillators' natural frequencies are not the same. In locally coupled networks, however, phase locking occurs even for nonidentical oscillators when the coupling strength is sufficiently strong.

Oscillations in large-scale cortical networks: map-based model.

We develop a new computationally efficient approach for the analysis of complex large-scale neurobiological networks. Its key element is the use of a new phenomenological model of a neuron capable of replicating important spike pattern characteristics and designed in the form of a system of difference equations (a map). We developed a set of map-based models that replicate spiking activity of cortical fast spiking, regular spiking and intrinsically bursting neurons. Interconnected with synaptic currents these model neurons demonstrated responses very similar to those found with Hodgkin-Huxley models and in experiments. We illustrate the efficacy of this approach in simulations of one- and two-dimensional cortical network models consisting of regular spiking neurons and fast spiking interneurons to model sleep and activated states of the thalamocortical system. Our study suggests that map-based models can be widely used for large-scale simulations and that such models are especially useful for tasks where the modeling of specific firing patterns of different cell classes is important.

Multimodal synchronization of chaos.

An elementary notion of master-slave synchronization that accepts multimodal synchronization is introduced. We prove rigorously that the attractor of a coupled pair in a regime of multimodal synchronization is the graph of a multivalued function. Our framework provides the theoretical basis for some practical tools for detection of multimodal synchrony in experiments. Results are illustrated with the analysis of experiments with coupled electronic oscillators.

Generalized synchronization of chaos in noninvertible maps.

The properties of functional relation between a noninvertible chaotic drive and a response map in the regime of generalized synchronization of chaos are studied. It is shown that despite a very fuzzy image of the relation between the current states of the maps, the functional relation becomes apparent when a sufficient interval of driving trajectory is taken into account. This paper develops a theoretical framework of such functional relation and illustrates the main theoretical conclusions using numerical simulations.

Chaotic free-space laser communication over a turbulent channel.

The dynamics of errors caused by atmospheric turbulence in a self-synchronizing chaos-based communication system that stably transmits information over an approximately 5 km free-space laser link is studied experimentally. Binary information is transmitted using a chaotic sequence of short-term pulses as a carrier. The information signal slightly shifts the chaotic time position of each pulse depending on the information bit. We report the results of an experimental analysis of the atmospheric turbulence in the channel and the impact of turbulence on the bit-error-rate performance of this chaos-based communication system.

Multivalued mappings in generalized chaos synchronization.

The onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system. A recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single-valued function. In this paper, we explore generalized synchronization in a regime where the synchronization mapping can become a multivalued function. Specifically, we study the properties of the multivalued mapping that occurs between the drive and response systems when the systems are synchronized with a frequency ratio other than one-to-one, and address the issues of the existence and continuity of such mappings. The basic theoretical framework underlying the considered synchronization regimes is then developed.

Subharmonic destruction of generalized chaos synchronization.

A bifurcation of transition that destroys generalized chaos synchronization is considered. This transition frequently occurs in regimes of subharmonic chaos entrainment where synchronization can be abruptly terminated due only to an almost unnoticeable change in the shape of the driving attractor. We explore the main cause of this sensitivity and ascertain the mechanism behind this transition.

Regularization of synchronized chaotic bursts.

The onset of regular bursts in a group of irregularly bursting neurons with different individual properties is one of the most interesting dynamical properties found in neurobiological systems. In this paper we show how synchronization among chaotically bursting cells can lead to the onset of regular bursting. In order to clearly present the mechanism behind such regularization we model the individual dynamics of each cell with a simple two-dimensional map that produces chaotic bursting behavior similar to biological neurons.

Synchronized action of synaptically coupled chaotic model neurons.

Experimental observations of the intracellular recorded electrical activity in individual neurons show that the temporal behavior is often chaotic. We discuss both our own observations on a cell from the stomatogastric central pattern generator of lobster and earlier observations in other cells. In this paper we work with models with chaotic neurons, building on models by Hindmarsh and Rose for bursting, spiking activity in neurons. The key feature of these simplified models of neurons is the presence of coupled slow and fast subsystems. We analyze the model neurons using the same tools employed in the analysis of our experimental data. We couple two model neurons both electrotonically and electrochemically in inhibitory and excitatory fashions. In each of these cases, we demonstrate that the model neurons can synchronize in phase and out of phase depending on the strength of the coupling. For normal synaptic coupling, we have a time delay between the action of one neuron and the response of the other. We also analyze how the synchronization depends on this delay. A rich spectrum of synchronized behaviors is possible for electrically coupled neurons and for inhibitory coupling between neurons. In synchronous neurons one typically sees chaotic motion of the coupled neurons. Excitatory coupling produces essentially periodic voltage trajectories, which are also synchronized. We display and discuss these synchronized behaviors using two "distance" measures of the synchronization.