Biomedical subjects

V B Kazantsev

Publications and source records attributed to V B Kazantsev.

9 recordsLinked to original sources

PubMed2005

Spiking dynamics of interacting oscillatory neurons.

Spiking sequences emerging from dynamical interaction in a pair of oscillatory neurons are investigated theoretically and experimentally. The model comprises two unidirectionally coupled FitzHugh-Nagumo units with modified excitability (MFHN). The first (master) unit exhibits a periodic spike sequence with a certain frequency. The second (slave) unit is in its excitable mode and responds on the input signal with a complex (chaotic) spike trains. We analyze the dynamic mechanisms underlying different response behavior depending on interaction strength. Spiking phase maps describing the response dynamics are obtained. Complex phase locking and chaotic sequences are investigated. We show how the response spike trains can be effectively controlled by the interaction parameter and discuss the problem of neuronal information encoding.

Algorithms↗

PubMed2004

Self-referential phase reset based on inferior olive oscillator dynamics.

The olivo-cerebellar network is a key neuronal circuit that provides high-level motor control in the vertebrate CNS. Functionally, its network dynamics is organized around the oscillatory membrane potential properties of inferior olive (IO) neurons and their electrotonic connectivity. Because IO action potentials are generated at the peaks of the quasisinusoidal membrane potential oscillations, their temporal firing properties are defined by the IO rhythmicity. Excitatory inputs to these neurons can produce oscillatory phase shifts without modifying the amplitude or frequency of the oscillations, allowing well defined time-shift modulation of action potential generation. Moreover, the resulting phase is defined only by the amplitude and duration of the reset stimulus and is independent of the original oscillatory phase when the stimulus was delivered. This reset property, henceforth referred to as selfreferential phase reset, results in the generation of organized clusters of electrically coupled cells that oscillate in phase and are controlled by inhibitory feedback loops through the cerebellar nuclei and the cerebellar cortex. These clusters provide a dynamical representation of arbitrary motor intention patterns that are further mapped to the motor execution system. Being supplied with sensory inputs, the olivo-cerebellar network is capable of rearranging the clusters during the process of movement execution. Accordingly, the phase of the IO oscillators can be rapidly reset to a desired phase independently of the history of phase evolution. The goal of this article is to show how this selfreferential phase reset may be implemented into a motor control system by using a biologically based mathematical model.

Action Potentials↗

PubMed2004

Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons.

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.

Action Potentials↗

PubMed2003

Olivo-cerebellar cluster-based universal control system.

The olivo-cerebellar network plays a key role in the organization of vertebrate motor control. The oscillatory properties of inferior olive (IO) neurons have been shown to provide timing signals for motor coordination in which spatio-temporal coherent oscillatory neuronal clusters control movement dynamics. Based on the neuronal connectivity and electrophysiology of the olivo-cerebellar network we have developed a general-purpose control approach, which we refer to as a universal control system (UCS), capable of dealing with a large number of actuator parameters in real time. In this UCS, the imposed goal and the resultant feedback from the actuators specify system properties. The goal is realized through implementing an architecture that can regulate a large number of parameters simultaneously by providing stimuli-modulated spatio-temporal cluster dynamics.

Animals↗

PubMed2003

Spiking patterns emerging from wave instabilities in a one-dimensional neural lattice.

The dynamics of a one-dimensional lattice (chain) of electrically coupled neurons modeled by the FitzHugh-Nagumo excitable system with modified nonlinearity is investigated. We have found that for certain conditions the lattice exhibits a countable set of pulselike wave solutions. The analysis of homoclinic and heteroclinic bifurcations is given. Corresponding bifurcation sets have the shapes of spirals twisting to the same center. The appearance of chaotic spiking patterns emerging from wave instabilities is discussed.

Journal Article↗

PubMed2001

Selective communication and information processing by excitable systems.

The phenomena of selective response of an excitable system to external pulse stimulation relating to interneuron communication and information processing problems are discussed. Subthreshold dynamics of the FitzHugh-Nagumo-like excitable system modeling of a neuron with the synaptic input is investigated. It is shown that the system response on various incoming information messages can be described by one- and two-dimensional linear and nonlinear point maps. Nonlinear integrating and resonant properties of the system are analyzed.

Journal Article↗

PubMed2001

Theoretical and experimental study of two discrete coupled Nagumo chains.

We analyze front wave (kink and antikink) propagation and pattern formation in a system composed of two coupled discrete Nagumo chains using analytical and numerical methods. In the case of homogeneous interaction among the chains, we show the possibility of the effective control on wave propagation. In addition, physical experiments on electrical chains confirm all theoretical behaviors.

Journal Article↗

PubMed2000

Synchronization, re-entry, and failure of spiral waves in a two-layer discrete excitable system.

A three-dimensional structure composed of two coupled discrete excitable lattices is considered. Each lattice (layer) is a discrete excitable subsystem and using a local model of excitation transfer and failure we have estimated the sufficient conditions for it to exhibit spiral waves. Then we show how interlayer synchronization of all motions is possible. Various effects of spiral wave synchronization, re-entry and failure are also investigated.

Journal Article↗

PubMed1997

The emergence of form by replication.

It is shown with a simple mathematical model that if a system exhibits a given form (a spatial structure) and is put in contact with another system of the same type but in a state of spatial disorder, then under certain conditions their mutual interaction as they evolve in time allows replication of form in the disordered system with a controllable degree of faithfulness.

Biological Evolution↗