0000000000471665

AUTHOR

V. B. Kazantsev

showing 3 related works from this author

Experimental study of electrical FitzHugh-Nagumo neurons with modified excitability

2006

International audience; We present an electronical circuit modelling a FitzHugh-Nagumo neuron with a modified excitability. To characterize this basic cell, the bifurcation curves between stability with excitation threshold, bistability and oscillations are investigated. An electrical circuit is then proposed to realize a unidirectional coupling between two cells, mimicking an inter-neuron synaptic coupling. In such a master-slave configuration, we show experimentally how the coupling strength controls the dynamics of the slave neuron, leading to frequency locking, chaotic behavior and synchronization. These phenomena are then studied by phase map analysis. The architecture of a possible ne…

BistabilityComputer scienceCognitive NeuroscienceModels Neurological[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ NLIN.NLIN-CD ] Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]ChaoticPhase mapAction PotentialsSynchronizationTopologyElectronic neuronsSynaptic Transmission01 natural sciencesSynchronization010305 fluids & plasmaslaw.inventionBiological ClocksArtificial IntelligencelawControl theoryOscillometry0103 physical sciencesmedicineAnimals010306 general physicsElectronic circuitNeuronsArtificial neural networkQuantitative Biology::Neurons and Cognition[SCCO.NEUR]Cognitive science/Neuroscience[SPI.TRON]Engineering Sciences [physics]/Electronics[ SPI.TRON ] Engineering Sciences [physics]/ElectronicsCoupling (electronics)medicine.anatomical_structureNonlinear DynamicsElectrical network[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD][ SCCO.NEUR ] Cognitive science/NeuroscienceChaosBifurcationSynaptic couplingNeural Networks ComputerNeuron
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PROPAGATING INTERFACES IN A TWO-LAYER BISTABLE NEURAL NETWORK

2006

The dynamics of propagating interfaces in a bistable neural network is investigated. We consider the network composed of two coupled 1D lattices and assume that they interact in a local spatial point (pin contact). The network unit is modeled by the FitzHugh–Nagumo-like system in a bistable oscillator mode. The interfaces describe the transition of the network units from the rest (unexcited) state to the excited state where each unit exhibits periodic sequences of excitation pulses or action potentials. We show how the localized inter-layer interaction provides an "excitatory" or "inhibitory" action to the oscillatory activity. In particular, we describe the interface propagation failure a…

propagation failureBistabilityComputer science[ PHYS.COND.CM-DS-NN ] Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]Interface (computing)Topology01 natural sciences010305 fluids & plasmas[NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS]Control theory0103 physical sciences[ NLIN.NLIN-PS ] Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS][PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]0101 mathematicsEngineering (miscellaneous)ComputingMilieux_MISCELLANEOUSRest (physics)Artificial neural networkApplied Mathematicsneural networksAction (physics)[ SPI.TRON ] Engineering Sciences [physics]/Electronics[SPI.TRON]Engineering Sciences [physics]/Electronics010101 applied mathematicsNonlinear systemNonlinear dynamicsModeling and SimulationExcited stateExcitationInternational Journal of Bifurcation and Chaos
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Heteroclinic contours and self-replicated solitary waves in a reaction–diffusion lattice with complex threshold excitation

2008

Abstract The space–time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. Heteroclinic orbits defining traveling wave front solutions are investigated in a moving frame system. A heteroclinic contour formed by separatrix manifolds of two saddle-foci is found in the phase space. The existence of such structure indicates the appearance of complex wave patterns in the network. Such solutions have been confirmed and analyzed numerically. Complex homoclinic orbits found in the neighborhood of the heteroclinic contour define …

Classical mechanicsPhase spaceReaction–diffusion systemComplex systemPattern formationHeteroclinic cycleStatistical and Nonlinear PhysicsHeteroclinic orbitHomoclinic orbitHeteroclinic bifurcationCondensed Matter PhysicsMathematicsPhysica D: Nonlinear Phenomena
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