Regular bursting emerging from coupled chaotic neurons (original) (raw)
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Chaotic bursting as chaotic itinerancy in coupled neural oscillators
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2003
We show that chaotic bursting activity observed in coupled neural oscillators is a kind of chaotic itinerancy. In neuronal systems with phase deformation along the trajectory, diffusive coupling induces a dephasing effect. Because of this effect, an antiphase synchronized solution is stable for weak coupling, while an in-phase solution is stable for very strong coupling. For intermediate coupling, a chaotic bursting activity is generated. It is a mixture of three different states: an antiphase firing state, an in-phase firing state, and a nonfiring resting state. As we construct numerically the deformed torus manifold underlying the chaotic bursting state, it is shown that the three unstable states are connected to give rise to a global chaotic itinerancy structure. Thus we claim that chaotic itinerancy provides an alternative route to chaos via torus breakdown.
Chaotic phase synchronization in scale-free networks of bursting neurons
Physical Review E, 2007
There is experimental evidence that the neuronal network in some areas of the brain cortex presents the scale-free property, i.e., the neuron connectivity is distributed according to a power law, such that neurons are more likely to couple with other already well-connected ones. From the information processing point of view, it is relevant that neuron bursting activity be synchronized in some weak sense. A coherent output of coupled neurons in a network can be described through the chaotic phase synchronization of their bursting activity. We investigated this phenomenon using a two-dimensional map to describe neurons with spiking-bursting activity in a scale-free network, in particular the dependence of the chaotic phase synchronization on the coupling properties of the network as well as its synchronization with an externally applied time-periodic signal.
Emergence of bursting in two coupled neurons of different types of excitability
Chaos, Solitons & Fractals, 2020
In this manuscript, a spiking neuron of type I excitability and a silent neuron of type II excitability are coupled through a gap junction with unequal coupling strengths, and none of the coupled neurons can burst intrinsically. By applying the theory of dynamical systems (e.g. bifurcation theory), we investigate how the coupling strength affects the dynamics of the neurons, when one of the coupling strengths is fixed and the other varies. We report four different regimes of oscillations as the coupling strength increases. (1) Spike-Spike Phase-Locking, where both neurons are in tonic spiking mode but with different frequencies; (2) Spike-Burst mode, where the type II neuron bursts while the type I neuron remains in tonic spiking mode; (3) Burst-Burst synchronization, where the neurons burst synchronously, i.e., both neurons enter and exit the active phase almost together; (4) Spike-Spike Synchronization, where the neurons synchronize as two oscillators, i.e., they oscillate with equal time period and fraquency. An interesting finding is that there exist two different synchronous behaviours, one of them corresponds to 1 −burst synchronization of the neurons and the other corresponds to the synchronizations of 1 −bursting oscillations in type II neuron and tonic spiking oscillations in type I neuron. Finally it should be pointed out that all through increasing the coupling strength we observe sequences of intermittency in the neurons, which is an abrupt and irregular transition between periodic oscillations and chaotic dynamics.
Anti-phase regularization of coupled chaotic maps modelling bursting neurons
2007
We introduce a new class of maps that describe the chaotic activity of spikingbursting neurons observed in neurophysiological experiments. We show that, depending on the connection (diffusively or reciprocally synaptically), coupled maps demonstrate several modes of cooperative dynamics: i) weakly correlated chaotic pulsations, ii) anti-phase quasi-regular bursting activity and iii) chaotic synchronization. Such phenomena have been observed in recent experiments with central pattern generator chaotic neurons. Taking into account the fact that the shape and the amplitude of the spikes are not important for the organisation of such cooperative dynamics, we analyzed the timing of the bursts only. We showed that the regime of anti-phase regularisation is stable against noise.
Synchronization in time-discrete model of two electrically coupled spike-bursting neurons
Chaos, Solitons & Fractals, 2012
Dynamics of the ensemble of two model neurons interacting through electrical synapse is investigated. Both neurons are described by two-dimensional discontinuous map. It is shown that in four-dimensional phase space a chaotic attractor of relaxation type exists corresponding to spike-bursting chaotic oscillations. A new effect of recurrent transitory chaotic oscillations underlies a dynamical mechanism of chaotic bursts formation. It is shown that, under coupling, the transient from chaotic bursts generation into rest state occurs with a time delay. A new characteristic estimating the degree of spike-bursting synchronization is introduced. Dependence of the synchronism degree on the coupling strength is shown for some coupling interval where only activity synchronization occurs. A probabilistic study provides a dynamical explanation of these phenomena.
Ratcheting and energetic aspects of synchronization in coupled bursting neurons
Nonlinear Dynamics, 2015
In this paper, we investigate the dynamics of two coupled bursting neurons. The Hindmarsh-Rose mathematical model of the neuron subjected to an external periodic stimulus is considered. We transform this model into that of the one-dimensional problem of a particle driven by a periodic external force under the influence of a double-well potential. We study the bifurcation structures, chaotic behavior, and the synchronization dynamics of the transformed model. Numerical simulations reveal the existence of some bifurcation structures including saddle-node, symmetry-breaking, and period-doubling route to chaos. By varying the sys
Transitions to synchrony in coupled bursting neurons
2004
Certain cells in the brain, for example, thalamic neurons during sleep, show spike-burst activity. We study such spike-burst neural activity and the transitions to a synchronized state using a model of coupled bursting neurons. In an electrically coupled network, we show that the increase of coupling strength increases incoherence first and then induces two different transitions to synchronized states, one associated with bursts and the other with spikes.
Control and Synchronization of Chaotic Neurons Under Threshold Activated Coupling
Lecture Notes in Computer Science, 2007
We have studied the spatiotemporal behaviour of threshold coupled chaotic neurons. We observe that the chaos is controlled by threshold activated coupling, and the system yields synchronized temporally periodic states under the threshold response. Varying the frequency of thresholding provides different higher order periodic behaviors, and can serve as a simple mechanism for stabilising a large range of regular temporal patterns in chaotic systems. Further, we have obtained a transition from spatiotemporal chaos to fixed spatiotemporal profiles, by lengthening the relaxation time scale.
2020
Signal transmission time delays in a network of nonlinear oscillators are known to be responsible for a variety of interesting dynamic behaviors including phase-flip transitions leading to synchrony or out of synchrony. Here, we uncover that phase-flip transitions are general phenomena and can occur in a network of coupled bursting neurons with a variety of coupling types. The transitions are marked by nonlinear changes in both temporal and phase-space characteristics of the coupled system. We demonstrate these phase-transitions with Hindmarsh-Rose and Leech-Heart interneuron models and discuss the implications of these results in understanding collective dynamics of bursting neurons in the brain. A large body of experimental work on brain activity has demonstrated that phase synchronization of neuronal oscillations is the basis for various percepts and actions, such as perceptual decision-making, attention and memory processes, awareness, sensory-motor, or multisensory integration....
Regularization of Synchronized Chaotic Bursts
2000
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.