Feedback particle filter with mean-field coupling

2013 ◽

Vol 23 (12) ◽

pp. 1330041 ◽

Cited By ~ 9

Author(s):

HONGJUN CAO ◽

YANGUO WU

Keyword(s):

Parameter Space ◽

Single Neuron ◽

Complex Dynamics ◽

Mean Field ◽

Flip Bifurcation ◽

Neuron Network ◽

Square Wave ◽

Field Coupling ◽

The Mean ◽

Stable Domains

Based on the detailed bifurcation analysis and the master stability function, bursting types and stable domains of the parameter space of the Rulkov map-based neuron network coupled by the mean field are taken into account. One of our main findings is that besides the square-wave bursting, there at least exist two kinds of triangle burstings after the mean field coupling, which can be determined by the crisis bifurcation, the flip bifurcation, and the saddle-node bifurcation. Under certain coupling conditions, there exists two kinds of striking transitions from the square-wave bursting (the spiking) to the triangle bursting (the square-wave bursting). Stable domains of fixed points, periodic solutions, quasiperiodic solutions and their corresponding firing regimes in the parameter space are presented in a rigorous mathematical way. In particular, as a function of the intrinsic control parameters of each single neuron and the external coupling strength, a stable coefficient of the Neimark–Sacker bifurcation is derived in a parameter plane. These results show that there exist complex dynamics and rich firing regimes in such a simple but thought-provoking neuron network.

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Effect of asymmetry on stochastic resonance and stochastic resonance induced by multiplicative noise and by mean-field coupling

Physical Review E ◽

10.1103/physreve.66.031104 ◽

2002 ◽

Vol 66 (3) ◽

Cited By ~ 76

Author(s):

Jing-hui Li

Keyword(s):

Stochastic Resonance ◽

Multiplicative Noise ◽

Mean Field ◽

Field Coupling

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Controlling phase synchrony in the mean field coupled Hindmarsh–Rose neurons

International Journal of Modern Physics C ◽

10.1142/s0129183122500589 ◽

2021 ◽

Author(s):

T. Remi ◽

P. A. Subha ◽

K. Usha

Keyword(s):

Pulse Width ◽

Order Parameter ◽

Phase Synchronization ◽

Mean Field ◽

External Input ◽

Phase Synchrony ◽

Field Coupling ◽

Temporal Domain ◽

Coefficient Of Variability ◽

Neural Disorders

The phase synchronization in a network of mean field coupled Hindmarsh–Rose neurons and the control of phase synchrony by an external input has been analyzed in this work. The analysis of interspike interval, with varying coupling strength, reveals the dynamical change induced in each neuron in the network. The bursting phase lines depict that mean field coupling induces phase synchrony in excitatory mode and desynchrony in inhibitory mode. The coefficient of variability, in spatial and temporal domain, signifies the deviations in firing times of neurons, in a collective manner. The Kuramoto order parameter quantifies the intermittent and complete phase synchrony, induced by excitatory mean field coupling. The capability of external input, in the form of spikes, to control the intermittent and complete phase synchrony has been analyzed. The coefficient of variability and Kuramoto order parameter has been studied by varying the amplitude, pulse width and frequency of the input. The studies have shown that high-frequency spike input, with optimum amplitude and pulse width, has high desynchronizing ability, which is substantiated by the parameter space analysis. The control of synchrony in the network of neurons may find application in rectifying neural disorders.

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Analysis of the feedback particle filter with diffusion map based approximation of the gain

Foundations of Data Science ◽

10.3934/fods.2021023 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Sahani Pathiraja ◽

Wilhelm Stannat

Keyword(s):

Particle Filter ◽

Mean Field ◽

Future Research ◽

Bayesian Filtering ◽

Gain Function ◽

Mean Field Limit ◽

Research Directions ◽

Type Particle ◽

Future Research Directions ◽

Filtering Problem

<p style='text-indent:20px;'>Control-type particle filters have been receiving increasing attention over the last decade as a means of obtaining sample based approximations to the sequential Bayesian filtering problem in the nonlinear setting. Here we analyse one such type, namely the feedback particle filter and a recently proposed approximation of the associated gain function based on diffusion maps. The key purpose is to provide analytic insights on the form of the approximate gain, which are of interest in their own right. These are then used to establish a roadmap to obtaining well-posedness and convergence of the finite <inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula> system to its mean field limit. A number of possible future research directions are also discussed.</p>

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Ageing transitions in a network of Rulkov neurons

Scientific Reports ◽

10.1038/s41598-021-03844-1 ◽

2022 ◽

Vol 12 (1) ◽

Author(s):

Dhrubajyoti Biswas ◽

Sayan Gupta

Keyword(s):

Coupling Strength ◽

Order Parameter ◽

Additive Noise ◽

Mean Field ◽

Network Connectivity ◽

Stochastic Networks ◽

Field Coupling ◽

Neuronal Interactions ◽

Standard Order ◽

Free Network

AbstractThe phenomenon of ageing transitions (AT) in a Erdős–Rényi network of coupled Rulkov neurons is studied with respect to parameters modelling network connectivity, coupling strength and the fractional ratio of inactive neurons in the network. A general mean field coupling is proposed to model the neuronal interactions. A standard order parameter is defined for quantifying the network dynamics. Investigations are undertaken for both the noise free network as well as stochastic networks, where the interneuronal coupling strength is assumed to be superimposed with additive noise. The existence of both smooth and explosive AT are observed in the parameter space for both the noise free and the stochastic networks. The effects of noise on AT are investigated and are found to play a constructive role in mitigating the effects of inactive neurons and reducing the parameter regime in which explosive AT is observed.

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Mean-Field Coupling of Identical Expanding Circle Maps

Journal of Statistical Physics ◽

10.1007/s10955-016-1568-y ◽

2016 ◽

Vol 164 (4) ◽

pp. 858-889 ◽

Cited By ~ 3

Author(s):

Fanni Sélley ◽

Péter Bálint

Keyword(s):

Mean Field ◽

Circle Maps ◽

Field Coupling ◽

Expanding Circle

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AN EXPERIMENTAL STUDY OF A POPULATION OF RELAXATION OSCILLATORS WITH A PHASE-REPELLING MEAN-FIELD COUPLING

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127496000692 ◽

1996 ◽

Vol 06 (07) ◽

pp. 1211-1253 ◽

Cited By ~ 11

Author(s):

ADAM A. BRAILOVE ◽

PAUL S. LINSAY

Keyword(s):

Exponential Distribution ◽

Dynamical Behavior ◽

Mean Field ◽

Transient Behavior ◽

Geometrical Model ◽

The Novel ◽

Op Amp ◽

Relaxation Oscillators ◽

Field Coupling ◽

Simple Geometrical Model

The dynamical behavior of a system of coupled relaxation oscillators is studied experimentally. A population of up to 15 coupled electronic op-amp relaxation oscillators is used as a prototype for the real collections of limit-cycle oscillators frequently found in many physical, biological, and technological systems. The oscillators interact via an all-to-all or mean-field coupling. The rarely studied case of antiferromagnetic interactions, in which oscillators tend to repel each other in phase, is considered. The behavior of the system is significantly different from the predictions of the limited theory that is currently available. The novel behavior observed includes the existence of numerous distinguishable phase-locked states and an exponential distribution of the duration of transients. The critical coupling strength necessary for the oscillator system to completely phase-lock is measured. A simple geometrical model of the dynamics of the system during the transient is presented as a means of understanding the exponential distribution of transient lengths. In addition, a phase-response oscillator model is shown to exhibit similar transient behavior.

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