Revival and death of oscillation under mean-field coupling: Interplay of intrinsic and extrinsic filtering

2019 ◽  
Vol 100 (5) ◽  
Author(s):  
Krishna Kumar ◽  
Debabrata Biswas ◽  
Tanmoy Banerjee ◽  
Wei Zou ◽  
J. Kurths ◽  
...  
Keyword(s):  
Mean Field ◽  
Field Coupling

BURSTING TYPES AND STABLE DOMAINS OF RULKOV NEURON NETWORK WITH MEAN FIELD COUPLING

2013 ◽  
Vol 23 (12) ◽  
pp. 1330041 ◽  
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.

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

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.

scholarly journals Ageing transitions in a network of Rulkov neurons

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.

scholarly journals Mean-Field Coupling of Identical Expanding Circle Maps

2016 ◽  
Vol 164 (4) ◽  
pp. 858-889 ◽  
Author(s):  
Fanni Sélley ◽  
Péter Bálint
Keyword(s):  
Mean Field ◽  
Circle Maps ◽  
Field Coupling ◽  
Expanding Circle

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

1996 ◽  
Vol 06 (07) ◽  
pp. 1211-1253 ◽  
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.

scholarly journals Trade-off between filtering and symmetry breaking mean-field coupling in inducing macroscopic dynamical states

2020 ◽  
Vol 22 (9) ◽  
pp. 093024 ◽  
Author(s):  
Uday Singh ◽  
K Sathiyadevi ◽  
V K Chandrasekar ◽  
W Zou ◽  
J Kurths ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Mean Field ◽  
Trade Off ◽  
Field Coupling

Mean field coupling mechanisms explaining the impact of the precessing vortex core on the flame transfer function

2021 ◽  
Vol 223 ◽  
pp. 254-266
Author(s):  
Finn Lückoff ◽  
Thomas Ludwig Kaiser ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Transfer Function ◽  
Vortex Core ◽  
Mean Field ◽  
Field Coupling ◽  
Precessing Vortex Core ◽  
The Impact ◽  
Coupling Mechanisms

GLOBAL DYNAMICS IN NETWORKS OF 1D ELEMENTS WITH TIME DELAYED MEAN FIELD COUPLING SUBJECT TO NOISE: SYNCHRONIZATION THRESHOLD, MULTISTABILITY AND HYSTERESIS

2010 ◽  
Vol 20 (06) ◽  
pp. 1825-1836 ◽  
Author(s):  
A. POTOTSKY ◽  
N. JANSON
Keyword(s):  
Boundary Value Problem ◽  
Mean Field ◽  
Planck Equation ◽  
Global Dynamics ◽  
Polynomial Potential ◽  
One Dimensional ◽  
Field Coupling ◽  
Exact Location ◽  
Continuation Technique ◽  
Fokker Planck

We determine the boundary of the synchronization domain of a large number of one-dimensional continuous stochastic elements with time delayed nonhomogeneous mean-field coupling. The exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker–Planck equation. Here the synchronization threshold is found by solving this BVP using the continuation technique (AUTO). Approximate analytics is obtained using expansion into eigenfunctions of the stationary Fokker–Planck operator. Multistability and hysteresis are demonstrated for the case of bistable elements with a polynomial potential.

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