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 Phase Synchrony Analysis of Rolling Bearing Vibrations and Its Application to Failure Identification

Sensors ◽  
2020 ◽  
Vol 20 (10) ◽  
pp. 2964 ◽  
Author(s):  
Qing Zhang ◽  
Tingting Jiang ◽  
Joseph D. Yan
Keyword(s):  
Phase Synchronization ◽  
Chaotic Behavior ◽  
Rolling Bearing ◽  
Bearing Failure ◽  
Phase Synchrony ◽  
Vibration Signals ◽  
Mode Decomposition ◽  
Initial Stage ◽  
Failure Evolution ◽  
Band Limited

As the failure-induced component (FIC) in the vibration signals of bearings transmits through housings and shafts, potential phase synchronization is excited among multichannel signals. As phase synchrony analysis (PSA) does not involve the chaotic behavior of signals, it is suitable for characterizing the operating state of bearings considering complicated vibration signals. Therefore, a novel PSA method was developed to identify and track the failure evolution of bearings. First, resonance demodulation and variational mode decomposition (VMD) were combined to extract the mono-component or band-limited FIC from signals. Then, the instantaneous phase of the FIC was analytically solved using Hilbert transformation. The generalized phase difference (GPD) was used to quantify the relationship between FICs extracted from different vibration signals. The entropy of the GPD was regarded as the indicator for quantifying failure evolution. The proposed method was applied to the vibration signals obtained from an accelerated failure experiment and a natural failure experiment. Results showed that phase synchronization in bearing failure evolution was detected and evaluated effectively. Despite the chaotic behavior of the signals, the phase synchronization indicator could identify bearing failure during the initial stage in a robust manner.

scholarly journals DISORDER INDUCED BCS-BEC CROSSOVER

2012 ◽  
Vol 11 ◽  
pp. 120-126 ◽  
Author(s):  
AYAN KHAN
Keyword(s):  
Order Parameter ◽  
Chemical Potential ◽  
Random Potential ◽  
Mean Field ◽  
Superconducting Order Parameter ◽  
Interesting Issue ◽  
Coupled Equations ◽  
Weak Regime ◽  
The Mean ◽  
Superconducting Fluctuations

Of late, the study of BCS-BEC crossover in the presence of weak random impurity is an interesting issue. In this proceedings we study the effect of this disorder which is included through the Nozières and Smith-Rink theory of superconducting fluctuations. In the weak regime, the random potential leaves an effect on the superconducting order parameter but it spares the chemical potential. Here we present the exact behavior of the mean field quantities as a function of the disorder by self-consistently solving the coupled equations.

CRITICAL DIMENSIONS OF SYSTEMS WITH JOINT MULTICRITICAL AND LIFSHITZ-POINT-LIKE BEHAVIOR

2011 ◽  
Vol 25 (22) ◽  
pp. 1839-1845 ◽  
Author(s):  
ARTEM V. BABICH ◽  
LESYA N. KITCENKO ◽  
VYACHESLAV F. KLEPIKOV
Keyword(s):  
Field Theory ◽  
Critical Phenomena ◽  
Critical Points ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Critical Dimensions ◽  
Lifshitz Point ◽  
The Mean ◽  
Derivatives Of

In this article, we consider a model that allows one to describe critical phenomena in systems with higher powers and derivatives of order parameter. The systems considered have critical points with joint multicritical and Lifshitz-point-like properties. We assess the lower and upper critical dimensions of these systems. These calculation enable us to find the fluctuation region where the mean field theory description does not work.

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.

scholarly journals Energy occupation of waves and structures in 3D compressive MHD turbulence

2019 ◽  
Vol 488 (1) ◽  
pp. 859-867 ◽  
Author(s):  
L P Yang ◽  
H Li ◽  
S T Li ◽  
L Zhang ◽  
J S He ◽  
...  
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Turbulent Energy ◽  
Mhd Turbulence ◽  
Linear Cascade ◽  
Temporal Domain ◽  
Propagating Waves ◽  
Cascade Processes ◽  
Parallel Direction ◽  
The Waves

Abstract Structures and propagating waves are often observed in solar wind turbulence. Their origins and features remain to be uncovered. In this work, we use 3D driven, compressible MHD turbulence simulations to investigate the global signatures of the driven fluctuations in whole spatial and temporal domain. With four-dimensional spatial-temporal (x, y, z, t) Fourier transformations implemented, we have identified two distinct main populations: waves, which satisfy the $\omega -\boldsymbol {k}$ dispersion relations and are propagating; and structures, which satisfy the polarization relations but non-propagating (ω = 0). Whereas the overall turbulent energy spectrum is still consistent with k−5/3, the contributions from waves and structures show very different behaviour in $\boldsymbol {k}$ space, with structures dominating at small k but waves becomes comparable to structures at large k. Overall, the fluctuations in the directions perpendicular to the large-scale mean field $\boldsymbol {B_0}$ are a manifestation of structures, while along the parallel direction, the fluctuations are dominated by waves. Also, a significant portion of the incompressible structures are the Alfvénic nature, and with imbalanced increased, the waves predominantly propagate in one direction and nearly perpendicular to $\boldsymbol {B_0}$. Differentiating the relative contributions from waves and structures could have important implications for understanding the non-linear cascade processes in the inertial range as well as particle-fluctuation interactions at small scales.

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