arXiv subjects

Prosenjit Kundu

Publications and source records attributed to Prosenjit Kundu.

24 records · Page 2Linked to original sources

arXiv2019

Emergent dynamics in delayed attractive-repulsively coupled networks

We investigate different emergent dynamics namely oscillation quenching and revival of oscillation in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking localized repulsive delayed interaction. Starting from the oscillatory states (OS) we systematically identify three types of transition phenomena in the parameter space: (1) The system may reach inhomogeneous steady states (IHSS) from the homogeneous steady state (HSS) sometimes called as the transition from amplitude death (AD) to oscillation death (OD) state i.e. OS-AD-OD scenario, (2) Revival of oscillation (OS) from the AD state (OS-AD-OS) and (3) Emergence of OD state from oscillatory state (OS) without passing through AD i.e. OS-OD. The dynamics of each node in the network is assumed to be governed either by identical limit cycle Stuart-Landau system or by chaotic Rossler system. Based on clustering behavior observed in oscillatory network we derive a reduced low-dimensional model of the large network. Using the reduced model, we investigate the effect of time delay on these transitions and demarcate OS, AD and OD regimes in the parameter space. We also explore and characterize the bifurcation transitions present in both systems. The generic behavior of the low dimensional model and full network are found to match satisfactorily.

nlin.AO↗

arXiv2018

Generalized Meta-Analysis for Multiple Regression Models Across Studies with Disparate Covariate Information

Meta-analysis, because of both logistical convenience and statistical efficiency, is widely popular for synthesizing information on common parameters of interest across multiple studies. We propose developing a generalized meta-analysis approach for combining information on multivariate regression parameters across multiple different studies which have varying level of covariate information. Using algebraic relationships between regression parameters in different dimensions, we specify a set of moment equations for estimating parameters of a maximal model through information available from sets of parameter estimates from a series of reduced models available from the different studies. The specification of the equations requires a reference dataset to estimate the joint distribution of the covariates. We propose to solve these equations using the generalized method of moments approach, with the optimal weighting of the equations taking into account uncertainty associated with estimates of the parameters of the reduced models. We describe extensions of the iterated reweighted least square algorithm for fitting generalized linear regression models using the proposed framework. Based on the same moment equations, we also propose a diagnostic test for detecting violation of underlying model assumptions, such as those arising due to heterogeneity in the underlying study populations. Methods are illustrated using extensive simulation studies and a real data example involving the development of a breast cancer risk prediction model using disparate risk factor information from multiple studies.

stat.ME↗

arXiv2018

Explosive synchronization in phase-frustrated multiplex networks

We investigate the phenomenon of first order transition (explosive synchronization (ES)) in adaptively coupled phase-frustrated bi-layer multiplex network. We consider Sakaguchi-Kuramoto (SK) dynamics over the top of multiplex networks and we establish that ES can emerge in all layers of a multiplex network even when one of the layers may not exhibit ES in the absence of the inter layer connections. We clearly identify the regions of the parameter space, in which the multiplexity wins over frustration parameter and network structure for the emergence of ES. Based on the mean field analysis around the coherent state and a perturbative approach around the incoherent state we analytically derive the synchronization transition points (backward and forward) of all layers of multiplex network as well as its mono-layer counterpart satisfying a close agreement with the numerical results.

nlin.AO↗

arXiv2018

Perfect synchronization in networks of phase-frustrated oscillators

Synchronizing phase frustrated Kuramoto oscillators, a challenge that has found applications from neuronal networks to the power grid, is an eluding problem, as even small phase-lags cause the oscillators to avoid synchronization. Here we show, constructively, how to strategically select the optimal frequency set, capturing the natural frequencies of all oscillators, for a given network and phase-lags, that will ensure perfect synchronization. We find that high levels of synchronization are sustained in the vicinity of the optimal set, allowing for some level of deviation in the frequencies without significant degradation of synchronization. Demonstrating our results on first and second order phase-frustrated Kuramoto dynamics, we implement them on both model and real power grid networks, showing how to achieve synchronization in a phase frustrated environment.

nlin.AO↗

arXiv2018

Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation

We investigate transition to synchronization in Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage ($f$) of higher degree nodes of the network are assumed to be correlated with their degrees and that of the remaining nodes are drawn from some standard distribution namely Lorenz distribution. The effects of variation of $f$ and phase frustration parameter $α$ on transition to synchronization are investigated in detail. Self-consistent equations involving critical coupling strength ($λ_c$) and group angular velocity ($Ω_c$) at the onset of synchronization have been derived analytically in the thermodynamic limit. For the detailed investigation we considered SK model on scale-free as well as Erdős-Rényi (ER) networks. Interestingly explosive synchronization (ES) has been observed in both the networks for different ranges of values of $α$ and $f$. For scale-free networks, as the value of $f$ is set within $10\% \leq f \leq 70\%$, the range of the values of $α$ for existence of the ES is greatly enhanced compared to the fully degree-frequency correlated case. On the other hand, for random networks, ES observed in a narrow window of $α$ when the value of $f$ is taken within $30\% \leq f \leq 50\%$. In all the cases critical coupling strengths for transition to synchronization computed from the analytically derived self-consistent equations show a very good agreement with the numerical results.

nlin.AO↗

arXiv2017

Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model

We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order parameter for the model in the thermodynamic limit. Using the self-consistent equations we investigate transition to synchronization in SK model on uncorrelated scale-free (SF) and Erdős-Rényi (ER) networks in detail. Depending on the degree distribution exponent ($γ$) of SF networks and phase-frustration parameter, the population undergoes from first order transition (explosive synchronization (ES)) to second order transition and vice versa. In ER networks transition is always second order irrespective of the phase-lag parameter. We observe that the critical coupling strength for the onset of synchronization is decreased by phase-frustration parameter in case of SF network where as in ER network, the phase-frustration delays the onset of synchronization. Extensive numerical simulations using SF and ER networks are performed to validate the analytical results. An analytical expression of critical coupling strength for the onset of synchronization is also derived from the self consistent equations considering the vanishing order parameter limit.

nlin.AO↗