arXiv subjects

Sarika Jalan

Publications and source records attributed to Sarika Jalan.

At least 37 records · Page 2Linked to original sources

arXiv2023

Solitary death in coupled limit-cycle oscillators with higher-order interactions

Coupled limit cycle oscillators with pairwise interactions depict phase transitions to amplitude or oscillation death. This Letter introduces a scheme for higher-order interactions, which can not be decomposed into pairwise interactions. We investigate Stuart Landau oscillators' dynamical evolution under the impression of such a coupling scheme and discover a particular type of oscillator death where a coupling-dependent stable death state, away from the origin, arises in isolation without being accompanied by any other stable state. We call such a state a Solitary death state. Moreover, the explosive transition to the death state is preceded by a surge in amplitude, followed by the revival of the oscillations. Such versatile dynamical states are further enriched with sensitivity to initial conditions. Finally, we point out the resemblance of the results with different dynamical states associated with epileptic seizures.

nlin.AO↗

arXiv2023

Impact of Black Swan Events on Ethereum Blockchain ERC20 Token Transaction Networks

The Ethereum blockchain and its ERC20 token standard have revolutionized the landscape of digital assets and decentralized applications. ERC20 tokens developed on the Ethereum blockchain have gained significant attention since their introduction. They are programmable and interoperable tokens, enabling various applications and token economies. Transaction graphs, representing the flow of the value between wallets within the Ethereum network, have played a crucial role in understanding the system's dynamics, such as token transfers and the behavior of traders. Here, we explore the evolution of daily transaction graphs of ERC20 token transactions, which sheds light on the trader's behavior during the Black Swan Events -- 2018 crypto crash and the COVID-19 pandemic. By using the tools from network science and differential geometry, we analyze 0.98 billion of ERC20 token transaction data from November 2015 to January 2023. Our analysis reveals that ERC20 financial ecosystem has evolved from a localized wealth formation period to a more mature financial ecosystem where wealth has dispersed among the traders in the network after the crypto crash and during the pandemic period. Before the crash, most sellers only sell the tokens, and buyers only buy the tokens. However, after the crash and during the pandemic period, sellers and buyers both performed buying and selling activities. In addition, we observe no significant negative impact of the COVID-19 pandemic on user behavior in the financial ecosystem.

nlin.AO↗

arXiv2023

Explosive death in coupled oscillators with higher-order interactions

We investigate the dynamical evolution of globally connected Stuart-Landau oscillators coupled through conjugate or dis-similar variables on simplicial complexes. We report a first-order explosive phase transition from oscillatory state to death state, with 2-simplex (triadic) interactions, as opposed to the second-order transition with only 1-simplex (dyadic) interactions. Moreover, the system displays four distinct homogeneous steady states in the presence of triadic interactions, in contrast to the two homogeneous steady states observed with dyadic interactions. We calculate the backward transition point analytically, confirming the numerical results and providing the origin of the dynamical states in the transition region. The study will be useful in understanding complex systems, such as ecological and epidemiological, having higher-order interactions and coupling through conjugate variables.

nlin.CD↗

arXiv2023

Onset of synchronization in contrarians with higher-order interactions

We investigate the impact of contrarians (via negative coupling) in a multilayer network of phase oscillators having higher-order interactions. We show that the multilayer framework facilitates synchronization onset in the negative pairwise coupling regime. The multilayering strength governs the onset of synchronization and the nature of the phase transition, whereas the backward critical couplings depend on higher-order interaction strength. The system does not synchronize below a critical value of multilayering strength. The numerical results agree with the analytical predictions using the Ott-Antonsen approach. The results presented here may be useful for understanding emergent behaviors in real-world complex systems with contrarians and higher-order interactions, such as the brain and society.

nlin.AO↗

arXiv2023

Multiplexing-based control of wavefront propagation: the interplay of inter-layer coupling, asymmetry and noise

We show how multiplexing influences propagating fronts in multilayer networks of coupled bistable oscillators. Using numerical simulation, we investigate both deterministic and noise-sustained propagation. In particular, we demonstrate that the multiplexing allows to reduce the intra-layer dynamics to a common regime where the front propagation speed in all the interacting layers attains the same fixed value. In the presence of noise the dynamics is more complicated and is characterized by the ability of the system to adjust to the common propagation speed for varying the multiplexing strength. In addition, we find that the noise-induced stabilization of wavefront propagation in multilayer networks allows to obtain less pronounced deviations of the wavefront compared to the stabilization achieved in the isolated layer. Finally, we demonstrate that the reduction of the wavefront deviations can be enhanced by increasing the number of interacting layers.

nlin.AO↗

arXiv2023

Smallworldness in Hypergraphs

Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies trying to reveal possible mechanisms through which the pairwise interactions amongst the units of a network are structured in a way to determine such observed regularity. Here we show that smallworldness occurs also when interactions are of higher order. Namely, by considering Q-uniform hypergraphs and a process through which connections can be randomly rewired with given probability p, we find that such systems may exhibit prominent clustering properties in connection with small average path lengths for a wide range of p values, in analogy to the case of dyadic interactions. The nature of small-world transition remains the same at different orders Q of the interactions, however, the increase in the hyperedge order reduces the range of rewiring probability for which smallworldness emerge.

physics.soc-ph↗

arXiv2023

Spacing ratio statistics of multiplex directed networks

Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex networks consisting of directed Erdos-Renyi random networks layers represented as, first, weighted non-Hermitian random matrices and then weighted Hermitian random matrices. We report that the multiplexing strength rules the behavior of average spacing ratio statistics for multiplexing networks represented by the non-Hermitian and Hermitian matrices, respectively. Additionally, for both these representations of the directed multiplex networks, the multiplexing strength appears as a guiding parameter for the eigenvector delocalization of the entire system. These results could be important for driving dynamical processes in several real-world multilayer systems, particularly, understanding the significance of multiplexing in comprehending network properties.

physics.soc-ph↗

arXiv2023

Estimation of Correlation Matrices from Limited time series Data using Machine Learning

Correlation matrices contain a wide variety of spatio-temporal information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the entire underlying system. This information can help to predict the underlying network structure, e.g., inferring neuronal connections from spiking data, deducing causal dependencies between genes from expression data, and discovering long spatial range influences in climate variations. Traditional methods of predicting correlation matrices utilize time series data of all the nodes of the underlying networks. Here, we use a supervised machine learning technique to predict the correlation matrix of entire systems from finite time series information of a few randomly selected nodes. The accuracy of the prediction validates that only a limited time series of a subset of the entire system is enough to make good correlation matrix predictions. Furthermore, using an unsupervised learning algorithm, we furnish insights into the success of the predictions from our model. Finally, we employ the machine learning model developed here to real-world data sets.

cs.LG↗

arXiv2023

Tiered synchronization in adaptive Kuramoto oscillators on simplicial complexes

An incorporation of higher-order interactions is known to lead an abrupt first-order transition to synchronization in otherwise smooth second-order one for pair-wise coupled systems. Here, we show that adaptation in higher-order coupling strength may yield completely different phenomena, notably, second-order transition to synchronization and tiered synchronization. Using the Ott-Antonsen approach, we perform rigorous theoretical calculations illustrating the origin of these emerging phenomena along with a complete description of all (un)stable states. Numerical simulations for limited-size networks are in agreement with the analytical predictions. These results would be important to comprehend dynamical behaviors of real-world complex systems with inherent higher-order interactions and adaptation through feedback coupling.

nlin.AO↗

arXiv2022

Oscillation Quenching in Stuart-Landau Oscillators via Dissimilar Repulsive Coupling

Quenching of oscillations, namely amplitude and oscillations death, is an emerging phenomenon exhibited by many real-world complex systems. Here, we introduce a scheme that combines dissimilar couplings and repulsive feedback links for the interactions of Stuart Landau oscillators and analytically derives the conditions required for the amplitude death. Importantly, this analysis is independent of the network size, presents a generalized approach to calculate the stability conditions for various different coupling schemes, and befits for non-identical oscillators as well. Last, we discuss the similarities of the quenching of oscillations phenomenon with the postictal generalized EEG suppression in convulsive seizures.

nlin.AO↗

arXiv2022

Eigenvector localization in hypergraphs: pair-wise vs higher-order links

Localization behaviours of Laplacian eigenvectors of complex networks provide understanding to various dynamical phenomena on the corresponding complex systems. We numerically investigate role of hyperedges in driving eigenvector localization of hypergraphs Laplacians. By defining a single parameter γwhich measures the relative strengths of pair-wise and higher-order interactions, we analyze the impact of interactions on localization properties. For, γ< 1 there exists no impact of pairwise links on eigenvector localization while the higher-order interactions instigate localization in the larger eigenvalues. For γ> 1, pair-wise interactions cause localization of eigenvector corresponding to small eigenvalues, where as higherorder interactions, despite being much lesser than the pair-wise links, keep driving localization of the eigenvectors corresponding to larger eigenvalues. The results will be useful to understand dynamical phenomena such as diffusion, and random walks on a range of real-world complex systems having higher-order interactions.

cond-mat.stat-mech↗

arXiv2022

Multiple synchronization transitions in simplicial complexes on multilayer networks

The presence of higher-order interactions (simplicial complexes) in networks and certain types of multilayer networks has shown to lead to the abrupt first-order transition to synchronization. We discover that simplicial complexes on multilayer networks can yield multiple basins of attraction, leading to multiple routes to the abrupt first-order transition to synchronization. Using the Ott-Antonsen approach, we develop an analytical framework for simplicial complexes on multilayer networks, which thoroughly explains the origin and stability of all possible dynamical states, including multiple synchronization transitions, of the associated coupled dynamics. The study illustrating rich dynamical behaviours could be pivotal to comprehending the impacts of higher-order interactions on dynamics of complex real-world networks, such as brain, social and technological, which have inherent multilayer networks architecture.

nlin.AO↗

arXiv2022

First-order route to antiphase clustering in adaptive simplicial complexes

This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights alter with time through a rate-based adaptive mechanism inspired by the Hebbian learning rule. These simultaneously evolving disparate adaptive coupling weights lead to a phenomenon in which the in-phase synchronization is completely obliterated; instead, the anti-phase synchronization is originated. In addition, the onsets of antiphase synchronization and desynchronization are manageable through both dyadic and triadic learning rates. The theoretical validation of these numerical assessments is delineated thoroughly by employing Ott-Antonsen dimensionality reduction. The framework and results of the Letter could help in the understanding of the underlying synchronization behavior of a range of real-world systems, such as brain functions and social systems where interactions evolve with time.

cond-mat.dis-nn↗

arXiv2022

Eigenvalue ratio statistics of complex networks: Disorder vs. Randomness

The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios distribution of various model networks, namely, small-world, Erdős-Rényi random, and (dis)assortative random having a diagonal disorder in the corresponding adjacency matrices. Without any diagonal disorder, the eigenvalues ratio distribution of these model networks depict Gaussian orthogonal ensemble (GOE) statistics. Upon adding diagonal disorder, there exists a gradual transition from the GOE to Poisson statistics depending upon the strength of the disorder. The critical disorder (wc) required to procure the Poisson statistics increases with the randomness in the network architecture. We relate wc with the time taken by the maximum entropy random walker to reach the steady-state. These analyses will be helpful to understand the role of eigenvalues other than the principal one for various network dynamics such as transient behaviour.

cond-mat.dis-nn↗

arXiv2022

Hebbian plasticity rules abrupt desynchronization in pure simplicial complexes

This Letter investigates the upshots of adaptive development of pure 2- and 3- simplicial complexes (triad and tetrad) on the nature of the transition to desynchrony of the oscillator ensembles. The adaptation exercised in the pure simplicial coupling takes a cue from the Hebbian learning rule, i.e., the coupling weight of a triad (tetrad) is prone to increase if the oscillators forming it are in phase and decrease if they are out of phase. The coupling weights in these pure simplicial complexes experiencing such adaptation give rise to first-order routes to desynchronization, whose onsets are entirely characterized by respective Hebbian learning parameters. Mean-field analyses presented for the order parameters for the adaptive 2- and 3- simplicial complexes strongly corroborate with the respective numerical assessments.

nlin.AO↗

arXiv2022

Explosive synchronization and chimera in interpinned multilayer networks

This Letter investigates the nature of synchronization in multilayered and multiplexed populations in which the interlayer interactions are randomly pinned. First, we show that a multilayer network constructed by setting up all-to-all interlayer connections between the two populations leads to explosive synchronization in the two populations successively, leading to the coexistence of coherent and incoherent populations forming chimera states. Second, a multiplex formation of the two populations in which only the mirror nodes are interconnected espouses explosive transitions in the two populations concurrently. The occurrence of both explosive synchronization and chimera are substantiated with rigorous theoretical mean-field analysis. The random pinning in the interlayer interactions concerns the practical problems where the impact of dynamics of one network on that of other interconnected networks remains elusive, as is the case for many real-world systems.

nlin.AO↗

arXiv2021

Network construction: A learning framework through localizing principal eigenvector

Information of localization properties of eigenvectors of the complex network has applicability in many different areas which include networks centrality measures, spectral partitioning, development of approximation algorithms, and disease spreading phenomenon. For linear dynamical process localization of principal eigenvector (PEV) of adjacency matrices infers condensation of the information in the smaller section of the network. For a network, an eigenvector is said to be localized when most of its components are near to zero with few taking very high values. Here, we provide three different random-sampling-based algorithms which, by using the edge rewiring method, can evolve a random network having a delocalized PEV to a network having a highly localized PEV. In other words, we develop a learning framework to explore the localization of PEV through a random sampling-based optimization method. We discuss the drawbacks and advantages of these algorithms. Additionally, we show that the construction of such networks corresponding to the highly localized PEV is a non-convex optimization problem when the objective function is the inverse participation ratio. This framework is also relevant to construct a network structure for other lower-order eigenvectors.

physics.soc-ph↗

arXiv2021

Random Matrix Analysis of Multiplex Networks

We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two random networks, the spectra of the combined multiplex network exhibit superposition of two Gaussian orthogonal ensemble (GOE)s for very small multiplexing strength followed by a smooth transition to the GOE statistics with an increase in the multiplexing strength. Interestingly, randomness in the connection architecture, introduced by random rewiring to 1D lattice, of at least one layer may govern nearest neighbor spacing distribution (NNSD) of the entire multiplex network, and in fact, can drive to a transition from the Poisson to the GOE statistics or vice versa. Notably, this transition transpires for a very small number of the random rewiring corresponding to the small-world transition. Ergo, only one layer being represented by the small-world network is enough to yield GOE statistics for the entire multiplex network. Spectra of adjacency matrices of underlying interaction networks have been contemplated to be related with dynamical behaviour of the corresponding complex systems, the investigations presented here have implications in achieving better structural and dynamical control to the systems represented by multiplex networks against structural perturbation in only one of the layers.

cond-mat.stat-mech↗