arXiv subjects

Chandrakala Meena

Publications and source records attributed to Chandrakala Meena.

At least 19 recordsLinked to original sources

arXiv2026

Stability of large dynamical systems using Gershgorin Disc Theorem

Understanding the stability of large nonlinear dynamical systems is a fundamental problem in many fields, including biological, technological, and social networks. Traditional stability methods often rely on explicit eigenvalue calculations or the construction of Lyapunov functions, which become computationally difficult for large interconnected systems. In this work, we introduce a stability classifier that provides a computationally efficient way to determine the stability of complex systems without performing full spectral analysis. Our approach combines the Dynamical Jacobian Ensemble framework, which uses the network structure and the underlying dynamics to construct a Jacobian, with the Gershgorin disc theorem, which provides bounds on the eigenvalues of the system's Jacobian matrix. Using this combination, we derive an analytical classifier that predicts whether a dynamical system is asymptotically stable, unstable, or sensitively stable based on a small set of dynamical and network parameters. The analysis reveals that the stability of large dynamical systems is strongly influenced by highly connected hub nodes. This observation allows the stability condition to be simplified by focusing on the contribution of the hub-associated Gershgorin disc. Extensive numerical simulations on large ensembles of Jacobian matrices confirm that the proposed classifier accurately separates stable, unstable, and sensitively stable regimes across a wide range of dynamical parameters and network structures. The resulting framework provides a simple and scalable tool for predicting the stability of large dynamical networks while capturing the interplay between network topology and interaction dynamics.

math.DS↗

arXiv2026

Chimera States in Wheel Networks

Chimera states, characterized by the coexistence of coherent and incoherent dynamics, are a hallmark of symmetry-breaking phenomena in networks of coupled oscillators. Here, we investigate the role of higher-order interactions in the emergence of chimera states in wheel networks of Rössler and Lorenz oscillators with pairwise and higher-order interactions under diffusive, conjugate, and mean-field diffusive coupling. Using multiple random initial conditions, we quantify the prevalence of synchronized, desynchronized, chimera, and synchronized cluster states. Chimera states emerge across all three coupling mechanisms as symmetry-broken states among the structurally and dynamically equivalent peripheral oscillators. Higher-order interactions substantially reorganize the dynamical landscape; in particular, they shift chimera states toward weaker pairwise coupling under diffusive coupling, predominantly support them at moderate coupling strengths under conjugate coupling, and yield comparatively less prevalent chimera states under mean-field diffusive coupling. These effects depend strongly on the intrinsic oscillator dynamics, particularly at larger higher-order coupling strengths. Overall, higher-order interactions neither universally promote nor suppress chimera states; rather, their influence is governed by the interplay between network symmetry, coupling mechanism, and intrinsic oscillator dynamics. The observed collective states are quantitatively characterized using two proposed statistical measures, while master-stability-function analysis provides a stability-based explanation for the loss of complete synchronization and the emergence of nonsynchronous dynamical regimes.

nlin.CD↗

arXiv2026

Postselection-induced localization and coherence in quantum walks on heterogeneous networks

Postselection of quantum trajectories is known effectively introduce nonlinearity into dynamics of open quantum systems. We study the effect of such non-linearity in continuous-time quantum walks (CTQWs) on networks with homogeneous and heterogeneous degree distributions. Using the recently proposed nonlinear Lindblad master equation (NLME), we investigate the dynamics under two decoherence mechanisms: Haken-Strobl and quantum stochastic walk (QSW). Our analysis reveals a striking dichotomy: under Haken-Strobl decoherence the nonlinear contributions precisely cancel, yielding a uniform steady state independent of postselection details under imperfect detection. In stark contrast, QSW decoherence permits postselection in this regime to break dynamical balance on heterogeneous networks, inducing robust localization preferentially at low-degree (peripheral) nodes. Remarkably, this localized state maintains finite quantum coherence. Extending our results to many-body spin systems, we demonstrate that degree heterogeneity similarly stabilizes localization of spin-up excitations in spin-down backgrounds, enhancing entanglement preservation. These findings establish degree heterogeneity and postselection as joint control parameters for engineering quantum transport and localization in dissipative dynamics.

quant-ph↗

arXiv2026

Gravity-Driven Eco-Epidemiological Dynamics in Tri-Trophic Food Chains

Ecological communities are shaped by the interplay between trophic interactions and infectious disease, yet how spatially mediated interactions influence disease-driven ecosystem dynamics remains poorly understood. Here, we develop a gravity-based eco-epidemiological framework for a tri-trophic food chain in which trophic interaction depends on species abundances and effective interaction distance. The disease-free food chain system supports a stable coexistence equilibrium, providing a baseline for investigating disease-induced ecological transitions. Introducing infection at the intermediate trophic level destabilizes this equilibrium through a Hopf bifurcation, leading to sustained oscillations, whereas infection at the top predator level results in a qualitatively different transition from persistence to extinction. By systematically varying the gravity coupling strength, we show that gravity-mediated trophic interactions regulate the thresholds separating these ecological regimes, while the trophic position of infection determines the nature of the transition. Together, these findings establish a unified framework for understanding how spatially mediated trophic interactions and infectious disease jointly govern ecosystem stability, providing new insights into disease-driven dynamics in ecological communities.

q-bio.PE↗

arXiv2026

Effect of Colored Noise on Coupled Thermoacoustic Oscillators

Noise can significantly influence thermoacoustic dynamics, yet the role of noise color in coupled thermoacoustic oscillators remains largely unexplored. Here, we examine the influence of colored noise on the dynamics of coupled thermoacoustic systems. The system consists of two coupled Rijke tube oscillators with time-delay and dissipative coupling. Stochastic forcing is modeled as an additive Ornstein-Uhlenbeck (OU) process, such that white and colored noise contain equal power within a band around the system's natural frequency. We find that noise influences the system most prominently near the transition between limit-cycle oscillations (LCO) and amplitude death (AD) states, where increasing noise amplitude smoothen the transition and reduces the extent of the AD regions. Our analysis reveals the emergence of coherence resonance near instability threshold under both white and colored noise. The peak coherence factor varies with the noise color, with the largest peak coherence observed for colored noise whose correlation time is much shorter than the acoustic time scale. White noise and the shortest-correlated OU noise exert the strongest influence on both the pressure amplitude response and the coherence resonance. Overall, our results show that, under both coupling mechanisms, colored noise induces qualitatively similar trends in the system response, governed by its amplitude and correlation time.

nlin.CD↗

arXiv2026

Synchronization in Networks of Heterogeneous Kuramoto-Sakaguchi Oscillators with Higher-order Interactions

How do the combined effects of phase frustration, noise, and higher-order interactions govern synchronization in globally coupled heterogeneous Kuramoto oscillators? To address this question, we investigate a globally coupled network of Kuramoto-Sakaguchi oscillators that includes both pairwise (1-simplex) and higher-order (2-simplex) interactions, together with additive stochastic forcing. Systematic numerical simulations across a broad range of coupling strengths, phase-lag values, and noise intensities reveal that synchronization emerges through a nontrivial interplay among these parameters. In general, weak frustration combined with mutually reinforcing coupling promotes synchronization, whereas strong frustration favors coherence under repulsive coupling. Forward and backward parameter sweeps reveal the coexistence of synchronized and desynchronized states. The presence and width of this bistable region depend sensitively on phase frustration, noise intensity, and higher-order coupling strength, with higher-order interactions significantly widening the bistable interval. To explain these behaviors, we employ the Ott-Antonsen reduction to derive a low-dimensional amplitude equation that predicts the forward critical point in the thermodynamic limit, the backward saddle-node point, and the width of the bistable region. Higher order interactions widen this region by shifting the saddle-node point without affecting the forward critical point. Further analysis of Kramer's escape rate explains how noise destabilizes coexistence states and diminishes bistability. Overall, our results provide a unified theoretical and numerical framework for frustrated, noisy, higher-order oscillator networks, revealing that synchronization is strongly influenced by the combined action of phase frustration, stochasticity, and both pairwise and higher-order interactions.

nlin.CD↗

arXiv2026

Deep learning for classifying dynamical states from time series via recurrence plots

Recurrence Quantification Analysis (RQA) is a widely used method for capturing the dynamical structure embedded in time series data, relying on the analysis of recurrence patterns in the reconstructed phase space via recurrence plots (RPs). Although RQA proves effective across a range of applications, it typically requires the computation of multiple quantitative measures, making it both computationally intensive and sensitive to parameter choices. In this study, we adopt an alternative approach that bypasses computation of recurrence measures by directly using images of RP as input to a deep learning model. We propose a new dual-branch deep learning model named DBResNet-50 built on the ResNet-50 architecture. We compare its performance with standard ResNet-50 and MobileNetV2. Our DBResNet-50 model, trained exclusively on simulated time series, accurately classifies seven dynamical regimes: periodic, quasi-periodic, chaotic, hyperchaotic, white noise, pink noise, and red noise. Further, to assess its generalizability, we test the trained model on RP images generated from standard dynamical systems not included in the training set, as well as experimental datasets from a Chua circuit, X-ray light curves from the black-hole system GRS 1915+105, and observational light curves of the variable stars AC Her, SX Her, and Chi Cygni. In all cases, DBResNet-50 outperforms the baselines and correctly predicts the known dynamics of these systems. The model further used to infers the relative contributions of deterministic and stochastic components within a signal, as observed in temperature data from Ladakh and Ranchi. These results demonstrate the robustness and versatility of our deep learning framework and underscore the potential of RP image-based models as fast, accurate, and scalable tools for classifying dynamical states in both synthetic and real-world time series data.

nlin.CD↗

arXiv2026

Stability of Continuous Time Quantum Walks in Complex Networks

We investigate the stability of continuous-time quantum walks (CTQW) across cycle, complete, star, Erdős-Rényi, small-world, and scale-free topologies under energy-based intrinsic decoherence, node-based Haken-Strobl noise, and edge-based quantum stochastic walk (QSW) decoherence. Defining stability as the preservation of quantum properties, we characterize it using node probabilities, $\ell_1$-norm of coherence, fidelity, quantum-classical distance, and von Neumann entropy. Our results show that intrinsic decoherence preserves coherence longest while QSW causes rapid decay. Stability rankings vary and depend on the decoherence types, network structure, and properties of node where the walker is initialized specifically in heterogeneous networks. Dense connected network like complete and heterogenous networks, for instance, star, and scale-free are stable under Haken-Strobl noise but become uniquely fragile under QSW when initialized on high degree nodes. However, these same networks, due to their inherent localization, exhibit lower coherence in the noiseless regime, highlighting a fundamental trade-off between localization and coherence. Furthermore, the centrality of the initialization node has a pronounced impact on relaxation time and stability measures, underscoring the critical role of local topological features in quantum dynamics.

quant-ph↗

arXiv2025

Origins of Instability in Dynamical Systems on Undirected Networks

Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general class of networked dynamical systems, which contains information on how perturbations to a stationary state develop over time. We find that stability is always determined by a spectral outlier, but with pronounced differences to the corresponding eigenvector in different regimes. We show that, depending on model details, instability may originate in nodes of anomalously low or high degree, or may occur everywhere in the network at once. Importantly, the dependence on extremal degrees results in considerable finite-size effects with different scaling depending on the ensemble degree distribution. Our results have potentially useful applications in network monitoring to predict or prevent catastrophic failures, and we validate our analytical findings through applications to epidemic dynamics and gene regulatory systems.

nlin.AO↗

arXiv2025

Perplexity-Homophily Index: Homophily through Diversity in Hypergraphs

Real-world complex systems are often better modeled as hypergraphs, where edges represent group interactions involving multiple entities. Understanding and quantifying homophily (similarity-driven association) in such networks is essential for analyzing community formation and information flow. We propose a hyperedge-centric framework to quantify homophily in hypergraphs. Each interaction is represented as a hyperedge, and its interaction perplexity measures the effective number of distinct attributes it contains. Comparing this observed perplexity with a degree-preserving random baseline defines the diversity gap, which quantifies how diverse an interaction is than expected by chance. The global homophily score for a network, called Perplexity-Homophily Index, is computed by averaging the normalized diversity gap across all hyperedges. Experiments on synthetic and real-world datasets show that the proposed index captures the full distribution of homophily and reveals how homophilic and heterophilic tendencies vary with interaction size in hypergraphs.

cs.SI↗

arXiv2025

Scientific mobility patterns of Indian researchers: Impact on career growth

Scientific mobility shapes individual research careers and national innovation by enabling knowledge exchange, fostering collaborations, and providing access to leading research environments. Studying international mobility patterns of researchers from developing countries offers insights into strengthening domestic scientific ecosystems and addressing talent migration. We analyze the international mobility of India-affiliated researchers using longitudinal affiliation trajectories from the OpenAlex database, covering 157,471 researchers categorized as immobile, returnees, or settled abroad after moving to the US, EU, or other high-income countries. Our analysis shows that 28% experience at least one international move, yet over 73% never return, highlighting persistent brain drain. Internationally mobile researchers predominantly originate from premier Indian institutions. Matched pair analyses demonstrate that mobility yields lasting benefits: citation impact increases, publication rates align with immobile peers, and international collaboration rises-foreign co-author share grows from 52% to 83-87% at transition abroad and remains elevated among returnees (32-40 percentage points across disciplines). Returnees maintain global networks, bridging Indian science with global research. These patterns are consistent across major research disciplines, emphasizing that scientific mobility drives excellence and engagement while posing challenges for developing nations seeking to reintegrate talent.

physics.soc-ph↗

arXiv2025

Homophily in Complex Networks: Measures, Models, and Applications

Homophily, the tendency of individuals to connect with others who share similar attributes, is a defining feature of social networks. Understanding how groups interact, both within and across, is crucial for uncovering the dynamics of network evolution and the emergence of structural inequalities in these network. This tutorial offers a comprehensive overview of homophily, covering its various definitions, key properties, and the limitations of widely used metrics. Extending beyond traditional pairwise interactions, we will discuss homophily in higher-order network structures such as hypergraphs and simplicial complexes. We will further discuss network generating models capable of producing different types of homophilic networks with tunable levels of homophily and highlight their relevance in real-world contexts. The tutorial concludes with a discussion of open challenges, emerging directions, and opportunities for further research in this area.

cs.SI↗

arXiv2025

IPSR Model: Misinformation Intervention through Prebunking in Social Systems

The rapid dissemination of misinformation through online social networks poses a growing threat to public understanding and societal stability. Prebunking, a proactive strategy based on inoculation theory, has recently emerged as an effective intervention to build cognitive resilience against misinformation before exposure. In this work, we investigate the impact of prebunking on misinformation dynamics using a compartmental modeling framework. We first analyze the classical Ignorant-Spreader-Stifler (ISR) model, its parameters are determined using empirical rumor data from Twitter. We then propose an extended model, the Ignorant-Prebunked-Spreader-Stifler (IPSR) model, which incorporates prebunking as a preventive state and includes a forgetting mechanism to account for the decay of cognitive immunity over time. Using mean-field approximations, we derive steady-state solutions and examine the effect of prebunking on the spreading of misinformation. We further investigate the robustness of the IPSR model by varying network size and average degree. In addition, we analyze the model's behavior on Watts-Strogatz and Barabasi-Albert networks to assess the role of small-world and scale-free structures in shaping intervention outcomes. Our results show that the inclusion of prebunking significantly reduces the scale of misinformation outbreaks across different network structures. These findings highlight the efficacy of prebunking as a scalable intervention strategy and underscore the utility of compartmental models in understanding and mitigating information-based contagion in complex networks.

physics.soc-ph↗

arXiv2025

Master Stability Functions in Complex Networks

Synchronization is an emergent and fundamental phenomenon in nature and engineered systems. Understanding the stability of a synchronized phenomenon is crucial for ensuring functionality in various complex systems. The stability of the synchronization phenomenon is extensively studied using the Master Stability Function (MSF). This powerful and elegant tool plays a pivotal role in determining the stability of synchronization states, providing deep insights into synchronization in coupled systems. Although MSF analysis has been used for 25 years to study the stability of synchronization states, a systematic investigation of MSF across various networked systems remains missing from the literature. In this article, we present a simplified and unified MSF analysis for diverse undirected and directed networked systems. We begin with the analytical MSF framework for pairwise-coupled identical systems with diffusive and natural coupling schemes and extend our analysis to directed networks and multilayer networks, considering both intra-layer and inter-layer interactions. Furthermore, we revisit the MSF framework to incorporate higher-order interactions alongside pairwise interactions. To enhance understanding, we also provide a numerical analysis of synchronization in coupled Rössler systems under pairwise diffusive coupling and propose algorithms for determining the MSF, identifying stability regimes, and classifying MSF functions. Overall, the primary goal of this review is to present a systematic study of MSF in coupled dynamical networks in a clear and structured manner, making this powerful tool more accessible. Furthermore, we highlight cases where the study of synchronization states using MSF remains underexplored. Additionally, we discuss recent research focusing on MSF analysis using time series data and machine learning approaches.

nlin.AO↗

arXiv2024

Machine learning approach to detect dynamical states from recurrence measures

We integrate machine learning approaches with nonlinear time series analysis, specifically utilizing recurrence measures to classify various dynamical states emerging from time series. We implement three machine learning algorithms Logistic Regression, Random Forest, and Support Vector Machine for this study. The input features are derived from the recurrence quantification of nonlinear time series and characteristic measures of the corresponding recurrence networks. For training and testing we generate synthetic data from standard nonlinear dynamical systems and evaluate the efficiency and performance of the machine learning algorithms in classifying time series into periodic, chaotic, hyper-chaotic, or noisy categories. Additionally, we explore the significance of input features in the classification scheme and find that the features quantifying the density of recurrence points are the most relevant. Furthermore, we illustrate how the trained algorithms can successfully predict the dynamical states of two variable stars, SX Her and AC Her from the data of their light curves.

physics.data-an↗

arXiv2023

Emergent stability in complex network dynamics

The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any design for stability. What then are the naturally emerging organizing principles of complex-system stability? Encoded within the system's stability matrix, the Jacobian, the answer is obscured by the scale and diversity of the relevant systems, their broad parameter space, and their nonlinear interaction mechanisms. To make advances, here we uncover emergent patterns in the structure of the Jacobian, rooted in the interplay between the network topology and the system's intrinsic nonlinear dynamics. These patterns help us analytically identify the few relevant control parameters that determine a system's dynamic stability. Complex systems, we find, exhibit discrete stability classes, from asymptotically unstable, where stability is unattainable, to sensitive, in which stability abides within a bounded range of the system's parameters. Most crucially, alongside these two classes, we uncover a third class, asymptotically stable, in which a sufficiently large and heterogeneous network acquires a guaranteed stability, independent of parameters, and therefore insensitive to external perturbation. Hence, two of the most ubiquitous characteristics of real-world networks - scale and heterogeneity - emerge as natural organizing principles to ensure stability in the face of changing environmental conditions.

nlin.AO↗

arXiv2021

One-dimensional discrete-time quantum walks with general coin

Quantum walk (QW) is the quantum analog of the random walk. QW is an integral part of the development of numerous quantum algorithms. Hence, an in-depth understanding of QW helps us to grasp the quantum algorithms. We revisit the one-dimensional discrete-time QW and discuss basic steps in detail by incorporating the most general coin operator. We investigate the impact of each parameter of the general coin operator on the probability distribution of the quantum walker. We show that by tuning the parameters of the general coin, one can regulate the probability distribution of the walker. We provide an algorithm for the one-dimensional quantum walk driven by the general coin operator. The study conducted on general coin operator also includes the popular coins -- Hadamard, Grover, and Fourier coins.

quant-ph↗

arXiv2019

Resilience of networks of multi-stable chaotic systems to targetted attacks

We investigate the collective dynamics of chaotic multi-stable Duffing oscillators connected in different network topologies, ranging from star and ring networks, to scale-free networks. We estimate the resilience of such networks by introducing a variant of the concept of multi-node Basin Stability, which allows us to gauge the global stability of the collective dynamics of the network in response to large perturbations localized on certain nodes. We observe that in a star network, perturbing just the hub node has the capacity to destroy the collective state of the entire system. On the other hand, even when a majority of the peripheral nodes are strongly perturbed, the hub manages to restore the system to its original state. This demonstrates the drastic effect of the centrality of the perturbed node on the collective dynamics of the full network. Further, we explore scale-free networks of such multi-stable oscillators and demonstrate that targetted attacks on nodes with high centrality can destroy the collective dynamics much more efficiently than random attacks, irrespective of the nature of the nodal dynamics and type of perturbation. We also find clear evidence that the betweeness centrality of the perturbed node is most crucial for dynamical robustness, with the entire system being more vulnerable to attacks on nodes with high betweeness. These results are crucial for deciding which nodes to stringently safeguard in order to ensure the recovery of the network after targetted localized attacks.

nlin.CD↗