Chandrakala Meena

Adithya L J, Johannes Nokkala, Jyrki Piilo et al.

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.

Suman Acharyya, Priodyuti Pradhan, Chandrakala Meena

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.

Dheeraja Thakur, Athul Mohan, G. Ambika et al.

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.