Prosenjit Kundu

• PhD
• Professor (Assistant) at Dhirubhai Ambani Institute of Information and Communication Technology

This study aims to develop a generalised concept that will enable double explosive transitions in the forward and backward directions or a combination thereof. We found two essential factors for generating such phase transitions: the use of higher-order (triadic) interactions and the partial adaptation of a global order parameter acting on the tria...

We investigate the phenomenon of transition to synchronization in Sakaguchi-Kuramoto model in the presence of higher-order interactions and global order parameter adaptation. The investigation is done by performing extensive numerical simulations and low dimensional modeling of the system. Numerical simulations of the full system show both continuo...

The study of first order transition (explosive synchronization) in an ensemble (network) of coupled oscillators has been the topic of paramount interest among the researchers for more than one decade. Several frameworks have been proposed to induce explosive synchronization in a network and it has been reported that phase frustration in a network u...

Achieving perfect synchronization in a complex network, specially in the presence of higher-order interactions (HOIs) at a targeted point in the parameter space, is an interesting, yet challenging task. Here we present a theoretical framework to achieve the same under the paradigm of the Sakaguchi-Kuramoto (SK) model. We analytically derive a frequ...

The study of first order transition (explosive synchronization) in an ensemble (network) of coupled oscillators has been the topic of paramount interest among the researchers for more than onedecade. Several frameworks have been proposed to induce explosive synchronization in a network and it has been reported that phase frustration in a network us...

We investigate epidemic spreading in a deterministic susceptible-infected-susceptible model on uncorrelated heterogeneous networks with higher-order interactions. We provide a recipe for the construction of one-dimensional reduced model (resilience function) of the N-dimensional susceptible-infected-susceptible dynamics in the presence of higher-or...

We propose a framework for achieving perfect synchronization in complex networks of Sakaguchi-Kuramoto oscillators in presence of higher order interactions (simplicial complexes) at a targeted point in the parameter space. It is achieved by using an analytically derived frequency set from the governing equations. The frequency set not only provides...

Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multi-stage transitions in which some nodes experience a regime shift earlier than others as an environment gradually changes. Here we investigate early warning signals for networked syste...

Many complex dynamical systems in the real world, including ecological, climate, financial and power-grid systems, often show critical transitions, or tipping points, in which the system’s dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and crosse...

Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multistage transitions in which some nodes experience a regime shift earlier than others as an environment gradually changes. Here we investigate early warning signals for networked system...

Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics. One strategy of dimension reduction is to derive a low-dimensional dynamical system whose behavior approximates the observables of the original dynamical system that are weighted linear summations o...

Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and cross...

Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics. One strategy of dimension reduction is to derive a low-dimensional dynamical system whose behavior approximates the observables of the original dynamical system that are weighted linear summations o...

Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature (London) 530, 307 (2016)0028-083610.1038/nature16948] proposed a theoretical framework to reduce dynamical systems on networks, which are high dimensio...

Symmetries in a network connectivity regulate how the graph’s functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard, or even impossible, execution for large sized graphs. We here unveil that there is a direct connection between...

Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao {\it et al.} [Nature, {\bf{530}}, 307 (2016)] proposed a theoretical framework to reduce dynamical systems on networks, which are high-dimensional in general, to one-...

Symmetries in a network connectivity regulate how the graph’s functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard, or eve impossible, execution for large sized graphs. We here unveil that there is a direct connection between...

We present an adaptive coupling strategy to induce hysteresis/explosive synchronization in complex networks of phase oscillators (Sakaguchi–Kuramoto model). The coupling strategy ensures explosive synchronization with significant explosive width enhancement. Results show the robustness of the strategy, and the strategy can diminish (by inducing enh...

We present an analytical scheme to achieve optimal synchronization in multiplex networks of frustrated and non-frustrated phase oscillators. We derive a multiplex synchrony alignment function (MSAF) for that purpose, the expression of which consists of structural as well as dynamical information of the layers of the multiplex network. Analyzing the...

We study the spatiotemporal dynamics of a conductance-based neuronal cable. The processes of one-dimensional (1D) and 2D diffusion are considered for a single variable, which is the membrane voltage. A 2D Morris-Lecar (ML) model is introduced to investigate the nonlinear responses of an excitable conductance-based neuronal cable. We explore the par...

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 state (OS), we systematically identify thre...

We investigate the phenomenon of first-order transition [explosive synchronization (ES)] in an adaptively coupled phase-frustrated bilayer multiplex network. We consider Sakaguchi-Kuramoto 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...

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...

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...

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...

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 transi...