arXiv subjects

Sarika Jalan

Publications and source records attributed to Sarika Jalan.

At least 19 recordsLinked to original sources

arXiv2026

Multiple hysteresis widths in inertial Kuramoto model

Multistability is a well-known feature of the inertial Kuramoto system (KMI). Here, we demonstrate that an interplay of phase lag and triadic interactions in KMI leads to distinct hysteresis widths corresponding to different stable states. This phenomenon becomes more pronounced with increasing inertia. Theoretical calculations for the backward branch based on self-consistent analysis show that these multiple widths arise from saddle-node bifurcation occurring at different coupling strengths. Moreover, the forward branch corresponds to oscillatory state and does not admit steady-state solution. The study of multiple hysteresis widths may be useful in modeling power grid systems, information storage, and memory selection in real-word systems.

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arXiv2026

Finite-time Lyaponov analysis of a trained reservoir computer

We use finite-time Lyapunov exponent (FTLE) distributions to probe transition mechanisms in high-dimensional reservoir maps trained on low-dimensional chaotic dynamics across multiple regimes. While trained reservoirs accurately predict critical transitions and regime shifts, conventional analyses based on time series or bifurcation structure provide limited mechanistic insight, since distinct pathways in high dimensions can yield similar outputs. We show that FTLE statistics overcome this limitation. This is particularly important for interior crises, where direct identification of unstable periodic orbit collisions in the reservoir space is infeasible. Using the logistic map as a canonical example exhibiting intermittency, fully developed chaos, and crisis-induced transitions, we demonstrate that although such distinct regimes are difficult to characterize within the high dimensional reservoir space, their FTLE distributions are faithfully reproduced. This establishes FTLE analysis as a systematic and reliable framework for uncovering transition mechanisms in learned reservoir dynamics.

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arXiv2026

Interplay of inertia and external forcing in Kuramoto model

The impact of external forcing is well studied in the Kuramoto model without inertia, but remains unclear for inertial Kuramoto oscillators (KMI) with bimodal intrinsic frequency distributions. This article fills that gap, showing that competition between external forcing and intrinsic bimodality can suppress the intermediate standing wave states of bimodal KMI by entraining oscillators to the external forcing. Using a self-consistent analytical framework, we show that, for a bimodal distribution, forcing makes the backward transition discontinuous, unlike the continuous transition in the unimodal case. Further, for a bi-delta distribution, we derive a closed form expression for the backward solution branch. These results clarify how intrinsic frequency structure shapes the effect of external forcing, with implications for biological systems (e.g., photoreceptor and pacemaker cells) and for pinning-control strategies in multi-agent networks.

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arXiv2026

Second-order Kuramoto model with adaptive simplicial complex

We investigate the emergence of synchronization in the second-order Kuramoto model with adaptive simplicial interactions on a globally connected network. This inertial Kuramoto framework describes systems, where oscillator frequencies evolve over time. Unlike most previous work that ignores inertia, we examine how inertia combined with adaptive higher-order coupling alters synchronization transitions. Using self-consistency analysis, we derive the steady-state behavior and show that adaptation qualitatively reshapes the synchronization landscape. We find that the backward transition from synchronization to incoherence remains controlled by the adaptive feedback parameter, but the forward discontinuous jump to synchronization vanishes in the thermodynamic limit. In contrast, finite-size systems still display an abrupt transition to synchronization, with its onset precisely set by the adaptation control parameter. These results show how adaptive feedback and system size together govern the onset and robustness of synchronization in inertial oscillator networks with higher-order interactions.

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arXiv2025

Dynamics of reservoir computing for crises prediction

Reservoir computing has emerged as a powerful framework for time series modelling and forecasting including the prediction of discontinuous transitions. However, the mechanism behind its success is not yet fully understood. This letter elucidates the functioning of reservoir computing by examining its successful prediction of boundary and attractor merging crises. We investigate in detail how reservoirs's internal dynamics mimic the actual system, that enables it to accurately reproduce the scaling exponent near boundary crisis. We establish this across distinct systems, exemplified by the logistic and Gauss maps. The study contributes to the broader understanding of the internal dynamics that enable learning algorithms to anticipate critical transitions.

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arXiv2025

Scaling laws and relaxation rate at desynchronization in coupled oscillators

Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order transition i.e an abrupt jump in order parameter, we obtain the order parameter scaling exponent $1/2$ and show that the relaxation time diverges near the transition point, both numerically and analytically. We also verify a finite time finite size scaling by considering a correlation measure in the discrete set of all interacting units. Due to divergence in correlation measure at the transition point, the order parameter becomes a homogeneous function of all the relevent parameters. The homogeneity assumption is numerically verified using data collapse method. Various finite size scaling relations and exponents are also obtained. This study suggests that presence of non local interactions may allow for critical behaviour at a first order transition.

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arXiv2025

Low dimensional Watanabe-Strogatz approach for Kuramoto oscillators with higher-order interactions

Watanabe-Strogatz theory provides a low-dimensional description of identical Kuramoto oscillators via the framework of the M\"obius transformation. Here, using the Watanabe-Strogatz theory, we provide a unifying description for a broad class of identical Kuramoto oscillator models with pairwise and higher-order interactions and their corresponding higher harmonics. We show that the dynamics of the Watanabe-Strogatz parameters are the same as those of the mean-field parameters. Additionally, the poles of the M\"obius transformation serve as basin boundaries for both global and cluster synchronization in the models discussed here. We present numerical simulations that illustrate how the basins boundaries evolve for these extended models.

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arXiv2025

Finite size effect in Kuramoto oscillators with inertia on simplicial complex

We investigate the finite-size effects on the dynamical evolution of the Kuramoto model with inertia coupled through triadic interactions. Our findings reveal that fluctuations resulting from the finite size drive the system toward a synchronized state at finite coupling, which contrasts with the analytical predictions {in thermodynamic limit} made for the same system. Building on the analytical calculations performed at the thermodynamic limit, we identify the origin of the synchronization transition that arises because of the finite size. We discover a power-law relationship between the network size and the critical coupling at which the first-order transition to synchronization occurs. Additionally, as inertia increases, there is a significant shift in the critical coupling toward higher values, indicating that inertia counteracts the effects caused by finite size.

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arXiv2025

Dynamical phase transitions in postictal generalized EEG suppression

Postictal generalized EEG suppression (PGES) is a neurological condition that occurs in patients with generalized tonic-clonic seizures. It is marked by suppressed signals just after the seizure before the brain gradually recovers. Recovery from PGES involves a mixed state of amplitude suppression and high-amplitude oscillations, exhibiting a bimodal exponential distribution in power, unlike the unimodal exponential distribution of PGES. In this study, using the subcritical Hopf model, we explain the nature of phase transitions that underlie PGES. Our results reveal that recovery from PGES involves a change from a fixed point state to a bistable state (mixed phase), effectively captured by the noisy fixed-point and bistable regimes of the model. Consistent patterns across patients suggest a universal dynamical signature in PGES recovery. Our findings offer a mechanistic understanding of seizure termination and postictal brain state transitions.

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arXiv2025

Solitary states in spiking oscillators with higher-order interactions

We study a system of globally coupled FitzHugh-Nagumo oscillators, showing that the presence of higher-order interactions affects the character of the transition between synchronous and asynchronous states. In particular, we demonstrate that, around the synchronization transition, solitary states emerge due to the presence of second-order interactions. In difference to the phenomenology observed in systems of phase oscillators, we show that, at low coupling strengths, solitary states appear for both transition directions, whereas for higher couplings they only occur in the forward direction, with the backwards one characterized by explosive desynchronization.

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arXiv2024

Stochastic Kuramoto oscillators with inertia and higher-order interactions

Impact of noise in coupled oscillators with pairwise interactions has been extensively explored. Here, we study stochastic second-order coupled Kuramoto oscillators with higher-order interactions, and show that as noise strength increases the critical points associated with synchronization transitions shift toward higher coupling values. By employing the perturbation analysis, we obtain an expression for the forward critical point as a function of inertia and noise strength. Further, for overdamped systems we show that as noise strength increases, the first-order transition switches to second-order even for higher-order couplings. We include a discussion on nature of critical points obtained through Ott-Antonsen ansatz.

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arXiv2024

Dynamical analysis of a parameter-aware reservoir computer

Reservoir computing has been shown to be a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. Its utility is significant because in real-world scenarios, the exact model equations are unknown. This Letter shows how the theory of dynamical system provides the underlying mechanism behind the prediction. Using numerical methods, by considering dynamical systems which show Hopf bifurcation, we demonstrate that the map produced by the reservoir after a successful training undergoes a Neimark-Sacker bifurcation such that the critical point of the map is in immediate proximity to that of the original dynamical system. In addition, we have compared and analyzed different structures in the phase space. Our findings provide insight into the functioning of machine learning algorithms for predicting critical transitions.

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arXiv2024

Finite-size effect in Kuramoto phase oscillators with higher-order interactions

Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto phase oscillators with higher-order interactions, and observe that fluctuations inherent to finite-size systems drives the transition to the synchronized state occurring before the critical point in the thermodynamic limit. Using numerical methods, we plot the first exit time distribution of the magnitude of complex order parameter and obtain numerical transition probabilities across various system sizes. Further, we extend this study to a two-population oscillator system, and using velocity field of the associated order parameters, show the emergence of a new fixed point corresponding to a partially synchronized state arising due to the finite-size effect which is absent in the thermodynamics limit.

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arXiv2024

Prolonged hysteresis in the Kuramoto model with inertia and higher-order interactions

The inclusion of inertia in the Kuramoto model has been long reported to change the nature of phase transition, providing a fertile ground to model the dynamical behaviors of interacting units. More recently, higher-order interactions have been realized as essential for the functioning of real-world complex systems ranging from the brain to disease spreading. Yet, analytical insights to decipher the role of inertia with higher-order interactions remain challenging. Here, we study the Kuramoto model with inertia on simplicial complexes, merging two research domains. We develop an analytical framework in a mean-field setting using self-consistent equations to describe the steady-state behavior, which reveals a prolonged hysteresis in the synchronization profile. Inertia and triadic interaction strength exhibit isolated influence on system dynamics by predominantly governing, respectively, the forward and backward transition points. This work sets a paradigm to deepen our understanding of real-world complex systems such as power grids modeled as the Kuramoto model with inertia.

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arXiv2024

Rotating clusters in phase-lagged Kuramoto oscillators with higher-order interactions

The effect of phase-lag parameter in pairwise interactions has been a topic of great interest for long. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We investigate the effect of the inclusion of phase-lag in coupled Kuramoto oscillators with simplicial interactions and find that it shifts the critical points at which first-order transition from cluster synchronized state to incoherent state occurs. In the thermodynamic limit, using the Ott-Antonsen approach we derive a reduced equation for order parameter measuring cluster synchronization. Further, we progress through the self-consistency method to achieve a closed form of the order parameter measuring global synchronization which was lacking in Ott-Antonsen approach. Moreover, considering polar coordinates framework we obtain rotation frequency of the clusters which comes out to be a function of the phase-lag parameter further indicating that phase-lag can be used as a control parameter to achieve a desired cluster frequency.

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arXiv2023

Explosive synchronization in multiplex neuron-glial networks

Explosive synchronization refers to an abrupt (first order) transition to non-zero phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this phenomenon might be no less general then the celebrated Kuramoto scenario that belongs to the second order universality class. Importantly, the recent examples demonstrate that explosive synchronization can occur for certain network topologies and coupling types, like the global higher-order coupling, without specific requirements on the individial oscillator dynamics or dynamics-network correlations. Here we demonstrate a rich picture of explosive synchronization and desynchronization transitions in multiplex networks, where it is sufficient to have a single random sparsly connected layer with higher-order coupling terms (and not necessarily in the synchronization regime on its own), the other layer being a regular lattice without own phase transitions at all. Moreover, explosive synchronization emerges even when the random layer has only low-order pairwise coupling, althoug the hysteresis interval becomes narrow and explosive desynchronization is no longer observed. The relevance to the normal and pathological dynamics of neural-glial networks is pointed out.

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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.

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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.

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