arXiv subjects

Soumitro Banerjee

Publications and source records attributed to Soumitro Banerjee.

At least 19 recordsLinked to original sources

arXiv2026

Experimental Acquisition and Verification of Spectral Signatures of Dynamic Bifurcations

Spectral bifurcation diagrams (SBDs) have recently emerged as an efficient tool for identifying dynamical transitions in nonlinear systems through frequency-domain analysis. Previous studies have been limited to numerical investigations, and the experimental realization of SBDs has remained unexplored. In this work, we develop an automated framework using analog electronic circuits and data acquisition (DAQ) systems to obtain SBDs from real-time measurements. The method enables controlled parameter variation and simultaneous acquisition of time-series data for spectral analysis. Using this approach, we experimentally capture characteristic spectral signatures of dynamical bifurcations, such as period-doubling, quasiperiodicity (two- and three-frequency), and torus length-doubling. The experimental results show strong qualitative agreement with the numerical predictions, despite noise and parameter mismatches. This study establishes SBD as an effective tool for the experimental analysis of nonlinear dynamical systems.

nlin.CD↗

arXiv2026

Active Soft-Impact Oscillator: Dynamics of a Walking Droplet in a Non-Smooth Potential

Walking droplets are millimetric fluid drops that propel themselves across a vibrated liquid bath through interaction with their self-generated waves. They constitute classical active wave-particle entities and exhibit a range of hydrodynamic quantum analogs. We investigate an \emph{active soft-impact oscillator} as a minimal model for a walking droplet moving within a piecewise-smooth external potential, analogous to classical mass-spring soft-impact oscillators and recently explored quantum soft-impact oscillators. Our active soft-impact oscillator model couples a non-smooth soft-impact force to the Lorenz-like dynamics arising from the wave-particle entity. Theoretical and numerical exploration of the full parameter space reveals a wide variety of nonlinear behaviors and bifurcations driven by impact and grazing events. These include grazing-induced and impact-induced transitions between periodic and chaotic motion, as well as grazing-mediated attractor switching and impact-free (invisible) attractor switching. The active soft-impact oscillator thus provides a versatile platform for probing nonlinear impact dynamics in active systems and exploring hydrodynamic quantum analogs in non-smooth potentials.

nlin.CD↗

arXiv2025

Dynamical Chaos in a Dissipative Driven Quantum Soft Impact Oscillator

Dynamical chaos in a periodically driven, dissipative soft impact oscillator is investigated in the quantum regime using the complex-number quantum Langevin equation (c-number QLE). The averaged system dynamics are analyzed through a comprehensive suite of time-series diagnostics, including bifurcation diagrams, Lyapunov exponents, Fourier spectra, and the 0-1 test. Systematic variation of the wall position reveals a rich sequence of dynamical transitions and grazing bifurcations, progressing from periodic to multiperiodic motion and culminating in chaotic behavior. These results demonstrate the persistence of impact-induced chaos under quantum dissipation and elucidate how environmental fluctuations influence non-linear dynamics in open quantum systems.

quant-ph↗

arXiv2025

Dynamics of Quantum Analogs of Classical Impact Oscillators

This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum systems, governed by linear equations, appear to forbid such dynamics. Through simulations of unforced, forced, and dissipative quantum oscillators, we uncover quasiperiodicity, strange nonchaotic dynamics, and even chaos in the presence of dissipation. Using entropy time series, Fourier spectra, OTOCs, Lyapunov analysis, and the 0-1 test, we demonstrate that quantum systems can exhibit rich dynamical signatures analogous to classical nonlinear systems, bridging quantum mechanics and chaos theory.

quant-ph↗

arXiv2025

Doubling bifurcations of invariant closed curves in 3D maps

Numerous studies have reported two types of doubling of invariant closed curves (ICCs) in dynamical systems: (a) the creation of two disjoint ICCs such that iterations flip between them; and (b) the creation of a single ICC of double the length of the original ICC. Various methods have been proposed to analyze such bifurcations. We show that the methods proposed so far are not always adequate for analyzing and predicting these bifurcations. We propose a new method to overcome the difficulties.

math.DS↗

arXiv2025

Experimental verification of Generalised Synchronization

Generalized synchronization (GS) describes a state in which two coupled dynamical systems exhibit a functional relationship between their variables. GS can be achieved by appropriately designing the coupling to constrain the dynamics onto an invariant submanifold, a concept well established in theory. However, experimental validation remains crucial. In this work, we experimentally demonstrate GS using coupled chaotic Lorenz oscillators, implementing unidirectional coupling where the state variables of the slave oscillator are scaled according to a predefined relationship with those of the master oscillator.

nlin.CD↗

arXiv2023

How Network Topology Affects the Strength of Dangerous Power Grid Perturbations

Reasonably large perturbations may push a power grid from its stable synchronous state into an undesirable state. Identifying vulnerabilities in power grids by studying power grid stability against such perturbations can aid in preventing future blackouts. Probabilistic stability quantifiers such as basin stability, which measures the asymptotic stability of a system, and survivability, which measures the transient stability of a system, have been commonly used to quantify the stability of nodes in a power grid. However, these quantifiers do not provide information about the strength of perturbations that destabilize the system. To measure the strength of perturbations beyond which the stability of the system gets compromised, we employ two probabilistic distance-based stability measures -- basin stability bound, which deals with a system's asymptotic behaviour, and survivability bound, a newly defined stability measure that deals with a system's transient behaviour. Using these stability quantifiers, we conduct a detailed study on the impact of network topology on the strength of dangerous power grid perturbations. In this, we uncover a new class of highly vulnerable nodes that were previously unknown. Additionally, we establish connections with tree-like network structures and node connectivity to lowly stable nodes.

nlin.AO↗

arXiv2023

A Probabilistic Distance-Based Stability Quantifier for Complex Dynamical Systems

An attractor of a dynamical system may represent the system's 'desirable' state. Perturbations to the system may push the system out of the basin of attraction of the desirable attractor and into undesirable states. Hence, it is important to quantify the stability of such systems against reasonably large perturbations. In this paper, we introduce a distance-based measure of stability, called 'basin stability bound', to characterise the stability of dynamical systems against finite perturbations. This stability measure depends on both the size and the shape of the basin of attraction of the desirable attractor. A probabilistic sampling-based approach is used to estimate basin stability bound and quantify the associated estimation error. This approach allows for the easy estimation of basin stability bound regardless of the structure of the basin of attraction and is readily applicable to high-dimensional systems. We demonstrate the merit of the proposed stability measure using an ecological model of the Amazon rainforest, a ship capsize model, and a power grid model.

nlin.CD↗

arXiv2023

Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme

The problem of how measurement in quantum mechanics takes place has existed since its formulation. Von Neumann proposed a scheme where he treated measurement as a two-part process -- a unitary evolution in the full system-ancilla space and then a projection onto one of the pointer states of the ancilla (representing the "collapse" of the wavefunction). The Lindblad master equation, which has been extensively used to explain dissipative quantum phenomena in the presence of an environment, can effectively describe the first part of the von Neumann measurement scheme when the jump operators in the master equation are Hermitian. We have proposed a non-Hermitian Hamiltonian formalism to emulate the first part of the von Neumann measurement scheme. We have used the embedding protocol to dilate a non-Hermitian Hamiltonian that governs the dynamics in the system subspace into a higher-dimensional Hermitian Hamiltonian that evolves the full space unitarily. We have obtained the various constraints and the required dimensionality of the ancilla Hilbert space in order to achieve the required embedding. Using this particular embedding and a specific projection operator, one obtains non-Hermitian dynamics in the system subspace that closely follow the Lindblad master equation. This work lends a new perspective to the measurement problem by employing non-Hermitian Hamiltonians.

quant-ph↗

arXiv2023

Bifurcations of mode-locked periodic orbits in three-dimensional maps

In this paper, we report the bifurcations of mode-locked periodic orbits occurring in maps of three or higher dimensions. The `torus' is represented by a closed loop in discrete time, which contains stable and unstable cycles of the same periodicity, and the unstable manifolds of the saddle. We investigate two types of `doubling' of such loops: in (a) two disjoint loops are created and the iterates toggle between them, and in (b) the length of the closed invariant curve is doubled. Our work supports the conjecture of Gardini and Sushko, which says that the type of bifurcation depends on the sign of the third eigenvalue. We also report the situation arising out of Neimark-Sacker bifurcation of the stable and saddle cycles, which creates cyclic closed invariant curves. We show interesting types of saddle-node connection structures, which emerge for parameter values where the stable fixed point has bifurcated but the saddle has not, and vice versa.

math.DS↗

arXiv2023

Emulating the measurement postulates of quantum mechanics via non-Hermitian Hamiltonian

Ever since the formulation of quantum mechanics, there is very little understanding of the process of the collapse of a wavefunction. We have proposed a dynamical model to emulate the measurement postulates of quantum mechanics. We postulate that a non-Hermitian Hamiltonian operates during the process of measurement, which evolves any state to an attracting equilibrium state, thus, mimicking a "collapse". We demonstrate this using a 2-level system and then extend it to an N-level system. For a 2-level system, we also demonstrate that the dynamics generated by the Lindblad master equation can be replicated as an incoherent sum of the evolution by two separate non-Hermitian Hamiltonians.

quant-ph↗

arXiv2022

Sketching 1-D stable manifolds of 2-D maps without the inverse

Saddle fixed points are the centerpieces of complicated dynamics in a system. The one-dimensional stable and unstable manifolds of these saddle-points are crucial to understanding the dynamics of such systems. While the problem of sketching the unstable manifold is simple, plotting the stable manifold is not as easy. Several algorithms exist to compute the stable manifold of saddle-points, but they have their limitations, especially when the system is not invertible. In this paper, we present a new algorithm to compute the stable manifold of 2-dimensional systems which can also be used for non-invertible systems. After outlining the logic of the algorithm, we demonstrate the output of the algorithm on several examples.

nlin.CD↗

arXiv2021

Interaction-induced wavefunction collapse

Almost a century after the development of quantum mechanics, we still do not have a consensus on the process of collapse of wavefunctions. Some theories require the intervention of a conscious observer while some see it as a stochastic process, and most theories violate energy conservation. In this paper we hypothesise that the collapse of wavefunctions can be caused by interactions with other objects (macroscopic or microscopic) and energy is conserved in that process. To test various hypotheses regarding collapse of wavefunctions, we propose a model system which is the quantum analogue of a classical soft-impact oscillator. We propose some alternative postulates regarding the conditions for and the result of a collapse, and obtain the implication of each on the behavior of observable quantities, which can possibly be experimentally tested.

quant-ph↗

arXiv2021

Stellar mid-life crisis: subcritical magnetic dynamos of solar-like stars and the breakdown of gyrochronology

Recent observations reveal the surprising breakdown of stellar gyrochronology relations at about the Sun's age hinting that middle-aged, solar-like stars transition to a magnetically inactive future. We provide a theoretical basis for these intriguing observations inspired by simulations with a mathematical dynamo model that can explore long-term solar cycle fluctuations. We reproduce the observed bimodal distribution of sunspot numbers, but only for subcritical dynamos. Based on a bifurcation analysis, we argue that ageing of solar-like stars makes the magnetically-weak dynamo regime readily accessible. Weak magnetic field production in this regime compromises wind-driven angular momentum losses thus disrupting the hegemony of magnetic braking on stellar rotational spin-down. This hypothesis of {\emph{subcritical magnetic dynamos}} of solar-like stars provides a self-consistent, unifying physical basis for a diversity of solar-stellar phenomena such as why stars beyond their mid-life do not spin-down as fast as in their youth, the break-down of stellar gyrochronology relations, the observed bimodal distribution of long-term sunspot observations and recent findings suggesting that the Sun may be transitioning to a magnetically inactive future.

astro-ph.SR↗

arXiv2021

Limiting distribution of periodic position measurements of a quantum harmonic oscillator

We consider a particle in harmonic oscillator potential, whose position is periodically measured with an instrument of finite precision. We show that the distribution of the measured positions tends to a limiting distribution when the number of measurements tends to infinity. We derive the expression for the limiting position distribution and validate it with numerical simulation.

quant-ph↗

arXiv2020

Steady State Of Random Dynamical Systems

Random dynamical systems (RDS) evolve by a dynamical rule chosen independently with a certain probability, from a given set of deterministic rules. These dynamical systems in an interval reach a steady state with a unique well-defined probability density only under certain conditions, namely Pelikan's criterion. We investigate and characterize the steady state of a bounded RDS when Pelikan's criterion breaks down. In this regime, the system is attracted to a common fixed point (CFP) of all the maps, which is attractive for at least one of the constituent mapping functions. If there are many such fixed points, the initial density is shared among the CFPs; we provide a mapping of this problem with the well known hitting problem of random walks and find the relative weights at different CFPs. The weights depend upon the initial distribution.

cond-mat.stat-mech↗

arXiv2019

Shilnikov-type Dynamics in Three-Dimensional Piecewise Smooth Maps

We show the existence of Shilnikov-type dynamics and bifurcation behaviour in general discrete three-dimensional piecewise smooth maps and give analytical results for the occurence of such dynamical behaviour. Our main example in fact shows a `two-sided' Shilnikov dynamics, i.e. simultaneous looping and homoclinic intersection of the one-dimensional eigenmanfolds of fixed points on both sides of the border. We also present two complementary methods to analyse the return time of an orbit to the border: one based on recursion and another based on complex interpolation.

math.DS↗

arXiv2018

Origin and Recovery from Grand Solar Minima in a Time Delay Dynamo Model with Magnetic Noise as an Additional Poloidal Source

We explore a reduced Babcock-Leighton (BL) dynamo model based on delay differential equations using numerical bifurcation analysis. This model reveals hysteresis, seen in the recent mean-field dynamo model and the direct numerical simulations of turbulent dynamos. The BL model with 'magnetic noise' as an additional weak-source of the poloidal field recovers the solar cycle every time from grand minima, which BL source alone cannot do. The noise-incorporated model exhibits a bimodal distribution of toroidal field energy confirming two modes of solar activity. It also shows intermittency and reproduces phase space collapse, an experimental signature of the Maunder Minimum. The occurrence statistics of grand minima in our model agree reasonably well with the observed statistics in the reconstructed sunspot number. Finally, we demonstrate that the level of magnetic noise controls the duration of grand minima and even has a handle over its waiting period, suggesting a triggering effect of grand minima by the noise and thus shutting down the global dynamo. Therefore, we conclude that the 'magnetic noise' due to small-scale turbulent dynamo action (or other sources) plays a vital role even in Babcock-Leighton dynamo models.

astro-ph.SR↗