arXiv subjects

M. Senthilvelan

Publications and source records attributed to M. Senthilvelan.

At least 19 recordsLinked to original sources

arXiv2026

Second harmonic phase locking and synchronization blockade in quadratically coupled driven quantum van der Pol oscillators

We investigate the dynamics of a quadratically coupled system under the influence of an external drive applied to the second oscillator, where the coupling facilitates a high-order synchronization with phase-locking emerging in the form of 2:1 between the oscillators. Our analysis reveals a synchronization blockade in the first oscillator, characterized by the complete suppression of conventional 1:1 phase-locking with the drive. In contrast, we observe that the directly driven second oscillator synchronizes with the drive, showing 1:1 phase-locking but notably at second harmonic frequency. A classical mean-field analysis of the corresponding equations of motion reproduces this asymmetric phase-locking geometry which demonstrates that the phase-locking structure itself can be understood from the nonlinear classical dynamics. The quantum analysis, however, reveals the microscopic origin of the synchronization blockade. Furthermore, we show that the system exhibits mutual synchronization when both the oscillators satisfies the resonance condition, enabling coherent energy exchange facilitated by nonlinear quadratic coupling. The mutual synchronization shows synchronized regimes and also subtle suppression of synchronized regimes near resonance occurring due to spectral splitting of the energy states. Using perturbation analysis of the master equation within the low excitation subspace, we analyze steady-state phase distribution and synchronization measures, supported by population statistics and spectral responses. We also propose possible experimental realizations in trapped-ions and optomechanical setups. These findings highlight the crucial role of quadratic coupling in enabling nonclassical synchronization phenomena, offering deeper insights for quantum control strategies and the development of quantum information platforms.

quant-ph↗

arXiv2026

Normal mode splitting induced synchronization blockade in coupled quantum van der Pol oscillators

We report a normal-mode induced synchronization blockade in coupled quantum van der Pol oscillators under the influence of external drive. In this mechanism, the coupling hybridizes the oscillator modes into spectrally split normal modes. The destructive interference between the transitions to these modes blocks synchronization. We find that this blockade can be controlled simply by tuning the coupling strength and detuning allowing dynamic manipulation of quantum synchronization through collective mode dynamics. We analyze the phase-locking behaviour using perturbation analysis. Further, by deriving steady-state probability amplitudes we show how the energy redistribution and spectral splitting forms the basis of the blockade. Our results might provide new insights into how synchronization can be controlled in quantum systems.

quant-ph↗

arXiv2026

Controlling extreme events in neuronal networks: A single driving signal approach

We show that in a drive-response coupling framework extreme events are suppressed in the response system by the dominance of a single driving signal. We validate this approach across three distinct response network topologies, namely (i) a pair of coupled neurons, (ii) a monolayer network of N coupled neurons and (iii) a two-layer multiplex network each composed of FitzHugh-Nagumo neuronal units. The response networks inherently exhibit extreme events. Our results demonstrate that influencing just one neuron in the response network with an appropriately tuned driving signal is sufficient to control extreme events across all three configurations. In the two-neuron case, suppression of extreme events occurs due to the breaking of phase-locking between the driving neuron and the targeted response neuron. In the case of monolayer and multiplex networks, suppression of extreme events results from the disruption of protoevent frequency dynamics and a subsequent frequency decoupling of the driven neuron from the rest of the network. We also observe that when the size of the neurons in response network connected to the drive increases, the onset of control occurs earlier indicating a scaling advantage of the method.

nlin.CD↗

arXiv2025

Propagation of extreme events in multiplex neuronal networks

In previous studies, the propagation of extreme events across nodes in monolayer networks has been extensively studied. In this work, we extend this investigation to explore the propagation of extreme events between two distinct layers in a multiplex network. We consider a two-layer network, where one layer is globally coupled and exhibits extreme events, while the second layer remains uncoupled. The interlayer connections between the layers are either unidirectional or bidirectional. We find that unidirectional coupling between the layers can induce extreme events in the uncoupled layer, whereas bidirectional coupling tends to mitigate extreme events in the globally coupled layer. To characterize extreme and non-extreme states, we use probability plots to identify distinct regions in the parameter space. Additionally, we study the robustness of extreme events emergence by examining various network topologies in the uncoupled layer. The mechanism behind the occurrence of extreme events is explored, with a particular focus on the transition from asynchronous states to a fully synchronized excitable state. For numerical simulations, we use nonidentical FitzHugh-Nagumo neurons at each node, which captures the dynamical behavior of both coupled and uncoupled layers. Our findings suggest that extreme events in the uncoupled layer emerge through the gradual disappearance of disorder, accompanied by occasional bursts of synchronized activity. Results obtained in this work will serve a starting point in understanding the dynamics behind the propagation of extreme events in real-world networks.

nlin.CD↗

arXiv2025

Breather and Positon excitations in a nonlinear electrical transmission line modeled by the Kundu-Eckhaus Equation

In this study, we explore the dynamics of breathers and positons in a nonlinear electrical transmission line modeled by the modified Naguchi circuit, governed by the Kundu-Eckhaus equation. Utilizing the reductive perturbation method and a specific transformation, we analyze the influence of different time-dependent linear potentials on these nonlinear wave structures. The analysis is conducted for three representative cases: (i) a constant potential, which modifies the orientation and amplitude of breathers and positons, (ii) a periodically modulated potential, which transforms them into crescent-shaped structures with unique spatial characteristics, and (iii) an exponentially varying potential, which induces asymmetric crescent-shaped waveforms. Additionally, we show that linear potentials significantly influence breather and positon dynamics in the modified electrical transmission line by altering their position and positon amplitude-constant potentials maintain peaks at the origin, periodic potentials shift breathers forward and positons backward, while exponential potentials move breathers backward and positons forward. Our findings highlight the critical role of external modulation in shaping wave propagation, localizing waves, and altering their amplitude, demonstrating its potential for controlling wave dynamics in nonlinear transmission lines. Unlike previous studies that focused on rogue waves, this work provides new insights into the evolution of breathers and positons under external perturbations. The results may have significant implications for applications in electrical transmission networks.

nlin.PS↗

arXiv2025

Baseband Modulational Instability and Manifestation of Breather and Super Rogue Wave Phenomena in Modified Noguchi Electrical Transmission Line

In this paper, we report the emergence of breather and super rogue waves in a modified Noguchi electrical transmission line and demonstrate that both phenomena arise from baseband modulational instability. We then systematically examine the influence of three key parameters and time that appear in the solutions, on the structure and behavior of breathers and super rogue waves, how they control waveform amplitude, localization, and intensity. We also explore the intricate dynamics of wave propagation in nonlinear electrical line. Our findings provide valuable insights into the role of network parameters, such as inductances, capacitances, and nonlinear coefficients, in shaping wave behavior, offering not only practical guidelines for the design, stability, and experimental investigation of electrical transmission systems but also provides practical approaches for controlling and managing breather and super rogue wave phenomena in the transmission lines.

nlin.PS↗

arXiv2025

Transmission of Positons in a Modified Noguchi Electrical Transmission Line

In previous studies, the propagation of localized pulses (solitons, rogue waves and breathers) in electrical transmission lines has been studied. In this work, we extend this study to explore the transmission of positon solutions or positons in the modified Noguchi electrical transmission line model. By converting the circuit equations into the nonlinear Schrödinger equation, we identify positons, a special type of solution with algebraic decay and oscillatory patterns. Unlike solitons, which are used for stable energy transmission, positons provide persistent energy localization and controlled spreading over long distances. We consider second-order and third-order positon solutions and examine their transmission behaviour in electrical lines. We show that over long times, the amplitude and width of both second- and third-order positons remain largely unaffected, indicating stable transmission. We also analyze what are the parameters affect the amplitude and localization of this kind of waves. Our investigations reveal that the amplitude and localization of positons are significantly influenced by the parameter $ε$ that appear in the solution. Our findings have practical implications for improving energy transmission in electrical systems, where the management of wave localization and dispersion is crucial.

nlin.PS↗

arXiv2025

Quantum Squeezing Effects in Coupled van der Pol Oscillators

Achieving synchronized quantum states within the quantum realm is a significant goal. This regime is characterized by restricted excitation occurrences and a highly nonclassical stable state of the self-oscillating system. However, many existing approaches to observe synchronization in this quantum realm face a major challenge: the influence of noise tends to overshadow the synchronization phenomenon. In coupled van der Pol oscillators, synchronization occurs when a system of two or more oscillators interacts. Our investigation demonstrates that introducing the squeezing Hamiltonian in two coupled van der Pol oscillators enhances nonclassical effects, increases quantum correlations, and improves the robustness of synchronization dynamics. This was evidenced through the analysis of the Wigner function and power spectrum, showing significant improvements compared to systems without squeezing.

quant-ph↗

arXiv2025

Robustness of the solitons against perturbations in certain nonlocal nonlinear Schrödinger type equations in Nonlinear Physics

The nonlocal nonlinear evolution equations describe phenomena in which wave evolution is influenced by local and nonlocal spatial and temporal variables. These equations have opened up a new wave of physically important nonlinear evolution equations. Their solutions provide insights into the interplay between nonlinearity and nonlocality, making it a cornerstone in the study of nonlocal nonlinear systems. However, the stability of such solutions has not been extensively explored in the literature. Stability analysis ensures that these solutions are robust and capable of persisting under real-world perturbations, making them physically meaningful. In this work, we examine the stability of soliton solutions of four types of nonlocal nonlinear evolutionary equations: (i) the space-shifted nonlocal nonlinear Schrödinger equation, (ii) the nonlocal complex time-reversed Hirota equation, (iii) the nonlocal real space-time-reversed modified Korteweg-de Vries equation, and (iv) a fourth-order nonlocal nonlinear Schrödinger equation. These equations arise in various physical fields such as nonlinear optics, Bose-Einstein condensates, plasmas and so on where nonlocality and nonlinearity play significant roles. We introduce certain perturbations to the soliton solutions of these equations and analyze their stability. Our findings indicate that the soliton solutions of the aforementioned equations are stable under such perturbations. To the best of our knowledge, this approach to investigating the stability of these solutions is novel.

nlin.PS↗

arXiv2024

Mitigation of extreme events in an excitable system

Formulating mitigation strategies is one of the main aspect in the dynamical study of extreme events. Apart from the effective control, easy implementation of the devised tool should also be given importance. In this work, we analyze the mitigation of extreme events in a coupled FitzHugh-Nagumo (FHN) neuron model utilizing an easily implementable constant bias analogous to a constant DC stimulant. We report the route through which the extreme events gets mitigated in $Two$, $Three$ and $N-$coupled FHN systems. In all the three cases, extreme events in the observable $\bar{x}$ gets suppressed. We confirm our results with the probability distribution function of peaks, $d_{max}$ plot and probability plots. Here $d_{max}$ is a measure of number of standard deviations that crosses the average amplitude corresponding to $\bar{x}_{max}$. Interestingly, we found that constant bias suppresses the extreme events without changing the collective frequency of the system.

nlin.AO↗

arXiv2024

Predicting positon solutions of a family of Nonlinear Schrödinger equations through Deep Learning algorithm

We consider a hierarchy of nonlinear Schrödinger equations (NLSEs) and forecast the evolution of positon solutions using a deep learning approach called Physics Informed Neural Networks (PINN). Notably, the PINN algorithm accurately predicts positon solutions not only in the standard NLSE but also in other higher order versions, including cubic, quartic and quintic NLSEs. The PINN approach also effectively handles two coupled NLSEs and two coupled Hirota equations. In addition to the above, we report exact second-order positon solutions of the sextic NLSE and coupled generalized NLSE. These solutions are not available in the existing literature and we construct them through generalized Darboux transformation method. Further, we utilize PINNs to forecast their behaviour as well. To validate PINN's accuracy, we compare the predicted solutions with exact solutions obtained from analytical methods. The results show high fidelity and low mean squared error in the predictions generated by our PINN model.

nlin.PS↗

arXiv2024

Degenerate soliton solutions and their interactions in coupled Hirota equation with trivial and nontrivial background

We construct two kinds of degenerate soliton solutions, one on the zero background and another on the plane wave background for the coupled Hirota equation. In the case of zero background field, we derive positon solutions of various orders. We also study interaction dynamics between positon solutions through asymptotic analysis and show that the positons exhibit time dependent phase shift during collision. We also construct hybrid solutions which composed of positons and solitons and examine the interaction between higher order positon and multi-solitons in detail. From the interaction, we demonstrate that the occurrence of elastic and inelastic interaction between multi-solitons and higher order positons. Further, we construct bound states among solitons and positons for the coupled Hirota equation. In the case of plane wave background, we construct breather-positon solutions. For the coupled Hirota equation, the breather-positon solutions are being reported first time in the literature. From the breather-positon solutions, we bring out certain interesting collision dynamics between breather-positons and positons.

nlin.PS↗

arXiv2022

A study on Darboux polynomials and their significance in determining other integrability quantifiers: A case study in third-order nonlinear ordinary differential equations

In this paper, we present a method of deriving extended Prelle-Singer method's quantifiers from Darboux Polynomials for third-order nonlinear ordinary differential equations. By knowing the Darboux polynomials and its cofactors, we extract the extended Prelle-Singer method's quantities without evaluating the Prelle-Singer method's determining equations. We consider three different cases of known Darboux polynomials. In the first case, we prove the integrability of the given third-order nonlinear equation by utilizing the Prelle-Singer method's quantifiers from the two known Darboux polynomials. If we know only one Darboux polynomial, then the integrability of the given equation will be dealt as case $2$. Likewise, case $3$ discuss the integrability of the given system where we have two Darboux polynomials and one set of Prelle-Singer method quantity. The established interconnection not only helps in deriving the integrable quantifiers without solving the underlying determining equations. It also provides a way to prove the complete integrability and helps us in deriving the general solution of the given equation. We demonstrate the utility of this procedure with three different examples.

nlin.SI↗

arXiv2022

Instability of single- and double-periodic waves in the fourth-order nonlinear Schrödinger equation

We compute the instability rate for single- and double-periodic wave solutions of a fourth-order nonlinear Schrödinger equation. The single- and double-periodic solutions of a fourth-order nonlinear Schrödinger equation are derived in terms of Jacobian elliptic functions such as $dn$, $cn$, and $sn$. From the spectral problem, we compute Lax and stability spectrum of single-periodic waves. We then calculate the instability rate of single-periodic waves (periodic in the spatial variable). We also obtain the Lax and stability spectrum of double-periodic wave solutions for different values of the elliptic modulus parameter. We also highlight certain novel features exhibited by the considered system. We then compute instability rate for two families of double-periodic wave solutions of the considered equation for different values of the system parameter. Our results reveal that the instability growth rate is higher for the double-periodic waves due to the fourth-order dispersion parameter when compared to single-periodic waves.

nlin.SI↗

arXiv2022

Rogue waves with two different double-periodic wave backgrounds and their modulational instabilities of a fifth-order nonlinear Schrödinger equation

In this article, we derive rogue wave (RW) solutions of a fifth-order nonlinear Schrödinger equation over a double-periodic wave background. Choosing the elliptic functions (combinations of $cn$, $dn$ and $sn$) as seed solutions in the first iteration of Darboux transformation and utilizing the nonlinearization of Lax pair procedure, we create the double-periodic wave background for the fifth-order nonlinear Schrödinger equation. By introducing the second linearly independent solution, we generate the RW solutions on the created background for three different eigenvalues. We demonstrate the differences that occur in the appearance of RWs due to the lower-order and higher-order dispersions terms. We examine the derived solution in detail for certain system and elliptic modulus parameters values and highlight some interesting features that we obtain from our studies. We also calculate the growth rate for instability of double-periodic solutions under different values of elliptic modulus parameter.

nlin.SI↗

arXiv2022

Higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity

We construct certain higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity. We utilize the generalized Darboux transformation method to construct the aforementioned solutions. The three well-known equations, namely nonlinear Schrödinger equation, Hirota equation, and generalized nonlinear Schrödinger equation, are sub-cases of the considered extended nonlinear Schrödinger equation. The solutions which we construct are more general. We analyze how the positon and breather positon solutions of the constituent equations get modified by the higher order nonlinear and dispersion terms. Our results show that the width and direction of the smooth positon and breather-positon solutions are highly sensitive to higher-order effects. Further, we carryout an asymptotic analysis to predict the behaviour of positons. We observe that during collision positons exhibit a time-dependent phase shift. We also present the exact expression of time-dependent phase shift of positons. Finally, we show that this time-dependent phase shift is directly proportional to the higher order nonlinear and dispersion parameters.

nlin.PS↗

arXiv2022

Quantum Synchronization in quadratically coupled quantum van der Pol oscillators

We implement nonlinear anharmonic interaction in the coupled van der Pol oscillators to investigate the quantum synchronization behaviour of the systems. We study the quantum synchronization in two oscillator models, coupled quantum van der Pol oscillators and anharmonic self-oscillators. We demonstrate that the considered systems exhibit a high-order synchronization through coupling in both classical and quantum domains. We show that due to the anharmonicity of the nonlinear interaction between the oscillators the system exhibits phonon blockade in the phase locking regime which is a pure nonclassical effect and has not been observed in the classical domain. We also demonstrate that for coupled anharmonic oscillators the system shows a multiple resonance phase locking behaviour due to nonlinear interaction. We point out that the synchronization blockade arises due to strong anticorrelation between the oscillators which leads to phonon antibunching in the same parametric regime. In the anharmonic oscillator case we illustrate the simultaneous occurrence of bunching and antibunching effects as a consequence of simultaneous negative and positive correlation between the anharmonic oscillators. We examine the aforementioned characteristic features in the frequency entrainment of the oscillators using power spectrum where one can observe normal mode splitting and Mollow triplet in the strong coupling regime. Finally, we propose a possible experimental realization for the considered system in trapped ion and optomechanical setting.

quant-ph↗

arXiv2022

Suppression of extreme events and chaos in a velocity-dependent potential system with time-delay feedback

The foremost aim of this study is to investigate the influence of time-delayed feedback on extreme events in a non-polynomial system with velocity dependent potential. To begin, we investigate the effect of this feedback on extreme events for four different values of the external forcing parameter. Among these four values, in the absence of time-delayed feedback, for two values, the system does not exhibit extreme events and for the other two values, the system exhibits extreme events. On the introduction of time-delayed feedback and varying the feedback strength, we found that extreme events get suppressed as well as get induced. When the feedback is positive, suppression occurs for a larger parameter region whereas in the case of negative feedback it is restricted to the limited parameter region. We confirm our results through Lyapunov exponents, probability density function of peaks, $d_{max}$ plot and two parameter probability plot. Finally, we analyze the changes in the overall dynamics of this system under the influence of time-delayed feedback. We notice that complete suppression of chaos occurs in the considered system for higher values of the time-delayed feedback.

cond-mat.stat-mech↗