arXiv subjects

A. Venkatesan

Publications and source records attributed to A. Venkatesan.

At least 19 recordsLinked to original sources

arXiv2024

Reservoir computing with logistic map

Recent studies on reservoir computing essentially involve a high dimensional dynamical system as the reservoir, which transforms and stores the input as a higher dimensional state, for temporal and nontemporal data processing. We demonstrate here a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing using a nonlinear map, namely the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely Lorenz, Rossler, and Hindmarsh-Rose, for temporal tasks and a seventh order polynomial for nontemporal tasks with great accuracy. Also, the prediction is made in the presence of noise and found to closely agree with the target. Remarkably, the logistic map performs well and predicts close to the actual or target values. The low values of the root mean square error confirm the accuracy of this method in terms of efficiency. Our approach removes the necessity of continuous dynamical systems for constructing the reservoir in reservoir computing. Moreover, the accurate prediction for the three different nonlinear systems suggests that this method can be considered a general one and can be applied to predict many systems. Finally, we show that the method also accurately anticipates the time series of the all the three variable of Rossler system for the future (self prediction).

cond-mat.dis-nn↗

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↗

arXiv2023

Harnessing vibrational resonance to identify and enhance input signals

We report the occurrence of vibrational resonance (VR) and the underlying mechanism in a simple piecewise linear electronic circuit, namely the Murali-Lakshmanan-Chua (MLC) circuit, driven by an additional biharmonic signal with widely different frequency. When the amplitude of the high-frequency force is tuned, the resultant vibrational resonance is used to detect the low-frequency signal and also to enhance it into a high-frequency signal. Further, we also show that even when the low-frequency signal is changed from sine wave to square and sawtooth waves, vibrational resonance can be used to detect and enhance them into high-frequency signals. These behaviors, confirmed by experimental results, are illustrated with appropriate analytical and numerical solutions of the corresponding circuit equations describing the system. Finally, we also verify the signal detection in the above circuit even with the addition of noise.

nlin.AO↗

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↗

arXiv2021

Constant Bias and Weak Second Periodic Forcing : Tools to Mitigate Extreme Events

We propose two potentially viable non-feedback methods, namely (i) constant bias and (ii) weak second periodic forcing as tools to mitigate extreme events. We demonstrate the effectiveness of these two tools in suppressing extreme events in two well-known nonlinear dynamical systems, namely (i) Liénard system and (ii) a non-polynomial mechanical system with velocity dependent potential. As far as the constant bias is concerned, in the Liénard system, the suppression occurs due to the decrease in large amplitude oscillations and in the non-polynomial mechanical system the suppression occurs due to the destruction of chaos into a periodic orbit. As far as the second periodic forcing is concerned, in both the examples, extreme events get suppressed due to the increase in large amplitude oscillations. We also demonstrate that by introducing a phase in the second periodic forcing one can decrease the probability of occurrence of extreme events even further in the non-polynomial system. To provide a support to the complete suppression of extreme events, we present the two parameter probability plot for all the cases. In addition to the above, we examine the feasibility of the aforementioned tools in a parametrically driven version of the non-polynomial mechanical system. Finally, we investigate how these two methods influence the multistability nature in the Liénard system.

math.DS↗

arXiv2021

Emergence and mitigation of extreme events in a parametrically driven system with velocity-dependent potential

In this paper, we discuss the emergence of extreme events in a parametrically driven non-polynomial mechanical system with a velocity-dependent potential. We confirm the occurrence of extreme events from the probability distribution function of the peaks, which exhibits a long-tail. We also present the mechanism for the occurrence of extreme events. We found that the probability of occurrence of extreme events alternatively increase and decrease with a brief region where the probability is zero. At the point of highest probability of extreme events, when the system is driven externally, we find that the probability decreases to zero. Our investigation confirms that the external drive can be used as an useful tool to mitigate extreme events in this nonlinear dynamical system. Through two parameter diagrams, we also demonstrate the regions where extreme events gets suppressed. In addition to the above, we show that extreme events persits when the sytem is influenced by noise and even gets transformed to super-extreme events when the state variable is influenced by noise.

cond-mat.stat-mech↗

arXiv2021

Realization of all logic gates and memory latch in the SC-CNN cell of the simple nonlinear MLC circuit

We investigate the State-Controlled Cellular Neural Network (SC-CNN) framework of Murali-Lakshmanan-Chua (MLC) circuit system subjected to two logical signals. By exploiting the attractors generated by this circuit in different regions of phase-space, we show that the nonlinear circuit is capable of producing all the logic gates, namely OR, AND, NOR, NAND, Ex-OR and Ex-NOR gates available in digital systems. Further the circuit system emulates three-input gates and Set-Reset flip-flop logic as well. Moreover, all these logical elements and flip-flop are found to be tolerant to noise. These phenomena are also experimentally demonstrated. Thus our investigation to realize all logic gates and memory latch in a nonlinear circuit system paves the way to replace or complement the existing technology with a limited number of hardware.

cs.ET↗

arXiv2020

Temperature Dependent Non-linear Damping in Palladium Nano-mechanical Resonators

Advances in nano-fabrication techniques has made it feasible to observe damping phenomena beyond the linear regime in nano-mechanical systems. In this work, we report cubic non-linear damping in palladium nano-mechanical resonators. Nano-scale palladium beams exposed to a $H_2$ atmosphere become softer and display enhanced Duffing non-linearity as well as non-linear damping at ultra low temperatures. The damping is highest at the lowest temperatures of $\sim 110\: mK$ and decreases when warmed up-to $\sim 1\textrm{ }K$. We experimentally demonstrate for the first time a temperature dependent non-linear damping in a nano-mechanical system below 1 K. It is consistent with a predicted two phonon mediated non-linear Akhiezer scenario for ballistic phonons with mean free path comparable to the beam thickness. This opens up new possibilities to engineer non-linear phenomena at low temperatures.

cond-mat.mes-hall↗

arXiv2020

Route to logical strange nonchaotic attractors with single periodic force and noise

Strange nonchaotic attractors (SNAs) have been identified and studied in the literature exclusively in quasiperiodically driven nonlinear dynamical systems. It is an interesting question to ask whether they can be identified with other types of forcings as well, which still remains as an open problem. Here, we show that robust SNAs can be created by a small amount of noise in periodically driven nonlinear dynamical systems by a single force. The robustness of these attractors is tested by perturbing the system with logical signals leading to the emulation of different logical elements in the SNA regions.

nlin.AO↗

arXiv2018

Women Scientists Who Made Nuclear Astrophysics

Female role models reduce the impact on women of stereotype threat, i.e., of being at risk of conforming to a negative stereotype about one's social, gender, or racial group. This can lead women scientists to underperform or to leave their scientific career because of negative stereotypes such as, not being as talented or as interested in science as men. Sadly, history rarely provides role models for women scientists; instead, it often renders these women invisible. In response to this situation, we present a selection of twelve outstanding women who helped to develop nuclear astrophysics.

physics.hist-ph↗

arXiv2018

Strange nonchaotic attractors for computation

We investigate the response of quasiperiodically driven nonlinear systems exhibiting strange non- chaotic attractors (SNAs) to deterministic input signals. We show that if one uses two square waves in aperiodic manner as input to a quasiperiodically driven double-well Duffing oscillator system, the response of the system can produce logical output controlled by such a forcing. Changing the threshold or biasing of the system changes the output to another logic operation and memory latch. The interplay of nonlinearity and quasiperiodic forcing yields logic behaviour and the emergent out- come of such a system is a logic gate. It is further shown that the logical behaviours persist even for experimental noise floor. Thus the SNA turns out to be an efficient tool for computation.

nlin.CD↗

arXiv2017

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

A complex collective emerging behavior characterized by coexisting coherent and incoherent do- mains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators driven by a common dynamic environment. The latter facilitates the onset of phase-flip bifurcation/transitions among the coupled oscillators of the ensemble, while the nonlocal coupling induces a partial asynchronization among the out-of-phase synchronized oscillators at this onset. This leads to the manifestation of coexisting out-of-phase synchronized coherent domains interspersed by asynchronous incoherent domains elucidating the existence of a different type of chimera state. In addition to this, a rich variety of other collective behaviors such as clusters with phase-flip transition, conventional chimera, solitary state and com- plete synchronized state which have been reported using different coupling architectures are found to be induced by the employed couplings for appropriate coupling strengths. The robustness of the resulting dynamics is demonstrated in ensembles of two paradigmatic models, namely Rössler oscillators and Stuart-Landau oscillators.

nlin.CD↗

arXiv2017

Design and implementation of dynamic logic gates and R-S flip-flop using quasiperiodically driven Murali-Lakshmanan-Chua circuit

We report the propagation of a square wave signal in a quasi-periodically driven Murali-Lakshmanan-Chua (QPDMLC) circuit system. It is observed that signal propagation is possible only above a certain threshold strength of the square wave or digital signal and all the values above the threshold amplitude are termed as 'region of signal propagation'. Then, we extend this region of signal propagation to perform various logical operations like AND/NAND/OR/NOR and hence it is also designated as the 'region of logical operation'. Based on this region, we propose implementing the dynamic logic gates, namely AND/NAND/OR/NOR, which can be decided by the asymmetrical input square waves without altering the system parameters. Further, we show that a single QPDMLC system will produce simultaneously two outputs which are complementary to each other. As a result, a single QPDMLC system yields either AND as well as NAND or OR as well as NOR gates simultaneously. Then we combine the corresponding two QPDMLC systems in a cross-coupled way and report that its dynamics mimics that of fundamental R-S flip-flop circuit. All these phenomena have been explained with analytical solutions of the circuit equations characterizing the system and finally the results are compared with the corresponding numerical and experimental analysis.

nlin.CD↗

arXiv2016

Low temperature dissipation scenarios in palladium nano-mechanical resonators

We study dissipation in Pd nano-mechanical resonators at low temperatures in the linear response regime. Metallic resonators have shown characteristic features of dissipation due to tunneling two level systems (TLS). This system offers a unique tunability of the dissipation scenario by adsorbing hydrogen ($H_2$) which induces a compressive stress. The intrinsic stress is expected to alter TLS behaviour. We find a sub-linear power law $\sim T^{0.4}$ in dissipation. As seen in TLS dissipation scenarios we find a logarithmic increase of frequency characteristic from the lowest temperatures till a characteristic temperature $T_{co}$ is reached. In samples without $H_2$ the $T_{co} \sim 1K$ whereas with $H_2$ it is clearly reduced to $\sim 700 mK$. Based on standard TLS phenomena we attribute this to enhanced phonon-TLS coupling in samples with compressive strain. We also find with $H_2$ there is a saturation in low temperature dissipation which may possibly be due to super-radiant interaction between TLS and phonons. We discuss the data in the scope of TLS phenomena and similar data for other systems.

cond-mat.mes-hall↗

arXiv2015

Effect of asymmetry parameter on the dynamical states of nonlocally coupled nonlinear oscillators

We show that coexisting domains of coherent and incoherent oscillations can be induced in an ensemble of any identical nonlinear dynamical systems using the nonlocal rotational matrix coupling with an asymmetry parameter. Further, chimera is shown to emerge in a wide range of the asymmetry parameter in contrast to near $\fracπ{2}$ values of it employed in the earlier works. We have also corroborated our results using the strength of incoherence in the frequency domain ($S_ω$) and in the amplitude domain ($S$) thereby distinguishing the frequency and amplitude chimeras. The robust nature of the asymmetry parameter in inducing chimeras in any generic dynamical system is established using ensembles of identical Rössler oscillators, Lorenz systems, and Hindmarsh-Rose (HR) neurons in their chaotic regimes.

nlin.CD↗

arXiv2014

Mechanism for intensity induced chimera states in globally coupled oscillators

We identify the mechanism behind the existence of intensity induced chimera states in globally coupled oscillators. We find that the effect of intensity in the system is to cause multistability by increasing the number of fixed points. This in turn increases the number of multistable attractors and we find that their stability is determined by the strength of coupling . This causes the coexistence of different collective states in the system depending upon the initial state. We demonstrate that intensity induced chimera is generic to both periodic and chaotic systems. We have discussed possible applications of our results to real world systems like the brain and spin torque nano oscillators.

nlin.AO↗

arXiv2014

Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling

By developing the concepts of strength of incoherence and discontinuity measure, we show that a distinct quantitative characterization of chimera and multichimera states which occur in networks of coupled nonlinear dynamical systems admitting nonlocal interactions of finite radius can be made. These measures also clearly distinguish between chimera or multichimera states (both stable and breathing types) and coherent and incoherent as well as cluster states....

nlin.CD↗

arXiv2013

Applicability of 0-1 Test for Strange Nonchaotic Attractors

We show that the recently introduced 0-1 test can successfully distinguish between strange nonchaotic attractors(SNAs) and periodic/quasiperiodic/chaotic attractors, by suitably choosing the arbitrary parameter associated with the translation variables in terms of the golden mean number which avoids resonance with the quasiperiodic force. We further characterize the transition from quasiperiodic to chaotic motion via SNAs interms of the 0-1 test. We demonstrate that the test helps to detect different dynamical transitions to SNAs from quasiperiodic attractor or the transitions from SNAs to chaos. We illustrate the performance of the 0-1 test in detecting transitions to SNAs in quasiperiodically forced logistic map, cubic map, and Duffing oscillator.

nlin.CD↗