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In this paper nonlinear dynamical behaviour of an excitable DC magnetron sputtering plasma has been investigated. Initially, plasma exhibited fixed point dynamics whereas with the increase in the discharge voltage, spikes were observed in the floating potential fluctuations. Furthermore, the increasing of discharge voltage resulted the increase in spikes. Power spectrum plot, normalized variance, recurrence plot and Hurst exponent are employed to extract the underlying feature of the floating potential fluctuations. A dip in the plot of normalized variance with variation in the control parameter has been seen, which is strongly indicative of coherence resonance like behaviour in the system. Power spectrum plot and Hurst exponent estimation are confirming the presence of coherence resonance behaviour. Apart from quantitative confirmation, visual verification of coherence resonance behavior has been carried out using recurrence plot analysis. It is noticed that the noise component increases with the increase in the discharge voltage and a suitable intrinsic noise strength plays an important role in generating the coherence resonance. Keywords: Intrinsic coherence resonance, Floating potential fluctuation, DC magnetron plasma, Hurst exponent, Noise component

An experimental investigation on the self-excited spiky oscillations in a glow discharge plasma device is presented. The system showed a continuous transition from chaotic bursting to chaotic spiking states with the increase in the applied discharge voltage at a particular pressure. Below a threshold discharge voltage, the system exhibits a fixed point dynamical behaviour and with the increase in the discharge voltage bursting type oscillations appear which are identified as “fold/fold circle” type. The occurrence of the relaxation type spiky oscillations is attributed to the formation and disruption of anode double layer. The burst phases occurred intermittently and the frequency of their occurrence increased with increase in the discharge voltage and finally the oscillation turned into spiking behaviour. The intermittent oscillations manifested the scaling law of the average laminar phase with respect to the change in the discharge voltage. The scaling law of the intermittent oscillations was similar to type III intermittency. During the transition, the system changes its behaviour from long range correlation to long range anti correlation. Detrended fluctuation analysis technique has been used to identify the nature of long range correlations. We found that bursting oscillations show scale invariant, long-range correlation behaviour whereas spiking oscillations show scale invariant, long range anti correlation behaviour.

Nonlinear time series analysis of data related to the radioactivity profile of a hot spring area can explore the dynamics of the geothermal activities along with other different nonlinear features of the Earth system. However, not much work in this field has been done so far in India. In this paper nonlinear time series analysis of the radioactive gas Radon-222 ( 222 Rn) (time series) data recorded at Bakreswar hot spring area of West Bengal, India during the period 2005-2010 was carried out to investigate the dynamics of the radioactive gas emanation process and its relation with the Earth’s tide. Power spectral density and the Hurst exponents were obtained for the above said time series signal using the nonlinear techniques of Fast Fourier Transform (FFT) and power law scaling relationship. An attempt was also made to understand the system dynamics using the surrogate and truncated data of the original time series as well. The result shows that the seasonal variations of the 222 Rn emission from the hot spring is highly influenced by the Earth’s tidal effects, and the same has been confirmed by the power spectral density plot. The estimated Hurst exponent from log p-log f plot reflects the anti-persistent Brownian motion nature of the whole five years recorded data set.

We implement different statistical analysis techniques to investigate the presence of nonlinearity in the fluctuations of a steady state glow discharge plasma (GDP). We introduce a novel ‘delay vector variance’ analysis (DVV) to allow reliable detection of nonlinearity in a plasma in presence of external forcing and magnetic field by providing some easy to interpret diagrams. The analysis has also been implemented to study numerically simulated results for the first time. An estimate of the Zscore has been carried out to detect the presence of nonlinearity in a somewhat quantitative sense. An informal test for bicoherency has been applied to detect the interaction amongst different modes obtained by performing emperical mode decomposition to strengthen the analysis on nonlinearity. The results obtained from bicoherency test resemble those obtained by performing DVV. An attempt to model the experimental observations by a second order nonlinear ordinary differential equation derived from the fluid equations of plasma has revealed convincing results.

In this paper, multifractal detrended fluctuation analysis (MF-DFA) has been used to analyze the floating potential fluctuations obtained with a Langmuir probe from a dc glow discharge magnetized plasma device. The generalized Hurst exponents ( h ( q ) ) , local fluctuation function ( F q ( s ) ) , the Renyi exponents ( τ ( q ) ) and the multifractal spectrum F ( α ) have been calculated by applying the MF-DFA method. The result of the MF-DFA shows the multifractal nature of these fluctuations. We have investigated the influence of magnetic field on the multifractal nature of the fluctuations and it is seen that degree of multifractality is reduced with the increase in the magnetic field strength. The values of h ( q ) have been restricted between 0.7 and 1 for the magnetized fluctuations. This result is evidence of the existence of long-range correlations in the fluctuations. Furthermore, we employed shuffle and surrogate approaches to analyze the origins of multifractality. Comparing the MF-DFA results for the data set to those for shuffled and surrogate series, we have found that its multifractal nature is due to the existence of significant long-term correlation.

In this work, we present an electronic implementation of a damped Korteweg-de Vries equation modeled as a third order nonlinear autonomous ordinary differential equation (jerk equation). The circuit has been realized using operational amplifiers, multipliers, and passive electronic components which provides the time series solution of the equation in agreement with the numerical simulation results. Using nonlinear time series analysis on the acquired waveform data, we have obtained different types of phase space portraits and further analysis reflected long range correlation in the chaotic time series. Important findings include hysteresis induced bifurcation and self-organized criticality behavior in the system which is mentioned in this work.

Wavelet analysis is shown to be a more robust technique than previously used methods in the investigation of synchronization. The highlight of the technique is that it encompasses most of the information obtained by conventional methods into a single picture, while giving a deeper insight into the dynamics of the system. Order parameters derived from continuous wavelet transform coefficients are proposed, which can be used in the quantification of measure synchronization in Hamiltonian systems and identical synchronization in dissipative systems, irrespective of the nature of coupling, the nature of synchronization (complete or partial, quasiperiodic or chaotic), and the number of coupled subsystems.

Measure Synchronization (MS) is the generalization of synchrony to Hamiltonian Systems. Partial measure synchronization (PMS) and complete measure synchronization in a system of three nonlinearly coupled one-dimensional oscillators have been investigated for different initial conditions on the basis of numerical computation. The system is governed by the classical SU(2) Yang-Mills-Higgs (YMH) Hamiltonian with three degrees of freedom. Various transitions in the quasiperiodic (QP) region, namely, QP unsynchronized to PMS, PMS to PMS, and PMS to chaos are identified through the average bare energies and interaction energies route maps as the coupling strength is varied. The transition from quasiperiodicity to chaos is seen to be associated with a gradual transition to complete chaotic measure synchronization (CMS) which is followed by chaotic unsynchronized states, the most stable state in this case. The analyses illustrate the dependence on initial conditions. The explanation of the behavior in the QP regime is sought from the power spectral analysis. The existence of PMS is confirmed using the order parameter M (here M α β for different combination pairs of oscillators), best suited to identify MS in coupled two-oscillator systems, and this definition is extended to obtain a new order parameter, M 3, aiding to distinguish complete MS of three oscillators from other forms of motion. The study of wavelet coefficient spectra sheds new light on the relative phase information of the oscillators in the QP PMS regions, also highlighting the intertwined role played by the various frequency components and their amplitudes as they vary temporally. Furthermore, this technique helps to draw a sharp distinction between CMS and chaotic unsynchronized states. Based on the Continuous Wavelet Transform coefficients of the three oscillators, an order parameter M w a v is defined to indicate the extent of synchronization of the various scales (frequencies) for different coupling strengths in the chaotic regime.Measure Synchronization (MS) is the generalization of synchrony to Hamiltonian Systems. Partial measure synchronization (PMS) and complete measure synchronization in a system of three nonlinearly coupled one-dimensional oscillators have been investigated for different initial conditions on the basis of numerical computation. The system is governed by the classical SU(2) Yang-Mills-Higgs (YMH) Hamiltonian with three degrees of freedom. Various transitions in the quasiperiodic (QP) region, namely, QP unsynchronized to PMS, PMS to PMS, and PMS to chaos are identified through the average bare energies and interaction energies route maps as the coupling strength is varied. The transition from quasiperiodicity to chaos is seen to be associated with a gradual transition to complete chaotic measure synchronization (CMS) which is followed by chaotic unsynchronized states, the most stable state in this case. The analyses illustrate the dependence on initial conditions. The explanation of the behavior in the QP regi...

This paper presents a comparative study on the investigation of coherent modes in chaotic time series data based on two techniques: the empirical mode decomposition and the discrete wavelet transform. We have applied these techniques to the different types of chaotic time series data obtained from a glow discharge plasma. The discrete wavelet transform and empirical mode decomposition analysis of the chaotic time series, combined with some simple statistical estimations like variance and correlation coefficient, helps in identifying the presence of coherent modes. We carried out a bicoherency analysis on the coherent modes extracted using empirical mode decomposition to detect the interactions amongst them. It is quite likely that the interactions between the different plasma modes are responsible for such turbulent nonlinear oscillations.

Measure Synchronization is a general term used for weak synchronization in Hamiltonian systems. Route to measure synchronization in a system of two non-linearly coupled one-dimensional oscillators, the potential of which is represented by the Pullen-Edmonds Potential is investigated on the basis of numerical computation. Transitions to measure synchronization and unsynchronization, both quasiperiodic and chaotic, are investigated and distinguished on the basis of the variation of average bare energies, average interaction energy, root-mean-square value of oscillations, phase difference, and frequencies with the coupling strength. A suitable order parameter to identify and characterize both quasiperiodic and chaotic measure synchronous states is sought, and drawbacks of the various order parameters, suggested previously, are discussed.

We have carried out a detailed study of scaling region using detrended fractal analysis test by applying different forcing likewise noise, sinusoidal, square on the floating potential fluctuations acquired under different pressures in a DC glow discharge plasma. The transition in the dynamics is observed through recurrence plot techniques which is an efficient method to observe the critical regime transitions in dynamics. The complexity of the nonlinear fluctuation has been revealed with the help of recurrence quantification analysis which is a suitable tool for investigating recurrence, an ubiquitous feature providing a deep insight into the dynamics of real dynamical system. An informal test for stationarity which checks for the compatibility of nonlinear approximations to the dynamics made in different segments in a time series has been proposed. In case of sinusoidal, noise, square forcing applied on fluctuation acquired at P=0.12mbar only one dominant scaling region is observed whereas the forcing applied on fluctuation (P=0.004mbar) two prominent scaling regions have been explored reliably using different forcing amplitudes indicating the signature of crossover phenomena. Furthermore a persistence long range behaviour has been observed in one of these scaling regions. A comprehensive study of the quantifi- cation of scaling exponents has been carried out with the increase in amplitude and frequency of sinusoidal, square type of forcings. The scalings exponent is envisaged to be the roughness of the time series. The method provides a single quantitative idea of the scaling exponent to quantify the correlation properties of a signal., 17 pages, 12 figures, 2tables. arXiv admin note: text overlap with arXiv:chao-dyn/9909044 by other authors

The possibility of finding chaos in a KdV like system in the absence of any external forcing is explored without reducing its order by treating it as a third order Jerk equation. While bounded solutions with periodic nature exist for both right and left traveling wave solutions of the KdV equation, inclusion of terms that signify damping lead to chaotic behavior only for left moving waves. The bifurcation diagram obtained for suitable choice of the parameters shows interesting phenomena such as Hopf and period doubling bifurcations. To characterize the chaotic behavior, the spectrum of Lyapunov exponent is studied. Domains of stable and unstable solutions with the boundaries marking transitions have been identified in the parameter space.

Characterization of self-similarity properties of turbulence in magnetized plasma is being carried out in DC glow discharge plasma. The time series floating potential fluctuation experimental data are acquired from the plasma by Langmuir probe. Continuous wavelet transform (CWT) analysis considering db4 mother wavelet has been applied to the experimental data and self-similarity properties are detected by evaluating the Hurst exponent from the wavelet variance plotting. From the CWT spectrum, effort is made to extract a highly correlated frequency by locating the brightest spot. Accordingly, those signals are treated for finding out correlation dimension and the Liapunov exponent so that the exact frequency responsible for the chaotic behavior could be found out.

Present paper deals with a brief review of the research carried out to develop multi-parametric gas-geochemical monitoring facilities dedicated to earthquake prediction research in India by installing a network of seismo-geochemical monitoring observatories at different regions of the country. In an attempt to detect earthquake precursors, the concentrations of helium, argon, nitrogen, methane, radon-222 (222Rn), polonium-218 (218Po), and polonium-214 (214Po) emanating from hydrothermal systems are monitored continuously and round the clock at these observatories. In this paper, we make a cross correlation study of a number of geochemical anomalies recorded at these observatories. With the data received from each of the above observatories we attempt to make a time series analysis to relate magnitude and epicentral distance locations through statistical methods, empirical formulations that relate the area of influence to earthquake scale. Application of the linear and nonlinear statistical techniques in the recorded geochemical data sets reveal a clear signature of long-range correlation in the data sets.

We report an experimental observation of a phase-flip transition in the frequency synchronization of two dc glow discharge plasma sources that are coupled in a noninvasive fashion. When the fundamental oscillation frequency of the potential fluctuations of one of the sources is progressively increased, by raising its discharge voltage, a frequency pulling regime is observed, followed by a synchronized regime that shows a frequency jump phenomenon. The jump is associated with a phase-flip transition that takes the synchronized state from an in-phase to an antiphase state. When the process is reversed, the transition takes place at a different frequency, thereby exhibiting a hysteresis effect. A heuristic model, consisting of two van der Pol oscillators that are coupled to each other through a dynamic common medium, eminently captures the essential features of our experimental observations.

The behaviour of runaway electrons in the SINP tokamak, which can be operated in a normal edge safety factor (qa) (NQ) discharge configuration as well as in a low qa (LQ) configuration, was experimentally investigated, during the initial plasma generation phase. An energy analysis of the runaway electron dynamics in the rise phase of the SINP tokamak discharges was also made. A comparison of the runaway electron diffusion coefficients in NQ and LQ is carried out in this paper.

Dodecanethiol-capped gold nanoparticles (AuNPs) are self-organized in two different amphiphilic monolayers one of which is a single-tailed fatty acid Stearic acid (StA) and the other a double-tailed lipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). In the StA-AuNP film the AuNPs self-organize to form an interconnected network of nanoclusters on compression while in the DMPC-AuNP film the AuNPs aggregate to form random, isolated clusters in the film. The long time evolution of the films at constant surface pressure reveals ring structures in the former and diffusion limited aggregates in the latter that with time evolve into an irregular porous maze of AuNPs in the DMPC film. The difference in structure of the AuNP patterns in the two films can be attributed to a difference in the lipophilic interactions between the NPs and the amphiphilic molecules. The mean square intensity fluctuations f(ln) calculated along a typical line for the 2D structures in both the films at initial and final stages of lo...

A previous analysis of anomalous width variation for a single-ion rarefactive solitary wave [S. S. Ghosh and A. N. Sekar Iyengar, Phys. Plasmas, 4, 3204 (1997)] has been extended to a multi-ion species, and shows that the corresponding width–amplitude characteristics depend crucially on the respective ion concentrations; for example, with increasing light-ion concentration, an ‘increasing- width’ rarefactive solitary wave transforms to a ‘decreasing-width’ one for a constant Mach number exhibiting an overall U-shaped variation profile. The influence of the second ion species generally decreases with increasing amplitude, being maximum for the single to multi-ion transition. However, in the neighbourhood of double-layer-like solutions, the influence again becomes prominent, which may be associated with the corresponding energy–amplitude relations for both the ions.

A localized glowing, fireball like structure, appears near the cathode surface of a glow discharge plasma device when it is subjected to a magnetic dipole field produced by a bar magnet placed outside the plasma chamber. It is seen that the plasma density in the localized glow region and the luminous intensity of this structure increases with the increase in the magnetic field strength. The effect of such localized glow region on the plasma floating potential fluctuation dynamics is investigated. Floating potential fluctuations show that the emergence of such localized structure leads the system towards nonlinear dynamical regimes. Increasing the magnetic field strength reveals a transition from order to chaos via period doubling bifurcation. This transition is analyzed by using bifurcation diagram, phase space plots, power spectrum plots, Hilbert Huang transform, and by estimating the largest Lyapunov exponent. The interaction of plasma with a dipole magnetic field produces a non-monotonic potential stru...

The typical phenomena of mixed mode oscillations and their associated nonlinear behaviors have been investigated in collisionless magnetized plasma oscillations in a DC glow discharge plasma system. Plasma is produced between a cylindrical mesh grid and a constricted anode. A spherical mesh grid of 80% optical transparency is kept inside a cylindrical grid to produce an inverted fireball. Three Langmuir probes are kept in the ambient plasma to measure the floating potential fluctuations at different positions of the chamber. It has been observed that under certain conditions of discharge voltages and magnetic fields, the mixed mode oscillation phenomena (MMOs) appears, and it shows a sequential alteration with the variation of the magnetic fields and probe positions. Low frequency instability has been observed consistently in various experimental conditions. The mechanisms of the low frequency instabilities along with the origin of the MMOs have been qualitatively explained. Extensive linear and nonlinear...

Coherence resonance can be explained using differential entropy and mutual information. This theory explores the role of external noise in stabilising chaotic circuits such as the uni-junction transistor relaxation oscillator. The phenomenon of coherence resonance maximizes differential entropy and mutual information. Thus most natural chaotic oscillators show coherence resonance in the presence of an external driving noise.

A mixture of dodecanethiol-capped Au nanoparticles (AuNPs) and the amphiphilic fatty acid, stearic acid, spread as a monomolecular layer on water surface, is observed with Brewster angle microscopy (BAM) to form a two-dimensional network of AuNP clusters through demixing, at concentration of AuNPs by weight (ρ[over ¯])>10% and the surface pressure (π)≥10mNm^{-1}. For π=15mNm^{-1}, the number of nodes (n) remains unchanged till ∼2 hours and then changes over to a lower n state, where the pattern consists of almost perfect circles with greater in-plane thickness of the AuNP lamellae. For the higher n state the mean-square fluctuation of BAM intensity remains flat and then decays as f(ξ)=ξ^{2α} with α∼0.6 (correlated fluctuations) over the length scales of 400μm-6μm and below 6μm, respectively. For the lower n state the fluctuation decays almost over the entire length scale with α=0.3, indicating emergence of aperiodicity from quasiperiodicity and a changeover to anticorrelated fluctuations. These patterns can be looked at as two distinct chaotic trajectories in the I-I^{'} phase space of the system (I being the scattered light intensity at any position of the pattern and I^{'} its gradient) with characteristic Lyapunov exponents.

The multiscale dynamics of glow discharge plasma is analysed through wavelet transform, whose scale dependent variable window size aptly captures both transients and non-stationary periodic behavior. The optimal time-frequency localization ability of the continuous Morlet wavelet is found to identify the scale dependent periodic modulations efficiently, as also the emergence of neutral turbulence and dissipation, whereas the discrete Daubechies basis set has been used for detrending the temporal behavior to reveal the multi-fractality of the underlying dynamics. The scaling ex- ponents and the Hurst exponent have been estimated through wavelet based detrended fluctuation analysis,and also Fourier methods and rescale range analysis., 7 pages, 13 figures, 1 table

The experimental determination of the dependance of confinement time of runaways on various discharge parameters has been presented along with the angular distribution of hard X-rays (HXrays) emitted from the torus in presence and absence of Langmuir probes.

A fully nonlinear analysis has revealed large amplitude ion acoustic compressive solitary waves beyond the predicted limit (? < 3) (Goswami B N and Buti B 1976 Phys. Lett. A 57 149) of K-dV equation. In a hot electron dominated plasma, dispersion of a compressive solitary wave is found to increase with increasing Th which bounds thee corresponding solution by some minimum value of cold to hot electron temperature ratio.

The current penetration in the startup phase of the SINP tokamak discharge is investigated by using soft X ray diagnostics. It is found that the current penetration during the current rise phase is anomalous, and the results show that current driven ion acoustic instability must be the most prominent candidate for rapid current penetration.

Two interesting features of runaway behaviour are observed in the startup phase of the very low qa (VLQ) (1 < qa < 2) discharges in the SINP tokamak. As qa was reduced by lowering the toroidal field values, the hard X (HX) ray intensity (which indicates the presence of runaway electrons) fell considerably. The time at which the peak in the HX ray intensity occurs also shifts ahead in time, indicating premature dumping of the runaway electrons. This seems to aid the development of the rest of the discharge as exhibited by the diamagnetic loop signal.

Anomalous width–amplitude variations were observed in large amplitude rarefactive solitary waves which show increasing width with increasing amplitude, contrasting the usual reciprocal relation between the square of the width and the amplitude, beyond a certain value of the plasma parameters [S. S. Ghosh, K. K. Ghosh, and A. N. Sekar Iyengar, Phys. Plasmas, 3, 3939 (1996)]. For the limiting maximum amplitude, the “increasing width” solitary wave tends to a double layer-like solution. The overall variation was found to depend crucially on the specific parameter space. From a detailed investigation of the above behavior, a plausible physical explanation has been presented for such increases in the width. It is found that the ions’ initial kinetic energies and the cold electron concentration within the perturbed region play a significant role in determining the observed width–amplitude variation. This contradicts the investigation of Sayal, Yadav, and Sharma [Phys. Scr. 47, 576 (1993)].

It is observed that, there exist certain forbidden regions in ion temperatures, for a compressive solitary wave, which do not have any solitary wave solution. These regions exist for a two- as well as a single-electron temperature plasma. A physical model is proposed to explain this phenomenon on the basis of the energy relation. It is revealed that a one-dimensional single warm ion fluid consists of two distinct energy components. A simple algebraic condition has been derived which expresses the balance between nonlinearity and dispersion for a fully nonlinear solitary wave. It shows that both the nonlinearity and dispersion decrease with increasing ion temperature and that the balance condition is well maintained for the whole spectrum of solitary wave solutions.

The non-stationary dynamics of a bouncing ball, comprising of both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signature of self-similarity, complex scaling behavior and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding to neutral turbulence, viscous dissipation regions and different time varying periodic modulations., Comment: 17 pages, 10 figures, 1 table

An exact analytical form of Sagdeev pseudopotential has been derived for a two electron temperature warm ion plasma, from which ion acoustic rarefactive solitary wave solutions could be investigated for a wide range of different plasma parameters, viz., ion temperature (σ), cold to hot electron temperature ratio (β), and initial cold electron concentration (μ). Explicitly large Mach numbers have been obtained for increasing hot to cold electron temperature ratios, and an analytical condition for the upper bound of the Mach number has been derived for such a rarefactive solitary wave. It is found that the width of these waves obey Korteweg–de Vries soliton‐type behavior only for small amplitudes (i.e., eφ/Teff

Attempts to operate a tokamak at qa < 2 are normally found to terminate with a major disruption. In the SINP tokamak, however, it has been found possible to operate at qa < 1 with comparative ease. In this letter, an attempt is made to quantify the rate of current rise required to set up discharges having qa < 2 and qa < 1 by comparing the risetime with the resistive diffusion timescale. It has been observed that discharges with qa less than a particular value can be obtained if the time taken to cross the previous qa barrier is less than the resistive diffusion time. When the resistive diffusion time is less than the time taken to cross a particular qa barrier, it becomes extremely difficult to cross the next lower qa barrier

The paper presents an application of empirical mode decomposition (EMD) for the analysis of intermittent chaotic fluctuations from a glow discharge plasma. Here, the nature of the oscillations changes from an initial relaxation oscillation to a final chaotic oscillatory state via intermittent chaos. The time series data have been decomposed into several intrinsic mode functions (IMFs) using EMD. Furthermore, the estimation of the variance of the IMFs and the correlation of these IMFs with the original time series help us to identify the presence of coherent modes in the fluctuations. Through this analysis, we could clearly observe that initially during the relaxation oscillations the system was dominated by one type of coherent mode, whereas in the final chaotic state, it was dominated by another coherent mode. In the intermediate case, i.e., intermittent chaotic state, both the coherent modes are seen to be present. We have also used rescaled range ( R / S ) statistical method to identify the coherent mo...

Floating potential fluctuations associated with an anode fireball in a glow discharge plasma in the toroidal vacuum vessel of the SINP tokamak are found to exhibit different kinds of oscillations under the action of vertical magnetic field of different strengths. While increasing the vertical magnetic field, the fluctuations have shown transitions as: chaotic oscillation → inverse homoclinic transition → intermittency → chaotic oscillation. However, on decreasing the magnetic field, the fluctuations are seen to follow: chaotic oscillations → homoclinic transition → chaotic oscillation; that is the intermittent feature is not observed. Fireball dynamics is found to be closely related to the magnetic field applied; results of visual inspection with a high speed camera are in close agreement with the fluctuations, and the fireball dynamics is found to be closely related to the transitions. The statistical properties like skewness, kurtosis, and entropy of the fluctuations are also found to exhibit this hysteresis behaviour.

Recurrence is an ubiquitous feature which provides deep insights into the dynamics of real dynamical systems. A suitable tool for investigating recurrences is recurrence quantification analysis (RQA). It allows, e.g., the detection of regime transitions with respect to varying control parameters. We investigate the complexity of different coexisting nonlinear dynamical regimes of the plasma floating potential fluctuations at different magnetic fields and discharge voltages by using recurrence quantification variables, in particular, DET, Lmax, and Entropy. The recurrence analysis reveals that the predictability of the system strongly depends on discharge voltage. Furthermore, the persistent behaviour of the plasma time series is characterized by the Detrended fluctuation analysis technique to explore the complexity in terms of long range correlation. The enhancement of the discharge voltage at constant magnetic field increases the nonlinear correlations; hence, the complexity of the system decreases, which corroborates the RQA analysis.

Plasma fireballs are generated due to a localized discharge and appear as a luminous glow with a sharp boundary, which suggests the presence of a localized electric field such as electrical sheath or double layer structure. The present work reports the observation of normal and inverse homoclinic bifurcation phenomena in plasma oscillations that are excited in the presence of fireball in a double plasma device. The controlling parameters for these observations are the ratio of target to source chamber (nT/nS) densities and applied electrode voltage. Homoclinic bifurcation is noticed in the plasma potential fluctuations as the system evolves from narrow to long time period oscillations and vice versa with the change of control parameter. The dynamical transition in plasma fireball is demonstrated by spectral analysis, recurrence quantification analysis (RQA), and statistical measures, viz., skewness and kurtosis. The increasing trend of normalized variance reflects that enhancing nT/nS induces irregularity in plasma dynamics. The exponential growth of the time period is strongly indicative of homoclinic bifurcation in the system. The gradual decrease of skewness and increase of kurtosis with the increase of nT/nS also reflect growing complexity in the system. The visual change of recurrence plot and gradual enhancement of RQA variables DET, Lmax, and ENT reflects the bifurcation behavior in the dynamics. The combination of RQA and spectral analysis is a clear evidence that homoclinic bifurcation occurs due to the presence of plasma fireball with different density ratios. However, inverse bifurcation takes place due to the change of fireball voltage. Some of the features observed in the experiment are consistent with a model that describes the dynamics of ionization instabilities.

Glow discharge plasma in the excitable regime shows rich dynamical behavior under external forcing. By perturbing the plasma with a subthreshold sawtooth periodic signal, we obtained small subthreshold oscillations that showed resonance with the perturbation frequency. The resonance phenomenon can be useful to estimate characteristic of an excitable system. However, for suprathreshold perturbation, frequency entrainment was observed. In this case, the system showed harmonic frequency entrainment for the perturbation frequencies greater than the characteristic frequency of the system and the excitable behavior for the perturbation frequencies well below the characteristic frequency. The experiments were performed in a glow-discharge plasma where excitability was achieved at a suitable discharge voltage and gas pressure.

Operation of most tokamaks in limited byqa, the edge safety factor, which is usually about 2–3. In the SINP tokamak we have been able to obtain discharges withqa values as low as 0·8. In this paper we describe our results on the setting up processes and the MHD activity associated with these ultra lowqa discharges.

We have investigated a mode-coupling mechanism between kinetic Alfvén waves and a collisional drift wave in an inhomogeneous cylindrical plasma. Drift waves satisfying the condition k⊥D > 1/r0 (where r0 is the radius of the plasma cylinder) are stabilized by the low-frequency ponderomotive force generated by the kinetic Alfvén waves. For typical plasma parameters and a moderate level of Alfven-wave intensity the stabilization factor is comparable to the destabilization mechanism due to collisions.

We have presented a novel technique of detecting intermittencies in a financial time series of the foreign exchange rate data of U.S.- Euro dollar(US/EUR) using a combination of both statistical and spectral techniques. This has been possible due to Continuous Wavelet Transform (CWT) analysis which has been popularly applied to fluctuating data in various fields science and engineering and is also being tried out in finance and economics. We have been able to qualitatively identify the presence of nonlinearity and chaos in the time series of the foreign exchange rates for US/EURO (United States dollar to Euro Dollar) and US/UK (United States dollar to United Kingdom Pound) currencies. Interestingly we find that for the US-INDIA(United States dollar to Indian Rupee) foreign exchange rates, no such chaotic dynamics is observed. This could be a result of the government control over the foreign exchange rates, instead of the market controlling them.

Background: Investigation of the functioning of the brain in living systems has been a major effort amongst scientists and medical practitioners. Amongst the various disorder of the brain, epilepsy has drawn the most attention because this disorder can affect the quality of life of a person. In this paper we have reinvestigated the EEGs for normal and epileptic patients using surrogate analysis, probability distribution function and Hurst exponent. Results: Using random shuffled surrogate analysis, we have obtained some of the nonlinear features that was obtained by Andrzejak \textit{et al.} [Phys Rev E 2001, 64:061907], for the epileptic patients during seizure. Probability distribution function shows that the activity of an epileptic brain is nongaussian in nature. Hurst exponent has been shown to be useful to characterize a normal and an epileptic brain and it shows that the epileptic brain is long term anticorrelated whereas, the normal brain is more or less stochastic. Among all the techniques, used here, Hurst exponent is found very useful for characterization different cases. Conclusions: In this article, differences in characteristics for normal subjects with eyes open and closed, epileptic subjects during seizure and seizure free intervals have been shown mainly using Hurst exponent. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brain activity shows long range anticorrelation., Comment: Keywords:EEG, epilepsy, Correlation dimension, Surrogate analysis, Hurst exponent. 9 pages

Continuous wavelet transform (CWT) based time-scale and multi-fractal analyses have been carried out on the anode glow related nonlinear floating potential fluctuations in a hollow cathode glow discharge plasma. CWT has been used to obtain the contour and ridge plots. Scale shift (or inversely frequency shift) which is a typical nonlinear behaviour, has been detected from the undulating contours. From the ridge plots, we have identified the presence of nonlinearity and degree of chaoticity. Using the wavelet transform modulus maxima technique we have obtained the multi-fractal spectrum for the fluctuations at different discharge voltages and the spectrum was observed to become a monofractal for periodic signals. These multi-fractal spectra were also used to estimate different quantities like the correlation and fractal dimension, degree of multi-fractality and complexity parameters. These estimations have been found to be consistent with the nonlinear time series analysis., 6 pages, 5 figures, glow discharge plasma; Multifractal spectrum; contour plots, ridge plots, correlation dimension, complexity parameter

Stochastic Resonance (SR) and Coherence Resonance (CR) have been studied experimentally in the discharge plasma close to a homoclinic bifurcation. For the SR phenomena, it is observed that a superimposed subthreshold periodic signal can be recovered via stochastic modulations of the discharge voltage. Furthermore, it is realized that even in the absence of a subthreshold deterministic signal, the system dynamics can be recovered and optimized using noise. This effect is defined as CR in the literature. In the present experiments, induction of SR and CR are quantified using the Absolute Mean Difference (AMD) and Normalized Variance (NV) techniques respectively. AMD is a new statistical tool to quantify regularity in the stochastic resonance and is independent of lag., 6 page

We report on the experimental observation of canard orbit and mixed mode oscillations (MMOs) in an excitable glow discharge plasma induced by an external magnetic field perturbation using a bar magnet. At a small value of magnetic field, small amplitude quasiperiodic oscillations were excited, and with the increase in the magnetic field, large amplitude oscillations were excited. Analyzing the experimental results, it seems that the magnetic field could be playing the role of noise for such nonlinear phenomena. It is observed that the noise level increases with the increase in magnetic field strength. The experimental results have also been corroborated by a numerical simulation using a FitzHugh-Nagumo like macroscopic model derived from the basic plasma equations and phenomenology, where the noise has been included to represent the internal plasma noise. This macroscopic model shows MMO in the vicinity of the canard point when an external noise is added.

Floating potential fluctuations from a direct current magnetron sputtering plasma have been analysed using time series analysis techniques like phase space plots, power spectra, frequency bifurcation plot, etc. The system exhibits quasiperiodic-chaotic-quasiperiodic-chaotic transitions as the discharge voltage was increased. The transitions of the fluctuations, quantified using the largest Lyapunov exponent, have been corroborated by Hurst exponent and the Shannon entropy. The Shannon entropy is high for quasiperiodic and low for chaotic oscillations.

Floating potential fluctuations of a glow discharge plasma are found to exhibit different kinds of mixed mode oscillations. Power spectrum analysis reveals that with change in the nature of the mixed mode oscillation (MMO), there occurs a transfer of power between the different harmonics and subharmonics. The variation in the chaoticity of different types of mmo was observed with the study of Lyapunov exponents. Estimates of correlation dimension and the Hurst exponent suggest that these MMOs are of low dimensional nature with an anti persistent character. Numerical modeling also reflects the experimentally found transitions between the different MMOs.

Experimental results on the nonlinear dynamics of two coupled glow discharge plasma sources are presented. A variety of nonlinear phenomena including frequency synchronization and frequency pulling are observed as the coupling strength is varied. Numerical solutions of a model representation of the experiment consisting of two coupled asymmetric Van der Pol type equations are found to be in good agreement with the observed results.

Detection of nonlinearity has been carried out in periodic and aperiodic floating potential fluctuations of DC glow discharge plasma by generating surrogate data using iterative amplitude adjusted Fourier transform method. We introduce “delay vector variance” analysis (DVV) for the first time, which allows reliable detection of nonlinearity and provides some easy to interpret diagram conveying information about the nature of the experimental floating potential fluctuations (FPF). The method of false nearest neighbourhood is deployed on the FPF's to find a good embedding so as to be acquainted with the precise knowledge of m, which is desirable for carrying out DVV analysis. The emergence of nonlinearity with increase in discharge voltage has been ensured by taking into consideration the total energy present in different band of frequencies excited due to nonlinear processes. Rejection of null hypothesis has been verified by performing the rank test method that confirms the presence of nonlinearity quantitatively.

Experimental observations consistent with Self Organized Criticality (SOC) have been obtained in the electrostatic floating potential fluctuations of a dc glow discharge plasma. Power spectrum exhibits a power law which is compatible with the requirement for SOC systems. Also the estimated value of the Hurst exponent (self similarity parameter), H being greater than 0.5, along with an algebraic decay of the autocorrelation function, indicate the presence of temporal long-range correlations, as may be expected from SOC dynamics. This type of observations in our opinion has been reported for the first time in a glow discharge system., Key Words: Glow discharge; Self Organized Criticality; Hurst exponent; R/S technique; Power spectrum; Autocorrelation function; Nongaussian probability distribution function. Phys Lett A (article in Press)

Glow discharge plasmas exhibit various types of self excited oscillations for different initial conditions like discharge voltages and filling pressures. The behavior of such oscillations associated with the anode glow have been investigated using nonlinear techniques like correlation dimension, largest Lyapunov exponent etc. It is seen that these oscillations go to an ordered state from a chaotic state with increase in input energy i.e. with discharge voltages implying occurrence of inverse bifurcations. These results are different from the other observations wherein the fluctuations have been observed to go from ordered to chaotic state., Submitted to Chaos