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Interplay of transition of floating potential fluctuations in a glow discharge plasma in the toroidal vacuum vessel of SINP tokamak has been observed. With variation in the strength of the vertical and toroidal magnetic fields, regular and inverted relaxation oscillations as well as sinusoidal oscillations are observed with the slow and fast time scale of the relaxation oscillations reversing their nature at a high value of vertical magnetic field strength. However for small value of toroidal magnetic field the transitions follow relaxation $\rightarrow$ chaotic oscillations with the chaotic nature prevailing at higher values of toroidal magnetic field. Evolution of associated anode fireball dynamics under the action of increasing vertical, toroidal as well as increasing vertical field at a fixed toroidal field (mixed field) of different strength has been studied. Estimation of phase coherence index for each case has been carried out to examine the evidence of finite nonlinear interaction. A comprehensive study of the dynamics of the fireball is found to be associated with the values of phase coherence index. The index is found to take maximum values for the case of toroidal, mixed field when there is an existence of power/energy concentration in a large region of frequency band. A detailed study of the scaling region using detrended fluctuation analysis (DFA) by estimating the scaling exponent has been carried out for increasing values of discharge voltage, vertical, toroidal as well as the mixed field (toroidal plus vertical). A persistence long range behaviour associated with the nature of the anode glow has been investigated in case of higher values of toroidal, mixed field whereas increasing DV, vertical magnetic field leads to a perfectly correlated dynamics with values of scaling exponent greater than unity, 19 pages, 17 figures and 1 table

The evidence of finite nonlinear interaction in a DC glow discharge plasma has been demonstrated by estimating phase coherence index for different types external forcing techniques likewise noise, sinusoidal, square etc. The existence of finite phase coherence index i.e finite correlation prompts us to carry out nonlinearity analysis using delay vector variance (DVV). Finite nonlinear interaction obtained from phase coherence index values is observed to be predominant at a particular amplitude of square forcing which corroborates our nonlinearity analysis using DVV. Existence of phase coherence index has been demonstrated introducing continuous wavelet transform (CWT). Characterization of the difference in the phase distribution by the difference in the waveform in real space instead of dealing in Fourier space has been facilitated by introducing structure function or path length for different orders to study and identify the dynamical system. The expression of path length eventually enables us to evaluate the phase coherence index. The transition in the dynamics is observed through recurrence plot techniques which is an efficient method to observe the critical regime transitions in dynamics.

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.

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.

Regularity has always been attributed to periodicity. However, there has been a spurt of interest in another unique type of regularity called anitperiodicity. In this paper we have presented results of antiperiodic oscillations obtained from a forced duffing equation with negative linear stiffness wherein the increase in the number of peaks in anti periodic oscillation with the forcing strength has been observed. Similarity function has been used to identify the antiperiodic oscillation and further the bifurcation diagram has been plotted and stability analysis of the fixed points have been carried out to understand its dynamics. An analog electronic circuit governed by the forced Duffing equation has been designed and developed to investigate the dynamics of the antiperiodic oscillations. The circuit is quite robust and stable to enable the comparison of its analog output with the numerically simulated data. Power spectrum analysis obtained by fast Fourier transform has been corroborated using a nonlinear statistical technique called rescale range analysis method. By this technique we have estimated the Hurst exponents and detected the coherent frequencies present in the system. (C) 2015 Elsevier Ltd. All rights reserved.

Recurrence quantification analysis (RQA) is used to study dynamical systems and to identify the underlying physics when a system exhibits a transition due to changes in some control parameter. The tendency of reoccurrence of different states after certain interval reflects and reveals the hidden patterns of a complex time series data. The present work involves the study of the floating potential fluctuations of a glow discharge plasma obtained by using a Langmuir probe. Determinism, entropy and Lmax are important measures of RQA that show an increasing and decreasing trend with variation in the values of discharge voltages and indicate an order-chaos transition in the dynamics of the fluctuations. Statistical analysis techniques represented by skewness and kurtosis are also supportive of a similar phenomenon occurring in the system.