Detection of self-organized criticality behavior in an electronic circuit designed to solve a third order non-linear ODE (NL-ODE) for a damped KdV equation.

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.

Direct observation of the external force mediated conformational dynamics of an IHF bound Holliday junction.

We have investigated the isomerization dynamics and plausible energy landscape of 4-way Holliday junctions (4WHJs) bound to integration host factor (IHF, a DNA binding protein), considering the effect of applied external force, by single-molecule FRET methods. A slowing down of the forward as well as the backward rates of the isomerization process of the protein bound 4WHJ has been observed under the influence of an external force, which indicates an imposed restriction on the conformational switching. This has also been reflected by an increase in rigidity, as observed from the increase in the single-molecule FRET (smFRET)-anisotropy values (0.270 ± 0.012 to 0.360 ± 0.008). The application of an external force has assisted the conformational transitions to share the unstacked open structure intermediate, with different rate-limiting steps and a huge induced variation in the energy landscape. Furthermore, the associated landscape of the 4WHJ is visualized in terms of rarely interconverting states embedded into the two isoforms by using nonlinear dynamics analysis, which shows that the chaoticity of the system increases at intermediate force (0.4 to 1.6 pN). The identification of chaos in our investigation provides useful information for a comprehensive explanation of the origin of the complex behavior of the system, which effectively helps us to perceive the dynamics of IHF bound 4WHJs under the influence of external force, and also demonstrates the applicability of nonlinear dynamics analysis in the field of biology.

Intrinsic noise induced coherence resonance in a glow discharge plasma.

Experimental evidence of intrinsic noise induced coherence resonance in a glow discharge plasma is being reported. Initially the system is started at a discharge voltage (DV) where it exhibited fixed point dynamics, and then with the subsequent increase in the DV spikes were excited which were few in number and with further increase of DV the number of spikes as well as their regularity increased. The regularity in the interspike interval of the spikes is estimated using normalized variance. Coherence resonance was determined using normalized variance curve and also corroborated by Hurst exponent and power spectrum plots. We show that the regularity of the excitable spikes in the floating potential fluctuation increases with the increase in the DV, up to a particular value of DV. Using a Wiener filter, we separated the noise component which was observed to increase with DV and hence conjectured that noise can play an important role in the generation of the coherence resonance. From an anharmonic oscillator equation describing ion acoustic oscillations, we have been able to obtain a FitzHugh-Nagumo like model which has been used to understand the excitable dynamics of glow discharge plasma in the presence of noise. The numerical results agree quite well with the experimental results.

Non-stationary dynamics in the bouncing ball: a wavelet perspective.

The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures 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.

Multi-scale dynamics of glow discharge plasma through wavelets: self-similar behavior to neutral turbulence and dissipation.

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 exponents and the Hurst exponent have been estimated through wavelet based detrended fluctuation analysis, and also Fourier methods and rescale range analysis.

Coherence resonance in a unijunction transistor relaxation oscillator.

The phenomenon of coherence resonance is investigated in an unijunction transistor relaxation oscillator and quantified by estimating the normal variance (NV). Depending on the measuring points, two types of NV curves have been obtained. We have observed that the degradations in coherency at higher noise amplitudes in our system is probably the result of direct interference of coherent oscillations and the stochastic perturbation. Degradation of coherency may be minimal if this direct interference of noise and coherent oscillations is eliminated.

Using wavelet analysis to investigate synchronization.

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.

Experimental observation of phase-flip transitions in two inductively coupled glow discharge plasmas.

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.

Evolution of self-organized two-dimensional patterns of nanoclusters through demixing.

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.

Dynamics of an excitable glow-discharge plasma under external forcing.

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.