Controlling chaos in a discharge plasma

Numerical simulation of the bifurcation-remerging process and intermittency in an undriven direct current glow discharge

As a complex nonlinear medium, gas discharge plasma can exhibit various nonlinear discharge behaviors. In this study, in order to investigate the chaos phenomenon in the subnormal glow region of an undriven direct current glow discharge, a two-dimensional plasma fluid model is established coupled with a circuit model as a boundary condition. Using the applied voltage as control parameter in the simulation, the complete period-doubling bifurcation and inverse period-doubling bifurcation processes in the oscillation region are found, and the influence of the applied voltage on the spatiotemporal distribution of plasma parameters during the bifurcation-remerging process is examined. In addition, the spatial distribution of the plasma parameters of the bifurcation-remerging process is also examined. Also, a series of periodic windows are present in the chaotic region, where the positions and relative order are generally consistent with the universal sequence. Additionally, this study showed that the intermittent chaos appears near the period-3 window, and the bursts appearing in the approximate periodic motion becomes more and more frequent as the control parameters move away from the saddle-node bifurcation point, which shows the typical type-I intermittent chaos characteristics.

Quantitative control of noise in mammalian gene expression by dynamic histone regulation

Fluctuation ('noise') in gene expression is critical for mammalian cellular processes. Numerous mechanisms contribute to its origins, yet the mechanisms behind large fluctuations that are induced by single transcriptional activators remain elusive. Here, we probed putative mechanisms by studying the dynamic regulation of transcriptional activator binding, histone regulator inhibitors, chromatin accessibility, and levels of mRNAs and proteins in single cells. Using a light-induced expression system, we showed that the transcriptional activator could form an interplay with dual functional co-activator/histone acetyltransferases CBP/p300. This interplay resulted in substantial heterogeneity in H3K27ac, chromatin accessibility, and transcription. Simultaneous attenuation of CBP/p300 and HDAC4/5 reduced heterogeneity in the expression of endogenous genes, suggesting that this mechanism is universal. We further found that the noise was reduced by pulse-wide modulation of transcriptional activator binding possibly as a result of alternating the epigenetic states. Our findings suggest a mechanism for the modulation of noise in synthetic and endogenous gene expression systems.

Controlling spatiotemporal chaos in chains of dissipative Kapitza pendula

The control of chaos (suppression and enhancement) of a damped pendulum subjected to two perpendicular periodic excitations of its pivot (one chaos inducing and the other chaos controlling) is investigated. Analytical (Melnikov analysis) and numerical (Lyapunov exponents) results show that the initial phase difference between the two excitations plays a fundamental role in the control scenario. We demonstrate the effectiveness of the method in suppressing spatiotemporal chaos of chains of identical chaotic coupled pendula where homogeneous regularization is obtained under localized control on a minimal number of pendula. Additionally, we demonstrate the robustness of the control scenario against changes in the coupling function. In particular, synchronization-induced homogeneous regularization of chaotic chains can be highly enhanced by considering time-varying couplings instead of stationary couplings.

Controlling self-organized criticality in sandpile models

We introduce an external control to reduce the size of avalanches in some sandpile models exhibiting self-organized criticality. This rather intuitive approach seems to be missing in the vast literature on such systems. The control action, which amounts to triggering avalanches in sites that are near to become critical, reduces the probability of very large events, so that energy dissipation occurs most locally. The control is applied to a directed Abelian sandpile model driven by both uncorrelated and correlated depositions. The latter is essential to design an efficient and simple control heuristic, but has only small influence in the uncontrolled avalanche probability distribution. The proposed control seeks a trade-off between control cost and large event risk. Preliminary results hint that the proposed control works also for an undirected sandpile model.

Parametric investigation of nonlinear fluctuations in a dc glow discharge plasma

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 has 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 an 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.

Melnikov method approach to control of homoclinic/heteroclinic chaos by weak harmonic excitations

A review on the application of Melnikov's method to control homoclinic and heteroclinic chaos in low-dimensional, non-autonomous and dissipative oscillator systems by weak harmonic excitations is presented, including diverse applications, such as chaotic escape from a potential well, chaotic solitons in Frenkel-Kontorova chains and chaotic-charged particles in the field of an electrostatic wave packet.

Controlling chaos in a Lorenz-like system using feedback

We demonstrate that the dynamics of an autonomous chaotic laser can be controlled to a periodic or steady state under self-synchronization. In general, past the chaos threshold the dependence of the laser output on feedback applied to the pump is submerged in the Lorenz-like chaotic pulsation. However there exist specific feedback delays that stabilize the chaos to periodic behavior or even steady state. The range of control depends critically on the feedback delay time and amplitude. Our experimental results are compared with the complex Lorenz equations which show good agreement.

Transforming chaos to periodic oscillations

We demonstrate that the dynamics of an autonomous chaotic class C laser can be controlled to a periodic state via external modulation of the pump. In the absence of modulation, above the chaos threshold, the laser exhibits Lorenz-like chaotic pulsations. The average amplitude and frequency of these pulsations depend on the pump power. We find that there exist parameter windows where modulation of the pump power extinguishes the chaos in favor of simpler periodic behavior. Moreover we find a number of locking ratios between the pump and laser output follow the Farey sequence.

Phase synchronization and suppression of chaos through intermittency in forcing of an electrochemical oscillator

External periodic forcing was applied to a chaotic chemical oscillator in experiments on the electrodissolution of Ni in sulfuric acid solution. The amplitude and the frequency (Omega) of the forcing signal were varied in a region around Omega=omega(0), where omega(0) is the frequency of the unforced signal. Phase synchronization occurred with increase in the amplitude of the forcing. For Omega/omega(0) near 1 the signal remained chaotic after the transition to the phase-locked state; for Omega/omega(0) somewhat farther from 1 the transition was to a periodic state via intermittency. The experimental results are supported by numerical simulations using a general model for electrochemical oscillations.

Suppressing complexity via the slaving principle

The complexity of a nonlinear dynamic system can be suppressed by adding an external period force with appropriate choice of frequency and amplitude directly on the slowly changing variable of the system. Numerical results indicate that the method not only can suppress chaos but also is robust to the additive external noise.

Controlling chaos in low- and high-dimensional systems with periodic parametric perturbations

The effect of applying a periodic perturbation to an accessible parameter of various chaotic systems is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic systems can result in limit cycles for relatively small perturbations. Such perturbations can also control or significantly reduce the dimension of high-dimensional systems. Initial application to the control of fluctuations in a prototypical magnetic fusion plasma device will be reviewed.