Evidence of homoclinic chaos in the plasma of a glow discharge

Experimental investigation of the period-adding bifurcation route to chaos in plasma

Since the characteristic timescales of the various transport processes inside the discharge plasma span several orders of magnitude, it can be regarded as a typical fast-slow system. Interestingly, in this work, a special kind of complex oscillatory dynamics composed of a series of large-amplitude relaxation oscillations and small-amplitude near-harmonic oscillations, namely, mixed-mode oscillations (MMOs), was observed. By using the ballast resistance as the control parameter, a period-adding bifurcation sequence of the MMOs, i.e., from L^{s} to L^{s+1}, was obtained in a low-pressure DC glow discharge system. Meanwhile, a series of intermittently chaotic regions caused by inverse saddle-node bifurcation was embedded between the two adjacent periodic windows. The formation mechanism of MMOs was analyzed, and the results indicated that the competition between electron production and electron loss plays an important role. Meanwhile, the nonlinear time series analysis technique was used to study the dynamic behavior quantitatively. The attractor in the reconstructed phase space indicated the existence of the homoclinic orbits of type Γ^{-}. In addition, by calculating the largest Lyapunov exponent (LLE), the chaotic nature of these states was confirmed and quantitatively characterized. With the decrease in the ballast resistance, the return map of the chaotic state gradually changed from the nearly one-dimensional single-peak structure to the multibranch structure, which indicates that the dissipation of the system decreased. By further calculating the correlation dimension, it was shown that the complexity of the strange attractors increased for higher-order chaotic states.

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.

The Existence of Autonomous Chaos in EDM Process

The dynamical evolution of electrical discharge machining (EDM) has drawn immense research interest. Previous research on mechanism analysis has discussed the deterministic nonlinearity of gap states at pulse-on discharging duration, while describing the pulse-off deionization process separately as a stochastic evolutionary process. In this case, the precise model describing a complete machining process, as well as the optimum performance parameters of EDM, can hardly be determined. The main purpose of this paper is to clarify whether the EDM system can maintain consistency in dynamic characteristics within a discharge interval. A nonlinear self-maintained equivalent model is first established, and two threshold conditions are obtained by the Shilnikov theory. The theoretical results prove that the EDM system could lead to chaos without external excitation. The time series of the deionization process recorded in the EDM experiments are then analyzed to further validate this theoretical conclusion. Qualitative chaotic analyses verify that the autonomous EDM process has chaotic characteristics. Quantitative methods are used to estimate the chaotic feature of the autonomous EDM process. By comparing the quantitative results of the autonomous EDM process with the non-autonomous EDM process, a deduction is further made that the EDM system will evolve towards steady chaos under an autonomous state.

Heartbeat instability as auto-oscillation between dim and bright void regimes

We investigated the self-excited as well as optogalvanically stimulated heartbeat instability in RF discharge complex plasma. Three video cameras measured the motion of the microparticles, the plasma emission, and the laser-induced fluorescence simultaneously. Comprehensive studies of the optogalvanic control of the heartbeat instability revealed that the microparticle suspension can be stabilized by a continuous laser, whereas a modulated laser beam induces the void contraction either transiently or resonantly. The resonance occurred when the laser modulation frequency coincided with the frequency of small breathing oscillations of the microparticle suspension, which are known to be a prerequisite to the heartbeat instability. Based on the experimental results we suggest that the void contraction during the instability is caused by an abrupt void transition from the dim to the bright regime [Pikalev et al., Plasma Sources Sci. Technol. 30, 035014 (2021)PSTEEU0963-025210.1088/1361-6595/abe0a2]. In the bright regime, a time-averaged electric field at the void boundary heats the electrons causing bright plasma emission inside the void. The dim void has much lower electric field at the boundary and exhibits therefore no emission feature associated with it.

Average conservative chaos in quantum dusty plasmas

We consider a hydrodynamic model of a quantum dusty plasma. We prove mathematically that the resulting dust ion-acoustic plasma waves present the property of being conservative on average. Furthermore, we test this property numerically, confirming its validity. Using standard techniques from the study of dynamical systems, as, for example, the Lyapunov characteristic exponents, we investigate the chaotic dynamics of the plasma and show numerically its existence for a wide range of parameter values. Finally, we illustrate how chaotic dynamics organizes in the parameter space for fixed values of the initial conditions, as the Mach number and the quantum diffraction parameter are continuously varied.

Quasi-Static Pull-in: an Instability in Electrostatic Actuators

We identify a new instability in electrostatic actuators dubbed quasi-static pull-in. We report experimental evidence of the instability and study its characteristics in two types of micro actuators operating in ambient air. We found that the underlying mechanism is a fast-slow dynamic interaction between slowly-varying electrostatic excitation and fast resonator response that instigate large non-resonant oscillatory orbits and eventually disappears in a global Shilnikov bifurcation. Based on these findings, we formulate and present a new taxonomy of pull-in instabilities in electrostatic actuators.

Complex dynamics of a dc glow discharge tube: Experimental modeling and stability diagrams

We report a detailed experimental study of the complex behavior of a dc low-pressure plasma discharge tube of the type commonly used in commercial illuminated signs, in a microfluidic chip recently proposed for visible analog computing, and other practical devices. Our experiments reveal a clear quasiperiodicity route to chaos, the two competing frequencies being the relaxation frequency and the plasma eigenfrequency. Based on an experimental volt-ampere characterization of the discharge, we propose a macroscopic model of the current flowing in the plasma. The model, governed by four autonomous ordinary differential equations, is used to compute stability diagrams for periodic oscillations of arbitrary period in the control parameter space of the discharge. Such diagrams show self-pulsations to emerge remarkably organized into intricate mosaics of stability phases with extended regions of multistability (overlap). Specific mosaics are predicted for the four dynamical variables of the discharge. Their experimental observation is an open challenge.

Striated microdischarges in an asymmetric barrier discharge in argon at atmospheric pressure

The investigation of striated microdischarges in barrier discharges in argon at atmospheric pressure is reported. Microdischarges were investigated by means of electrical measurements correlated with intensified CCD camera imaging. The scaling law theory known from low-pressure glow discharge diagnostics was applied in order to describe and explain this phenomenon. The investigated microdischarge is characterized as a transient atmospheric-pressure glow discharge with a stratified column. It can be described by similarity parameters i/r≈0.13 A/cm, pr≈5 Torr cm, and 3<λ/r<5 with the current i, pressure p, interval of subsequent striations λ, and radius of the plasma channel r. An attempt to describe the mechanism of creation of a striated structure is given, based on an established model of the spatial electron relaxation.

Chaotically spiking attractors in suspended-mirror optical cavities

A high-finesse suspended-mirror Fabry-Perot cavity is experimentally studied in a regime where radiation pressure and photothermal effect are both relevant. The competition between these phenomena, operating at different timescales, produces unobserved dynamical scenarios where an initial Hopf instability is followed by the birth of small-amplitude chaotic attractors that erratically but deterministically trigger optical spikes. The observed dynamical regimes are well reproduced by a detailed physical model of the system.

Non-Shilnikov cascades of spikes and hubs in a semiconductor laser with optoelectronic feedback

Incomplete homoclinic scenarios were recently measured in a semiconductor laser with optoelectronic feedback. We show here that such a laser contains cascades of spirals of periodic oscillations and hubs which look identical to the familiar ones observed in complete homoclinic scenarios. This means that hubs are far more general than presumed so far, being not limited by Shilnikov's theorem. Laser hubs open the possibility of measuring complex distributions of non-Shilnikov laser oscillations, and we briefly discuss how to do it.

Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit

We report the discovery of a remarkable "periodicity hub" inside the chaotic phase of an electronic circuit containing two diodes as a nonlinear resistance. The hub is a focal point from where an infinite hierarchy of nested spirals emanates. By suitably tuning two reactances simultaneously, both current and voltage may have their periodicity increased continuously without bound and without ever crossing the surrounding chaotic phase. Familiar period-adding current and voltage cascades are shown to be just restricted one-parameter slices of an exceptionally intricate and very regular onionlike parameter surface centered at the focal hub which organizes all the dynamics.

Mixed-mode oscillations in complex-plasma instabilities

Instabilities in dusty plasmas are frequent phenomena. We show that some instabilities can be described by mixed-mode oscillations often encountered in chemical systems or neuronal dynamics and studied through dynamical system theories. The time evolution of these instabilities is studied through the change in the associated waveform. Frequency and interspike interval are analyzed and compared to results obtained in other scientific fields concerned by mixed-mode oscillations.

Accumulation boundaries: codimension-two accumulation of accumulations in phase diagrams of semiconductor lasers, electric circuits, atmospheric and chemical oscillators

We report high-resolution phase diagrams for several familiar dynamical systems described by sets of ordinary differential equations: semiconductor lasers; electric circuits; Lorenz-84 low-order atmospheric circulation model; and Rössler and chemical oscillators. All these systems contain chaotic phases with highly complicated and interesting accumulation boundaries, curves where networks of stable islands of regular oscillations with ever-increasing periodicities accumulate systematically. The experimental exploration of such codimension-two boundaries characterized by the presence of infinite accumulation of accumulations is feasible with existing technology for some of these systems.

Accumulation horizons and period adding in optically injected semiconductor lasers

We study the hierarchical structuring of islands of stable periodic oscillations inside chaotic regions in phase diagrams of single-mode semiconductor lasers with optical injection. Phase diagrams display remarkable accumulation horizons: boundaries formed by the accumulation of infinite cascades of self-similar islands of periodic solutions of ever-increasing period. Each cascade follows a specific period-adding route. The riddling of chaotic laser phases by such networks of periodic solutions may compromise applications operating with chaotic signals such as, e.g., secure communications.

Synchronization in coupled cells with activator-inhibitor pathways

The functional dynamics exhibited by cell collectives are fascinating examples of robust, synchronized, collective behavior in spatially extended biological systems. To investigate the roles of local cellular dynamics and interaction strength in the spatiotemporal dynamics of cell collectives of different sizes, we study a model system consisting of a ring of coupled cells incorporating a three-step biochemical pathway of regulated activator-inhibitor reactions. The isolated individual cells display very complex dynamics as a result of the nonlinear interactions common in cellular processes. On coupling the cells to nearest neighbors, through diffusion of the pathway end product, the ring of cells yields a host of interesting and unusual dynamical features such as, suppression of chaos, phase synchronization, traveling waves, and intermittency, for varying interaction strengths and system sizes. But robust complete synchronization can be induced in these coupled cells with a small degree of random coupling among them even where regular coupling yielded only intermittent synchronization. Our studies indicate that robustness in synchronized functional dynamics in tissues and cell populations in nature can be ensured by a few transient random connections among the cells. Such connections are being discovered only recently in real cellular systems.

Shilnikov homoclinic orbit bifurcations in the Chua's circuit

We analytically describe the complex scenario of homoclinic bifurcations in the Chua's circuit. We obtain a general scaling law that gives the ratio between bifurcation parameters of different nearby homoclinic orbits. As an application of this theoretical approach, we estimate the number of higher order subsidiary homoclinic orbits that appear between two consecutive lower order subsidiary orbits. Our analytical finds might be valid for a large class of dynamical systems and are numerically confirmed in the parameter space of the Chua's circuit.

Basic structures of the Shilnikov homoclinic bifurcation scenario

We find numerically small scale basic structures of homoclinic bifurcation curves in the parameter space of the Chua circuit. The distribution of these basic structures in the parameter space and their geometrical properties constitute a complete homoclinic bifurcation scenario of this system. Furthermore, these structures and the scenario are theoretically demonstrated to be generic to a large class of dynamical systems that presents, as the Chua circuit, Shilnikov homoclinic orbits. We classify the complexity of primary and subsidiary homoclinic orbits by their order given by the number of their returning loops. Our results confirm previous predictions of structures of homoclinic bifurcation curves and extend this study to high order primary orbits. Furthermore, we identify accumulations of bifurcation curves of subsidiary homoclinic orbits into bifurcation curves of both primary and subsidiary orbits.

Discrete homoclinic orbits in a laser with feedback

We provide experimental evidence of the discrete character of homoclinic chaos in a laser with feedback. We show that the narrow chaotic windows are distributed exponentially as a function of a control parameter. The number of consecutive chaotic regions corresponds to the number of loops around the saddle focus responsible for Shilnikov chaos. The characterization of homoclinic chaos is also done through the return map of the return times at a suitable reference point.

Experimental real-time phase synchronization of a paced chaotic plasma discharge

Experimental phase synchronization of chaos in a plasma discharge is studied using a phase variable lift technique (i.e., phase points separated by 2pi are not considered as the same). Real-time observation of synchronized and unsynchronized states is made possible through a real-time sampling procedure. Parameter space regions of synchronization and unsynchronization are identified, and a set of equations is suggested to model the real plasma circuit.

Mixed-mode oscillations and chaos in a glow discharge

We present results from numerical simulations on mixed-mode oscillations and chaos excited in a glow discharge, where a model of one-dimensional fluid equations coupled with an external circuit is used. Long duration of high ion and electron densities and fast recharge of a capacitor after a breakdown contribute to the generation of mixed-mode oscillations. The chaotic behavior is characterized by a one-dimensional multibranched map.