Chaos Appearance Research Articles

Chaotic antiferromagnetic nano-oscillator driven by spin torque

We theoretically describe the behavior of a terahertz nano-oscillator based on an anisotropic antiferromagnetic dynamical element driven by spin torque. We consider the situation when the polarization of the spin current is perpendicular to the external magnetic field applied along the anisotropy easy axis. We determine the domain of the parametric space (field, current) where the oscillator demonstrates chaotic dynamics. Characteristics of the chaotic regimes are analyzed using conventional techniques such as spectra of the Lyapunov exponents. We show that the threshold current of the chaos appearance is particularly low in the vicinity of the spin-flop transition. In this regime, we consider the mechanism of the chaos appearance in detail when the field is fixed and the current density increases. We show that the appearance of chaos is preceded by a regime of quasiperiodic dynamics on the surface of a two-frequency torus arising in phase space as a result of the Neimark-Sacker bifurcation.

Probability Calculation of Spatial Chaos Appearance in MIMO Cascade Nonlinear Systems Using Monte Carlo Method

In this work, Monte Carlo method is used for the probability calculation of the appearance of spatial chaos in MIMO cascade nonlinear systems. The obtained results are given in tables and presented graphically using probability histograms. Their validity is confirmed by comparison with the results of spatial chaos appearance analysis that uses bifurcation diagrams, Lyapunov diagrams and spatial phase portraits.

Analysis and control of spatial limit sets and spatial chaos appearance in mimo cascade connected nonlinear systems

AbstractThe oscillatory and chaotic dynamics of MIMO cascade connected nonlinear systems are analyzed in this paper. For that purpose the known theorems of limit sets existence in appropriate nonlinear discrete systems are used. Control of spatial limit sets and spatial chaos appearance in MIMO cascade connected nonlinear systems using modified Pyragas method is also analyzed. The results are illustrated by examples and confirmed with simulations.

Analysis of spatial chaos appearance in cascade connected nonlinear electrical circuits

The system consisting of several cascade connected electrical circuits is presented in this paper. Considering the system structure and the fact that the tunnel diodes have nonlinear characteristics, one of the properties of this system is the possibility of the chaos appearance. Necessary conditions and sufficient condition for the chaos appearance in the nonlinear cascade connected systems are given and analyzed, too. The results are confirmed by bifurcation and escape-time diagrams simulation.

Dynamic chaotisation of the electronic subsystem in a graphene superlattice subjected to the electromagnetic radiation

The chaotic behaviour of the electron subsystem in a graphene superlattice is studied by the Melnikov method. The dynamic chaos of electrons in a graphene superlattice is shown to appear for certain intervals of frequencies of incident electromagnetic radiation. The frequency dependence of the radiation critical amplitude which determines the bound of chaos appearance is investigated. The values of radiation frequency at which the critical amplitude increases indefinitely were found.

Alternating current-driven graphene superlattices: Kinks, dissipative solitons, dynamic chaotization.

The possibility of the solitary electromagnetic wave formation in graphene superlattice subjected to the electromagnetic radiation is discussed. The chaotic behavior of the electron subsystem in graphene superlattice is studied by Melnikov method. Dynamic chaos of electrons is shown to appear for certain intervals of frequencies of incident electromagnetic radiation. The frequency dependence of the radiation critical amplitude which determines the bound of chaos appearance is investigated. The values of radiation frequency at which the critical amplitude increases indefinitely were found.

Chaos modelling and simulation of cascade connected nonlinear electrical systems using MATLAB/Bondsim

In this paper, a system consisting of several cascade connected nonlinear electrical circuits is presented with tunnel diodes situated in each cascade. Tunnel diodes have nonlinear characteristics, enabling the possibility of chaos appearance in a system with several cascade connected electrical circuits. In this paper, Bondsim library and tools used to simplify modelling and simulation of cascade connected electrical circuits will be presented. This library enables direct drawing of the MATLAB/Simulink block diagrams from bond graphs. MATLAB M-files were also used for escape-time diagrams simulation and defining values of bifurcation amplification.

Extension of spatiotemporal chaos in glow discharge-semiconductor systems.

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].

Chaos Appearance during Domain Wall Motion under Electronic Transfer in Nanomagnets

In this paper, we study the likelihood of chaos appearance during domain wall motion induced by electronic transfer. Considering a time-varying current density theory, we proceed to a numerical investigation of the dynamics. Using the dissipation parameter, amplitude and frequency of current density as control parameters; we show how periodic regime as well as chaotic regime can be exhibited in nanomagnetic systems. Numerical results allow setting up the periodicity and quasi-periodicity of system and chaotic phenomena occurring during magnetization switching process in nanomagnet through electronic transfer.

К вопросу о сценариях возникновения хаоса у трехмерных отображений

К вопросу о сценариях возникновения хаоса у трехмерных отображений

Experimental investigations of deterministic chaos appearance in bubbling flow

In the experiment, bubbles were generated from the brass nozzle with the inner diameter of 1.1 mm submerged in the glass tank (400 × 400 × 700 mm) filled with distillated water. Pressure fluctuations and signal from the laser-phototransistor sensor were recorded simultaneously. The movement of bubble wall was measured using a high speed camera and image processing technique. Results of analysis of images have been correlated with pressure and laser-phototransistor signals. In the analysis the Fourier spectrum, wavelet spectrum and non-linear methods (mutual information, attractor reconstruction, largest Lyapunov exponent and correlation dimension) have been used. The three applied in the paper techniques of measurement of dynamical properties of bubbling allow us to discuss in detail the mechanisms of different chaotic behaviors of bubbling. Two ranges of the air volume flow rate with different kinds of bubble chaotic behaviors have been identified. For the air volume flow rate less than 0.2 l/min the air pressure chaotic fluctuations do not cause the significant chaotic changes of bubble departure frequencies. When the air volume flow rate increases above the 0.2 l/min, the interaction between departing bubbles causes nonperiodic bubble wall movement, and then the appearance of chaotic changes of bubble departure frequency.

Simulation of bifurcation and escape—time diagrams of cascade—connected nonlinear systems for rubber strip transportation

Systems consisting of several cascade-connected transporters for rubber strip transportation are presented in this paper. In consideration of the systems structure and the fact that the technological parameters of rubber materials are time variant, one of the characteristics of these systems is the possibility of oscillations and chaos appearance. In this paper the conditions for appearance of oscillations and chaos in mentioned systems are analysed. The results are confirmed by simulation of bifurcation and escape-time diagrams.

Analysis of CT manifestations and different risk groups CT findings of small intestinal stromal tumor

Objective To investigate the CT features and different risk CT findings of intestinal stromal tumor. Methods The CT imaging data of 25 cases of intestinal stromal tumor confirmed by pathology and compared with operative and pathologic findings were retrospectively studied. Analyzing the CT features based on Histopathologieal classification of the different risk groups and using chi-square test to compare the differences. Results There were 9 cases which tumors originated from the jejunum, and 13 cases from ileum, only 3 cases from duodenum. Among them, 2 cases were submucosal type, 13 cases were intramural type, and 10 cases were subserous type. The pathologic patterns of different risk which included high-risk, intermediated-risk, low-risk, and very low-risk were 12 cases, 7 cases, 5 cases and 1 cases respectively. A typical CT manifestations of intestinal stromal tumors were a outward growth of irregular or round soft tissue mass originated in small intestine which had clear boundary and the non-homogeneous density, which corresponding to necrosis, cystic change, mucoid degeneration and sinus or cavity. Mesenteric fat invaded by tumor showed high-density lines or points shape. The Enhancement of lesion was obvious and not homogeneous which showed little change in peak of enhancement between arterial phase and venous phase. Intestinal stromal tumors took 5 cm as the boundary which including different size, shape, density, and appearance vessel-like artery shadow at arterial phase between different risk groups(low, very low-risk group and intermediated, high-risk group) were statistically different (P ＜0.05), while enhanced degree without significant difference (P ＞ 0.05). Conclusion CT findings of small intestine stromal tumor have characteristics and CT features have significant difference between different risk groups. These features of more than 5 cm in diameter, non-homogeneous density, irregular shape and chaos appearance like vascular enhancement are showed in intermediated-high-risk group. Key words: Intestinal neoplasms; Gastrointestinal stromal tumors; Tomography, X-ray computed

Gas bubble dynamics—experiment and fractal analysis

In the paper, nonlinear features of the air bubbling from a submerged glass nozzles are discussed. The air bubbles were emitted from glass nozzles of different diameters submerged in distilled water at a depth of 15 cm in a cylindrical tank of 30 cm in diameter and 37 cm height. The air volume flow rate was changed from 1 l/h to 45 l/h. A laser-photodiode and an acoustic technique system have been used. Also photographic study of bubbles departure has been carried out. Measured data have been analysed using the fractal analysis method. It has been shown that bubbles dynamics is of deterministic chaos nature and behaviours of such system can be chaotic or periodic depending on the volume flow rate. The map of chaos appearance has been constructed. Data recorded by acoustic system has been used to analysis of bubble wall movement.

Chaos in nucleate boiling––nonlinear analysis and modelling

The artificial surfaces are applied to study the pool boiling features, including the surface temperature fluctuation and nucleation sites interaction. The nonlinear analysis of temperature fluctuation has been carried out. Under the single nucleation site the low dimensional deterministic chaos has been observed. It has been found that the thermal interaction between two nucleation sites decreases and the hydrodynamic interaction increases the frequency of bubble departure. It has been also found out that hydrodynamic interaction makes that the process of bubbles departure becomes more predictable. To explain the mechanism of deterministic chaos appearance the simple model of heat transfer under the nucleation sites has been presented. The obtained results of simulations show that the nonlinearity introduced to heat transfer as a result of changing in time the heat flux absorbed by bubbles leads to chaotic changes of heating surface temperature at nucleation site. The model has been used to analyse the behavior of thermal interaction between nucleation sites with chaotically departing bubbles. The results obtained from simulation explain experimental results.

Chaos in bubbling—nonlinear analysis and modelling

In the present paper, nonlinear features and analytical results for the chaotic bubbling from a submerged orifice are described. A chain of air bubbles was produced from the single orifice of 2 mm in diameter and micro-convection induced by the bubble generation was recorded using hot-probe anemometer located close to the orifice. The air flow rate was varied widely from q=100 to 2000 cc/ min and the aspects of bubbling were observed by high-speed video. The nonlinear analysis is performed for the time series data of hot-probe anemometer especially in the range of q=435– 1500 cc/ min . The calculated largest Lyapunov exponent shows that with increase of air volume flow rate, the time period for the process of liquid flow to lose stability becomes shorter and at high air flow rate such as q=1500 cc/ min , it is shorter than the time period between subsequent bubbles. To explain such chaotic behaviors of bubbling, a simple model has been proposed. The model simulates the process of interaction between the elastic bubble wall and liquid. Simulation results compared well with the analytical results of experimental data. Summarizing, it is concluded that one of the reasons for chaos appearance is the nonlinear character of interaction between an elastic bubble wall and the liquid stream.

Effect of magnetic field on the chaos appearance fields in a triglycine sulfate crystal

Effects of a constant magnetic field, the amplitude of an alternating electric field, and the temperature on the values of fields corresponding to the appearance and disappearance of chaotic oscillations were studied in the ferroelectric phase of a triglycine sulfate crystal. A mechanism of the appearance of a magnetic moment, induced by the repolarization current, during the lateral motion of a 180° domain wall is considered.

Synchronizing the chaotic oscillations by external force

The system of two coupled oscillators with inertial excitation is studied. The chaos and ‘hyperchaos’ regions are estimated numerically. The relation between a threshold of synchronization and a metric entropy is discussed. The hypothesis on power dependency between the threshold and the entropy is tested, the exponent being a universal one. It is shown that the power dependency approximately holds in the neighbourhood of boundaries of chaos appearance but the exponent is not a universal number.

Quasiperiodic transition to chaos in a multimode YAG:Nd3+laser with modulated parameters

Numerical and experimental investigations were made of the nature of the transition to chaos in the case of YAG:Nd3+ laser with modulated parameters. It was found that the interaction of longitudinal modes via a spatially distributed population inversion was responsible for the transition to chaos in accordance with the Ruelle–Takens–Newhouse scenario. The chaos appearance threshold was minimal near the frequency of purely relaxational oscillations.