Chaotic Mode Research Articles

РОЗРОБКА АЛГОРИТМУ ДЛЯ ШИФРУВАННЯ ПОВІДОМЛЕНЬ У СЕНСОРНИХ БЕЗПРОВІДНИХ МЕРЕЖАХ

An analysis of the physical characteristics of the node, which can be attacked by an attacker. A method of detecting a damaged node with a violation of the physical characteristics of the network node, which is based on the use of probability functions, calculation of the confidence interval and the probability of deviation of current values from the confidence interval. Its novelty lies in the possibility of detecting a damaged node by estimating the current value of the function in the confidence interval, without comparing the distribution function of the current node with the reference distribution. The analysis of physical parameters of network nodes for detection of the malefactor in contrast to existing systems of detection of attacks which allow to carry out only the analysis of network traffic is carried out. Based on the developed algorithm by modeling the transmission of chaotic signals in a wireless sensor network, the effectiveness of attack detection is determined through the analysis of residual energy and node congestion parameters, expanding the range of attacks that the network is able to counteract compared to system analogues. During the simulation of the behavior of the wireless sensor network, it was determined that the data transmission processes are chaotic. Therefore, to enhance the security of data transmission in a chaotic mode, we have proposed an encryption algorithm using dynamic chaos, coordinate delay methods and singular spectral analysis. A comparative analysis of the parameters of the input and output sequences of the developed encryption algorithm based on dynamic chaos with standard data encryption algorithms is performed. It is established that the encryption parameters that are characteristic of the original sequences of the encryption algorithm using dynamic chaos are not worse than the encryption parameters obtained for the source sequences of standard encryption algorithms. Estimation of node load by means of threshold analysis of their current values in the confidence interval is used to detect network deviations during a cyberattack. The developed algorithm allows to diagnose attacks such as "Denial of Service" and "Sibyl" at the beginning of their appearance and to determine possible ways to avoid them.

ЭФФЕКТЫ ДИСКРЕТИЗАЦИИ ПРИ ЧИСЛЕННОМ ИССЛЕДОВАНИИ МОДЕЛИ НЕЙРОНА ХОДЖКИНА - ХАКСЛИ

Computer design is a valuable tool in the course of designing neuro-morphic systems. In particular it allows investigating basic mechanisms of neuron pulse activities in networks. For computer modeling it is necessary to digitize a continuous model of the system by means of the application of discrete operators able to keep basic properties of a prototype. But the accuracy of discrete models may decrease because of negative effects caused by the type of the method used, by a discretization pitch and errors in rounding off. 
 This fact is significant for the analysis of non-linear systems to which belong the models of biological neurons. As a possible solution of the problem may be the development of specialized tools for the analysis of dynamic systems with the focus upon numerical methods used. In this paper by the example of the modeling of the neuron described by Hodgkin-Huxley classical equations there is considered a set of widespread methods for ODU solution. In the course of investigations there are shown possible negative consequences of incorrect use of some discrete operators. In the paper the results of two sets of computer experiments are presented. The first ones determine the limitations for the practical use of the methods of the first accuracy order during modeling neurons in the mode of resonance generation of action potentials. The second ones show discretization effects connected with chaotic modes of neurons functioning: incorrect behavior of discrete models which is manifested in the emergence of chaotic transition processes. The investigation results may be used at the formation of modeling tool packages both, non-linear dynamic systems in the whole, and neuro-morphic systems in particular.

INFLUENCE OF THE ß SOLAR WIND PARAMETER ON STATISTICAL CHARACTERISTICS OF THE Ap INDEX IN THE SOLAR ACTIVITY CYCLE

We have studied the effect of the β solar wind parameter (equal to the ratio of the plasma pressure to the magnetic pressure) on statistical characteristics of the Ap index reflecting the triggering behavior of the activity of Earth’s magnetosphere. The trigger effect of the dynamics of magnetospheric activity consists in the abrupt transition from the periodic mode to the chaotic mode in the solar activity cycle. It is shown that cumulative amplitude distribution functions and power spectra of the Ap index of both the periodic and chaotic modes are well approximated by power and exponential functions respectively. At the same time, the indices of power functions and the indices characterizing the slope of the Ap index spectrum differ significantly in magnitude for the periodic and chaotic modes. We have found that Ap nonlinearly depends on β for both the modes of magnetospheric dynamics. The maximum of the Ap index amplitude for periodic modes is observed when β>1; and for chaotic ones, when β<1. In almost every cycle of solar activity, the energy of the Ap index fluctuations of chaotic modes is higher than that of periodic ones. The results indicate intermittency and its associated turbulence of magnetospheric activity. The exponential character of the spectral density of the Ap index suggests that the behavior of magnetospheric activity is determined by its internal dynamics, which can be described by a finite number of deterministic equations. The trigger effect of magnetospheric activity is assumed to be due to the angle of inclination of the axis of the solar magnetic dipole to the ecliptic plane, on which the dynamics of the β parameter in the solar activity cycle depends.

Folded chaotic whispering-gallery modes in nonconvex, waveguide-coupled planar optical microresonators

Chaotic whispering-gallery modes have significance both for optical applications and for our understanding of the interplay between wave phenomena and the classical ray limit in the presence of chaotic dynamics and openness. In strongly non-convex geometries, a theorem by Mather rules out the existence of invariant curves in phase space corresponding to rays circulating in whispering-gallery patterns, so that no corresponding modes of this type are expected. Here we discuss numerical computations of the electromagnetic fields in planar dielectric cavities that are strongly non-convex becausethey are coupled to waveguides. We find a family of special states which retains many features of the chaotic whispering-gallery modes known from convex shapes: an intensity pattern corresponding to near-grazing incidence along extended parts of the boundary, and comparatively high cavity Q factors. The modes are folded into a figure-eight pattern, so overlap with the boundary is reduced in the region of self-intersection. The modes combine the phenomenology of chaotic whispering-gallery modes with an important technological advantage: the ability to directly attach waveguides without spoiling the Q factor of the folded mode. Using both a boundary-integral method and the FDTD technique, we explore the dependence of the phenomenon on wavelength in relation to cavity size, refractive-index contrast to the surrounding medium, and the degree of shape deformation. A novel feature that distinguishes folded from regular whispering gallery modes is that a given shape will support high-Q folded chaotic whispering gallery modes only in certain wavelength windows.

Asynchronous control of T‐S fuzzy chaotic systems via a unified model using the hidden Markov model subject to strict dissipativity

SummaryThe asynchronous control for the unified model of chaotic systems with Markovian jumping parameters is considered via the Takagi‐Sugeno (T‐S) fuzzy approach in this paper. According to jumping modes for chaotic systems and modes for the asynchronous controller, a double‐mode process is generated. By introducing the hidden Markov model (HMM), the asynchronization phenomenon is represented between the controller and chaotic systems. By linear matrix inequalities (LMIs), some conditions are received to guarantee the stochastic stability and the strict dissipativity for chaotic systems. Based on the stochastic stability theory and the dissipativity theory, the asynchronous controller is discussed. The proposed method can be applied to the mode‐independent controller and the synchronous controller. Finally, the effectiveness of the proposed controller is illustrated by two examples.

Regularities in the spectrum of chaoticp-modes in rapidly rotating stars

Context.Interpreting the oscillations of massive and intermediate mass stars remains a challenging task. In fast rotators, the oscillation spectrum ofp-modes is a superposition of sub-spectra which corresponds to different types of modes, among which island modes and chaotic modes are expected to be the most visible. This paper is focused on chaotic modes, which have not been thoroughly studied before.Aims.We study the properties of high frequency chaoticp-modes in a polytropic model. Unexpected peaks appear in the frequency autocorrelations of the spectra. Our goal is to find a physical interpretation for these peaks and also to provide an overview of the mode properties.Methods.We used the 2D oscillation code “TOP” to produce the modes and acoustic ray simulations to explore the wave properties in the asymptotic regime. Using the tools developed in the field of quantum chaos (or wave chaos), we derived an expression for the frequency autocorrelation involving the travel time of acoustic rays.Results.Chaotic mode spectra were previously thought to be irregular, that is, described only through their statistical properties. Our analysis shows the existence, in chaotic mode spectra, of a pseudo large separation. This means that chaotic modes are organized in series, such that the modes in each series follow a nearly regular frequency spacing. The pseudo large separation of chaotic modes is very close to the large separation of island modes. Its value is related to the sound speed averaged over the meridional plane of the star. In addition to the pseudo large separation, other correlations appear in the numerically calculated spectra. We explain their origin by the trapping of acoustic rays near the stable islands.

Chaotic synchronization of two optical cavity modes in optomechanical systems

The synchronization of the motion of microresonators has attracted considerable attention. In previous studies, the microresonators for synchronization were studied mostly in the linear regime. While the important problem of synchronizing nonlinear microresonators was rarely explored. Here we present theoretical methods to synchronize the motions of chaotic optical cavity modes in an optomechanical system, where one of the optical modes is strongly driven into chaotic motion and transfers chaos to other weakly driven optical modes via a common mechanical resonator. This mechanical mode works as a common force acting on each optical mode, which, thus, enables the synchronization of states. We find that complete synchronization can be achieved in two identical chaotic cavity modes. For two arbitrary nonidentical chaotic cavity modes, phase synchronization can also be achieved in the strong-coupling small-detuning regime.

Transition to chaos in a cross-corrugated channel at low Reynolds numbers

The pressure-gradient driven flow in a three-dimensional cross-corrugated channel is investigated based on large eddy simulations. The channel geometry is highly tortuous so that the flow unsteadiness can be triggered at a moderate Reynolds number. The objective of this paper is to provide a better understanding of the laminar-to-chaotic transition in this type of channel. The transition from steady to chaos is found to occur at a low Reynolds number range between 77.4 and 113.1. The nonlinear dynamics is analyzed based on the power spectra of the velocity and reconstructed phase space. The route to chaos is identified, which favors the Ruelle-Takens-Newhouse scenario. Moreover, the transition from quasiperiodic mode to chaotic mode is accompanied with temporal intermittencies. The fluid dynamics is analyzed. It is found that the cross-corrugated geometry prompts a recirculating-and-rotating wake behind each contact corner. Each wake is enfolded by a pair of curved free shear layers. They are destabilized by the Kelvin-Helmholtz instability, leading to the periodic flow oscillation. Subsequently, the centrifugal instability sets in and promotes a type of primary vortex structures, forming streamwise “zig-zag” vortex streets. The competition between the adjacent vortex streets leads to a quasiperiodic flow. Temporal intermittencies emerge as the Reynolds number is increased. Finally, the periodicities in both the streamwise and spanwise directions are broken, and the flow becomes chaotic. When further increasing the Reynolds number to 343.1, Taylor-Görtler-like vortexes and necklace-like vortexes are formed in the channel.

Modeling and dynamical analysis of a small-scale unmanned helicopter

A simple model comprising five differential equations reflecting the attitude dynamics of small-scale hovering helicopters is developed. From its force analysis, this helicopter system has the dynamic structure of a Kolmogorov model producing chaos. The stable-focus mode and chaotic mode are identified for the helicopter. The hidden chaotic attraction basin is identified, which demonstrates the multi-stability of the helicopter and highly sensitivity with initial location. Varying the configuration of the moment of inertia leads to a change in dynamics for the helicopter system. The analysis of its chaotic motion is significant for designing of the controller as well as the configuration of parameters so as to avoid instabilities that produce chaos through improper assembly or selection of materials. The Lyapunov exponent spectra and the two-parameter bifurcation in terms of moment of inertia exhibit rich dynamical modes: stable, periodic orbit, pseudo-periodic orbit, and chaotic. A perturbation feedback control method is applied to control the system subjecting to chaos situation to reach the periodic orbit or equilibrium point. This control just needs a single controller but does not need the control input computation. The proposed model and the discovery of chaos provide a benchmark for the design and research of control algorithms for similar helicopter systems.

Narrating Chaos: Theresa Hak Kyung Cha’s "DICTEE" and Korean American Fragmentary Writings

In The Wounded Storyteller: Body, Illness, and Ethics, sociologist Arthur Frank uses narratology to typologize the stories people tell about illness. Next to teleological stories of survival, which “reassure the listener that however bad things look, a happy ending is possible”, Frank discusses “the chaos narrative” in which “events are told as the storyteller experiences life: without sequence or discernible causality” 97. While the storytellers discussed by Frank mostly suffer from physical ailments and traumas, I would argue that the chaotic mode of telling also characterizes texts that explore other kinds of traumas, including those related to displacement and shaming experienced by several generations of Koreans and Americans of Korean descent. Drawing on affect studies, I analyze Theresa Hak Kyung Cha’s DICTEE 1982 alongside two essays, by Grace M. Cho and Hosu Kim published in The Affective Turn: Theorizing the Social 2007, all of which use the collage form to challenge the expectation that “in life as in story, one event [leads] to another” Frank 97. The speech act is foregrounded in all three texts; it is de-naturalized, deformed, shown as a recitation of prescribed language, and repeatedly interrupted. Nonetheless, as Frank suggests, “the physical act becomes the ethical act” because “to tell one’s life is to assume responsibility for that life.” It also allows others to “begin to speak through that story” xx–xxi.

Terahertz emission from a weakly-coupled GaAs/AlGaAs superlattice biased into three different modes of current self-oscillations

Radio-frequency modulated terahertz (THz) emission power from weakly-coupled GaAs/AlGaAs superlattice (SL) has been increased by parallel connection of several SL mesas. Each SL mesa is a self-oscillator with its own oscillation frequency and mode. In coupled non-identical SL mesas biased at different voltages within the hysteresis loop the chaotic, quasiperiodic and frequency-locked modes of self-oscillations of current arise. THz emission was detected when three connected in parallel SL mesas were biased into the frequency-locked and quasiperiodic modes of self-oscillations of current, while in the chaotic mode of those it falls to the noise level.

Model of the transducer based on Murali-Lakshmanan-Chua non-autonomous chaotic oscillator for discrete sensors intended for monitoring production processes

The article discusses the model of the detector of periodic signals under the background noise intended for discrete type control devices. It is proposed to construct the detector based on the non-autonomous chaotic Murali – Lakshmanan – Chua oscillator. To detect, the parameters of a chaotic oscillator must ensure proximity to the bifurcation boundary between the periodic and chaotic modes. In the absence of the detectable signal at the input of a chaotic oscillator, chaotic motion is observed in it, and if present, a bifurcation occurs and a periodic mode is established. The numerical model that allows solving the Cauchy problem for the system of differential equations of the chaotic oscillator Murali – Lakshmanan – Chua has compiled in Matlab / Simulink. The output informative parameter of the detector is the number of chaotic bursts during the detection time. The proposed model allowed us to obtain empirical dependencies for the number of bursts. On the basis of the obtained dependencies, the choice of the optimal parameters of the system is made. The study as a whole led to the conclusion about the possibility of using the proposed detector as a node of devices that receive the measuring signal under the action of non-stationary interference.

The dependence of the wave mode from external periodic excitation in the harbor of port Kholmsk

According to observations of the waves in 2006 in the harbor of Kholmsk, chaotic vibrations were detected. Studies have shown that with an increase in the amplitude of external excitation, wind waves and swell coming to the entrance of the harbor, the energy of oscillations in the system also increases. For incoming waves higher than 3.5 m the spectrum changes, the energy of movements in the harbor increases significantly in a wide range of periods and reaches the level of energy of the harbor’s eigen oscillations, which in this case are practically not allocated. The authors suggested that at large amplitudes of waves at the entrance of the harbor the fluctuations become chaotic. Verification of this assumption was performed on the basis of numerical simulation using the Duffing equation with external periodic excitation. The simulation showed the possibility of chaotic vibrations in the harbor. The system has intermittent chaotic and periodic modes of oscillations with increasing amplitude of external excitation for a wide range of periods and increasing the energy of chaotic vibrations.

Theoretical model for measuring parameters of laser radiation

The task of the work is creation of a theoretical model for measuring of the laser radiation parameter as a nonlinear dynamical system. The model provides for the measurement of the parameters in stationary and chaotic modes. The model can be used for ensuring the stability of the laser radiation parameters, and for controlling the chaotic radiation.

Modelling and analysis of an analogue MPPT‐based PV battery charging system utilising dc–dc boost converter

Nowadays, the research is being devoted to the development of rapid and precise maximum power point tracking (MPPT) for various photovoltaic (PV) applications. However, the constraints imposed by size, cost, efficiency, and tracking performances essentially limit the application of conventional MPPT techniques and their analysis methodologies. This study recommends a fast and robust analogue PV MPPT for the battery charging system using dc-dc boost converter. The fast dynamic performances with absolute robustness are ensured here by fast-scale stability analysis of actually switched boost converter using the concepts based on non-linear dynamics and bifurcation theory. Such concepts not only provide the information to design an efficient MPPT system under rapidly changing environmental conditions but also guarantee the system to operate either in period-1 or chaotic mode. The theoretical and mathematical analyses are experimentally verified using a prototype PV battery charging system utilising dc-dc boost converter. It is presented that operating the MPPT system in chaos not only yields the broader power spectrum with reduced spectral peaks at the multiples of converter's switching frequency but also exhibits high overall conversion efficiency.

Effect of Ferroresonance on Wind Turbine: Comparison of Atp/Emtp and Matlab/Simulink

Different developers have produced several software packages as solutions to model electrical power systems for the purpose of carrying out diverse analyses to solve immediate and unforeseen problems in power systems. In this study, ATP/EMTP and Matlab/Simulink packages were compared in regards to their capability to give accurate results, time of simulation and ease of simulation when modeling DFIG wind turbine. Furthermore, ferroresonance caused by one stuck pole during switching operations were analyzed on both software. Characterization of resulting ferroresonance was done using Fast Fourier Transformation (FFT) analysis, phase plane diagram and Poincaré mapping. Chaotic mode ferroresonance was found in both ferroresonance events. However, ATP could only perform FFT analysis while other analyses were performed on Matlab/Simulink. There are differences in the results obtained from the two packages; overvoltage of 4.22 P.U. and 3.77 P.U. was experienced during opening and closing operation on ATP/EMTP model while 6.36 P.U. and 4.63 P.U. respectively was obtained on Matlab. However, ATP is faster in regards to time of simulation with CPU time of 110.58 secs and simulink simulation time was 130.81 secs. Finally, it was easier to carry out the simulation on Simulink.

A predictive model for two-surface multipactor stability and growth based on chaos theory

In this paper, a novel theoretical approach on multipactor discharge based on principles from nonlinear dynamics and chaos theory is extended to a parallel-plate geometry with radio-frequency (RF) and DC electric-fields. Maps that relate the RF emission phase to the RF arrival phase are developed with no a priori assumptions on the electron trajectories (neglecting space-charge effects). A wide range of system parameters are scanned in the theory, resulting in bifurcation diagrams that recover a plethora of resonant and nonresonant modes. This new approach agrees well with conventional resonance theory where applicable but also provides insight on parameter regions where the former theory is limited. Further, it is found that the attractor form manifests in the exponential growth rate, where higher-periodicity and chaotic modes dilute multipactor growth. These theoretical predictions are validated against particle-in-cell simulations.

Properties of impact events in the model of forced impacting oscillator: Experimental and numerical investigations

The paper deals with the studies of the forced impacting oscillator when taking into account the dry and viscous resistance as well as the generalized Hertz contact law during an impact. Numerical investigations of the mathematical model are accompanied by validations obtained with an experimental rig. To study the solutions of the mathematical model, the sequences of impacts, when the system evolves in periodic and chaotic modes, is used. The statistical properties of chaotic impact events are considered in detail. In particular, successive iterations of the impact map, autocorrelation function and coefficient of variation for the impact train, histograms for the inter-impact intervals and values of obstacle penetrations are analyzed. It is revealed that the impact sequence is stationary but non-Poissonian and contains temporal scales that do not relate to the external stimulus. This sequence can be described by a bimodal distribution. The findings are confirmed by the analysis of experimental data.

Probing the degenerate pattern growth of {100} orientation in a directionally solidified Al-4.5 wt% Cu alloy

Degenerate pattern is a seemingly disordered morphology but it exhibits the inherently ordered crystal connected with tip-splitting and limited stability which makes it difficult to observe in the metallic system. Here we employ (100)[011] orientated planar-front seeds using directional solidification and reveal the fundamental origins of the degenerate pattern growth in an Al-4.5 wt% Cu alloy. We find that the spacing of the tip-splitting (λ) in the degenerate of the alloys followed a power law, λ∝V−0.5, and the frequency (f) of the splitting was related to the growth velocity (V) by ƒ∝V1.5. The dimensionless growth direction (θ/θ0) increased monotonously and approached 0.6 with faster velocity, attributed to its anisotropy in the interface kinetics. Once growth velocity exceeded a threshold, two types of pattern transitions from degenerate to regular dendrites were proposed. One of them exhibited a random and chaotic mode and the other underwent a rotation in growth direction.

Dynamic Behavior of Wind Turbine Generator Configurations during Ferroresonant Conditions

In this paper the dynamic behavior of different wind turbine generator configurations including doubly fed induction generators (DFIG), squirrel cage induction generator (SCIG), wound rotor induction generator (WRIG), and permanent magnet synchronous generator (PMSG) under ferroresonant conditions of energization and de-energization was investigated using Simulink/MATLAB (version 2017B, MathWorks, Natick, MA, USA). The result showed that SCIG had the highest overvoltage of 10.1 PU during energization, followed by WRIG and PMSG, while the least was DFIG. During de-energization, PMSG had the highest overvoltage of 9.58 PU while WRIG had the least. Characterization of the ferroresonance was done using a phase plane diagram to identify the harmfulness of the ferroresonance existing in the system. It was observed that for most of the wind turbine configurations, a chaotic mode of ferroresonance exists for both energization and de-energization scenarios. Although overvoltage during energization for wind turbine generator configurations was higher than in the de-energization with an exception of PMSG, their phase plane diagrams showed that de-energization scenarios were more chaotic than energization scenarios. The study showed that WRIG was the least susceptible to ferroresonance while PMSG was the most susceptible to ferroresonance.