Dynamical Chaos Research Articles

Comparative analysis of the secure communication schemes based on the generators of hyperbolic strange attractor and strange nonchaotic attractor

The purpose of this work is to analyse qualitative features of the information transmission process via several communication schemes based on the synchronization of transmitter and receiver, both being complex signal generators. For this purpose generators of the hyperbolic chaos and generators with the strange nonchaotic attractor are employed. Evaluation of advantages and disadvantages of such schemes is made comparing themselves with each other as well as with schemes based on the nonhyperbolic chaotic generators. Methods. The power spectra and the distributions of the largest finite-time Lyapunov exponent are used to confirm the complexity of the dynamics of the generators in use and to verify the wide-bandness, robustness and stochasticity of their signals. Confidentiality of the informational signal transmission is achieved using its nonlinear mixing to the dynamics of the transmitter. The special phase mixing is used since the model generators employed for the research demonstrate nontrivial dynamics for the angular variable — oscillations phase shift. The digital image is used as an information for transmission. Visual control during the transmission process allows to carry out the qualitative analysis of the success of the signal coding and its detecting by the receiver. Results. Successful transmission and decoding of information for all schemes under investigation are demonstrated for the case of identical transmitter and receiver. Parameter detuning of these generators leads to difficulties in separation of the informational signal from the chaotic/complex carrier due to loss of the full synchronization. For the nonhyperbolic chaos detuning of the parameter responsible for the amplitude of the signal leads to the bad quality of the detection while frequency detuning makes detection absolutely impossible. Schemes with the hyperbolic chaos and strange nonchaotic dynamics appear to demonstrate much better results. The information detection is much better in this case because of the robustness of the generalized synchronization. Conclusion. Robust chaotic and complex nonchaotic generators appear to have significant advantages for communication systems comparing to the chaotic generators of nonhyperbolic type.

Analysis and Simulation of BER Performance of Chaotic Underwater Wireless Optical Communication Systems

It is shown that modulation methods based on the phenomenon of dynamic chaos and correlation processing can improve the noise immunity of underwater wireless communication systems. This provides the possibility of signal recovery at negative values of the signal-to-noise

ЭНТРОПИЙНАЯ МОДЕЛЬ ДИНАМИЧЕСКОГО ХАОСА ГЕОЭКОЛОГИЧЕСКОЙ СИСТЕМЫ

Dynamic chaos systems are commonly described by the nonlinear cyclic Verhulst relation. In this study, its use was extended to track the degradation of ecological systems at different stages of their development. A new concept was introduced: the geochemical entropy of abiotic ecological systems, which varies in the interval [0, 4] and determines the level of their stability in the interval [0, 1]. The model was verified by assessing soil pollution in Lipetsk (Russia). Despite the high level of soil pollution in certain areas of the city, the overall ecological situation turned out to be “normal” with a high level of stability (0.98). Forecasts were made of how the ecological situation in Lipetsk might develop with a change in the anthropogenic load. If it remains unchanged, the sustainability of the ecological system will be virtually the same. With heavier soil pollution, the stability may be lost at different rates, depending on the entropy of the system. The proposed model is helpful for assessing the current geo-ecological state of large territories with high anthropogenic load and pollution levels varying considerably between different areas of these territories, as well as for predicting the level of living comfort in urban agglomerations and managing ecological systems.

Dynamics Analysis and Chaos Identification of Compound Pendulum Jaw Crusher with Joint Clearance

A dynamic model of the working mechanism of a compound pendulum jaw crusher with clearance is established by the Lagrange multiplier method (LMD) based on the L-N contact force model and modified Coulomb friction force model. The correctness of the dynamic model is verified by MATLAB and Adams comparison simulation, and the best selection range of driving speed and clearance size is determined according to the laminating crushing theory (LCT). The effects of driving speed and clearance size on the shock and chaos phenomenon in the clearance mechanism are analyzed, as well as the vibration force applied to the foundation. The results show that, under the premise of meeting the requirements of crusher production capacity, increasing the driving speed and reducing the clearance size can weaken the shock and chaos phenomenon during the operation of the mechanism, improve the dynamic performance and enhance the operation stability, and the service life of foundation is prolonged with the stability of vibration force. Furthermore, the optimal combination of driving speed and clearance size is determined, which provides a theoretical basis for the optimization of the vibration force of the jaw crusher.

A chaotic oscillation generator based on mixed dynamics of adaptively coupled Kuramoto oscillators

A chaotic oscillation generator based on the concept of mixed dynamics is implemented on the field programmable gate array (FPGA). This generator reproduces the dynamics of two adaptively coupled Kuramoto phase oscillators. It is experimentally shown that the generator exhibits oscillations corresponding to a chaotic attractor and a chaotic repeller (attractor in reversed time). We have shown that the chaotic attractor and the chaotic repeller intersect on a closed invariant set - a reversible core, which confirms the existence of the so-called mixed dynamics. It was found that for different values of the parameters of the generator, either ordinary dissipative chaos or mixed dynamics can be realized. It is shown that in the case of mixed dynamics the behavior of the trajectories in phase space becomes more complex and the spectral characteristics change towards a more uniform power distribution over the spectrum frequencies. The action of harmonic external force on the mixed dynamics of the generator is also investigated and it is shown that this leads to additional complexity of the dynamical behavior of the generator’s output signals.

Breakdown of planetary systems in embedded clusters

ABSTRACT We report the first simulations of planetary system dynamics as affected by an embedded cluster environment. Such environments are generally believed to be relevant for the large majority of newborn stars of solar type. Moreover, our cluster model is more realistic than in previous work. We focus on a giant planet system with five members, which represents a likely precursor of our solar system. Our main result is that the perturbing effects of close encounters with cluster stars trigger dynamical chaos leading to breakdown of the system with a significant probability, especially if the natal gas discs are short-lived and the clusters are highly concentrated. When breakdown occurs, all planets except Jupiter suffer a large risk of being ejected from the system or extracted into distant orbits with semimajor axes of hundreds or thousands of astronomical units. This is consistent with recent estimates of a large abundance of low-mass, free-floating planets. We demonstrate a possibility for Jupiter and Saturn to evolve into hot Jupiter orbits by tidal circularization during the chaotic evolution. Even so, the low occurrence rate of this outcome indicates that the real hot Jupiters in general have an origin unrelated to dynamical evolution in birth clusters.

A Fractional Atmospheric Circulation System under the Influence of a Sliding Mode Controller

The earth’s surface is heated by the large-scale movement of air known as atmospheric circulation, which works in conjunction with ocean circulation. More than 105 variables are involved in the complexity of the weather system. In this work, we analyze the dynamical behavior and chaos control of an atmospheric circulation model known as the Hadley circulation model, in the frame of Caputo and Caputo–Fabrizio fractional derivatives. The fundamental novelty of this paper is the application of the Caputo derivative with equal dimensionality to models that includes memory. A sliding mode controller (SMC) is developed to control chaos in this fractional-order atmospheric circulation system with uncertain dynamics. The proposed controller is applied to both commensurate and non-commensurate fractional-order systems. To demonstrate the intricacy of the models, we plot some graphs of various fractional orders with appropriate parameter values. We have observed the influence of thermal forcing on the dynamics of the system. The outcome of the analytical exercises is validated using numerical simulations.

Chaotic Synchronization in Mobile Robots

Chaos dynamics is an interesting nonlinear effect that can be observed in many chemical, electrical, and mechanical systems. The chaos phenomenon has many applications in various branches of engineering. On the other hand, the control of mobile robots to track unpredictable chaotic trajectories has a valuable application in many security problems and military missions. The main objective in this problem is to design a controller such that the robot tracks a desired chaotic path. In this paper, the concept of synchronization of chaotic systems is studied, and a new type-3 fuzzy system (T3FLS)-based controller is designed. The T3FLS is learned by some new adaptive rules. The new learning scheme of T3FLS helps to better stabilize and synchronize. The suggested controller has a better ability to cope with high-level uncertainties. Because, in addition to the fact that the T3FLSs have better ability in an uncertain environment, the designed compensator also improves the accuracy and robustness. Several simulations show better synchronization and control accuracy of the designed controller.

Density matrix formulation of dynamical systems.

Physical systems that are dissipating, mixing, and developing turbulence also irreversibly transport statistical density. However, predicting the evolution of density from atomic and molecular scale dynamics is challenging for nonsteady, open, and driven nonequilibrium processes. Here, we establish a theory to address this challenge for classical dynamical systems that is analogous to the density matrix formulation of quantum mechanics. We show that a classical density matrix is similar to the phase-space metric and evolves in time according to generalizations of Liouville's theorem and Liouville's equationfor non-Hamiltonian systems. The traditional Liouvillian forms are recovered in the absence of dissipation or driving by imposing trace preservation or by considering Hamiltonian dynamics. Local measures of dynamical instability and chaos are embedded in classical commutators and anticommutators and directly related to Poisson brackets when the dynamics are Hamiltonian. Because the classical density matrix is built from the Lyapunov vectors that underlie classical chaos, it offers an alternative computationally tractable basis for the statistical mechanics of nonequilibrium processes that applies to systems that are driven, transient, dissipative, regular, and chaotic.

Dynamical change under slowly changing conditions: the quantum Kruskal–Neishtadt–Henrard theorem

Adiabatic approximations break down classically when a constant-energy contour splits into separate contours, forcing the system to choose which daughter contour to follow; the choices often represent qualitatively different behavior, so that slowly changing conditions induce a sudden and drastic change in dynamics. The Kruskal–Neishtadt–Henrard (KNH) theorem relates the probability of each choice to the rates at which the phase space areas enclosed by the different contours are changing. This represents a connection within closed-system mechanics, and without dynamical chaos, between spontaneous change and increase in phase space measure, as required by the Second Law of Thermodynamics. Quantum mechanically, in contrast, dynamical tunneling allows adiabaticity to persist, for very slow parameter change, through a classical splitting of energy contours; the classical and adiabatic limits fail to commute. Here we show that a quantum form of the KNH theorem holds nonetheless, due to unitarity.

Resonant islands of effective-one-body dynamics

We study the chaotic signatures of the geodesic dynamics of a non-spinning test particle in the effective-one-body (EOB) formalism for the inspiral process of spinning binary black holes. We first show that the second order post-Newtonian (2PN) EOB dynamics is non-integrable by demonstrating that the EOB metric does not satisfy the criterion for the existence of Carter constant. We then employ the numerical study to find the plateaus of the rotation curve, which are associated with the existence of Birkhoff islands in the Poincar\'e surface of section, signifying the chaotic dynamics in the system. Our results show the signatures of chaos for the EOB dynamics, especially in the regime of interest for which the Kerr bounds of the component black holes hold. We also find that chaotic behavior is more obvious as the spin parameter $a$ of the deformed EOB background metric increases. Our results can help to uncover the implications of dynamical chaos in gravitational wave astronomy. Finally, we also present some preliminary results due to corrections at 3PN order.

Non-periodic input-driven magnetization dynamics in voltage-controlled parametric oscillator

Input-driven dynamical systems have attracted attention because their dynamics can be used as resources for brain-inspired computing. The recent achievement of human-voice recognition by spintronic oscillator also utilizes an input-driven magnetization dynamics. Here, we investigate an excitation of input-driven chaos in magnetization dynamics by voltage controlled magnetic anisotropy effect. The study focuses on the parametric magnetization oscillation induced by a microwave voltage and investigates the effect of random-pulse input on the oscillation behavior. Solving the Landau–Lifshitz–Gilbert equation, temporal dynamics of the magnetization and its statistical character are evaluated. In a weak perturbation limit, the temporal dynamics of the magnetization are mainly determined by the input signal, which is classified as input-driven synchronization. In a large perturbation limit, on the other hand, chaotic dynamics are observed, where the dynamical response is sensitive to the initial state. The existence of chaos is also identified by the evaluation of the Lyapunov exponent.

Reflections on the Life of Oleg A. Tretyakov [In Memoriam

Dr. Oleg Alexandrovich Tretyakov, 83, passed away on Tuesday, 25 January 2022, in Istanbul, Turkey, after a short battle with lung cancer. He was an outstanding expert in electrodynamics and radiophysics. He was the chair of Commission B of the International Union of Radio Science (URSI) Committee of Ukraine since 1993, a Member of IEEE, and a professor emeritus of the Department of Theoretical Radiophysics, V.N. Karazin Kharkiv National University (KhNU), Ukraine. He had experience in solving diffraction problems by mathematically rigorous methods, wave scattering from rough surfaces, and wave propagation in random media, linear and nonlinear phenomena, and dynamic chaos in microwave oscillators and amplifiers. With him, we lost an internationally well-known and highly regarded leading figure in electromagnetic theory. His intellect, integrity, humor, professionalism, and humanity will be greatly missed.

Фрактальные приложения радиоэлектроники как фрактальная инженерия

The use of the fractal paradigm is presented - the main directions for introducing textures, fractals, fractional operators, dynamic chaos and methods of nonlinear dynamics for the design and creation of real technical projects in radio electronics - fractal radio systems, taking into account the hereditarity, non-Gaussianity and scaling of physical signals and fields. The substantiation of the use of fractal-scaling and texture methods for the synthesis of fundamentally new topological texture-fractal methods for detecting signals in the space-time channel of scattering waves (a new type of radar) is discussed. It is shown that the use of fractal systems, sensors and nodes is a fundamentally new solution that significantly changes the principles of constructing intelligent radio engineering systems and devices. It is shown that the use of computational dielectric metasurfaces brings to a new level all the functional characteristics of a multifunctional system of topological texture-fractal processing of signals and fields in solving classical problems of detection, measurement, recognition and classification by intelligent radio engineering systems and devices. The concept of "fractal engineering" is introduced, the methodology of its use is discussed.

Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System

After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium \(E_3\) have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria \(E_1\), \(E_2\) and \(E_3\) to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations.

Spatiotemporal chaos induces extreme events in a three-element laterally coupled laser array.

Extreme events are observed in the spatiotemporal chaos dynamics of a three-element laterally coupled laser array. With the help of statistical and dynamical analyses, we confirm that spatiotemporal chaos induces extreme pulses that are high enough to be identified as extreme events and cannot be found in synchronization chaos. Interestingly, our results show that extreme events always preferentially appear in the middle laser as the laser separation ratio is decreased (i.e., upon increasing the coupling strength), and then in the two outer lasers. This thus reveals the importance of the middle laser in the transition between synchronization chaos and spatiotemporal chaos states. Additionally, we show the evolution of extreme events in the plane of the pump level and laser separation ratio by calculating the corresponding proportion. Our results build a relation between extreme events and the spatiotemporal dynamics, which makes it easy to understand the formation mechanism of extreme events.

Bifurcation structure and chaos in dynamics of nanomagnet coupled to Josephson junction.

Irregular easy axis reorientation features are observed in numerical simulations of the nanomagnet coupled to the Josephson junction. We study magnetization bifurcations and chaos that appear in this system due to the interplay of superconductivity and magnetism. The bifurcation structure of magnetization under the variation of Josephson to magnetic energy ratio as a control parameter demonstrates several precessional motions that are related to chaotic behavior and orbits with different periodicities in the ferromagnetic resonance region. The effect of an external periodic signal on the bifurcation structure is also investigated. The results demonstrate high-frequency modes of a periodic motion and a chaotic response near resonance. Far from the ferromagnetic resonance, we observe a quasiperiodic behavior. The obtained results explain the irregular reorientation of the easy axis and the transitions between different types of motion.

Simulation of multiple hadron production and transition to quark-gluon plasmas based on nonlinear dynamics

A dynamics of quark-gluon plasmas has been defined by the evolution parameter, which at high energies depends on collision energy of atomic nuclei for appropriate multiplicities of secondary hadrons. The paper is based on the solution of evolution equation for patrons momentum distribution. A transition from regular propagation to irregular chaotic is an indicator of the quark-gluon plasma emerging. Nonlinear renormalization group equation has been solved by the method of Poincaré mappings. The equation is a model of the evolution of the momentum distribution of partons due to competing processes of their creation and fusion. As the energy increases, sequential bifurcation (doubling) of phase trajectories occurs, and scale-invariant fractal structures are to create. At sufficiently high energies of quarks and gluons, a dynamically determined quark-gluon system, corresponding to QGP, arises in space. There are also hadron-like structures. Quantum coherence effects follow by dynamic chaos. As a result, quarks and gluons merge into stable attractor structures with their subsequent decay into hadrons. The nonlinear equation introduced for quark-gluon cascade, which comprises dynamical chaos, has include effects of parton recombination. The chaotic dynamics has been connected specifically to the transverse momenta of partons. Clearly, the formation of dynamically determined stable structures should be unknown before, attractor mechanism of quark hadronization.

Unfolding of COVID-19 Crisis in a Study-Abroad Program: Voices of Stakeholders Involved in the Evacuation

This qualitative case study documented the unfolding of the COVID-19 crisis that impacted a study-abroad program in Paris between December 2019 and May 2020, culminating in the urgent evacuation of U.S.-affiliated students from France. Framed by Complex Dynamic Systems Theory, chaos theory, and research on study abroad and crisis management, rich data from extensive interviews conducted with nine undergraduate students in the program and the four educational staff members responsible for them were triangulated with external correspondence (e.g., official university emails), local media sources, and governmental documents (e.g., White House statements). This merging allowed reconstructing the context necessary to capture the singular voices of these stakeholders, as they experienced threat, uncertainty, and urgency, filtered by the use of a foreign language and varying intercultural skills during the different phases of the crisis. Recommendations for the management of crises abroad and the future of study abroad are discussed.

Reduced Variations in Earth’s and Mars’ Orbital Inclination and Earth’s Obliquity from 58 to 48 Myr ago due to Solar System Chaos

The dynamical evolution of the solar system is chaotic with a Lyapunov time of only ∼5 Myr for the inner planets. Due to the chaos it is fundamentally impossible to accurately predict the solar system’s orbital evolution beyond ∼50 Myr based on present astronomical observations. We have recently developed a method to overcome the problem by using the geologic record to constrain astronomical solutions in the past. Our resulting optimal astronomical solution (called ZB18a) shows exceptional agreement with the geologic record to ∼58 Ma (Myr ago) and a characteristic resonance transition around 50 Ma. Here we show that ZB18a and integration of Earth’s and Mars’ spin vector based on ZB18a yield reduced variations in Earth’s and Mars’ orbital inclination and Earth’s obliquity (axial tilt) from ∼58 to ∼48 Ma—the latter being consistent with paleoclimate records. The changes in the obliquities have important implications for the climate histories of Earth and Mars. We provide a detailed analysis of solar system frequencies (g and s modes) and show that the shifts in the variation in Earth’s and Mars’ orbital inclination and obliquity around 48 Ma are associated with the resonance transition and caused by changes in the contributions to the superposition of s modes, plus g–s mode interactions in the inner solar system. The g–s mode interactions and the resonance transition (consistent with geologic data) are unequivocal manifestations of chaos. Dynamical chaos in the solar system hence not only affects its orbital properties but also the long-term evolution of planetary climate through eccentricity and the link between inclination and axial tilt.