Dynamical Chaos Research Articles

Dynamic chaos in cerebellum and electrical synapses between climbing fiber cells of inferior olives

Dynamic chaos in cerebellum and electrical synapses between climbing fiber cells of inferior olives

Signatures of Quantum Chaos of Rydberg-Dressed Bosons in a Triple-Well Potential

We studied signatures of quantum chaos in dynamics of Rydberg-dressed bosonic atoms held in a one-dimensional triple-well potential. Long-range nearest-neighbor and next-nearest-neighbor interactions, induced by laser dressing atoms to strongly interacting Rydberg states, drastically affect mean-field and quantum many-body dynamics. By analyzing the mean-field dynamics, classical chaos regions with positive and large Lyapunov exponents were identified as a function of the potential well tilting and dressed interactions. In the quantum regime, it was found that level statistics of the eigen-energies gain a Wigner–Dyson distribution when the Lyapunov exponents are large, giving rise to signatures of strong quantum chaos. We found that both the time-averaged entanglement entropy and survival probability of the initial state have distinctively large values in the quantum chaos regime. We further showed that population variances could be used as an indicator of the emergence of quantum chaos. This might provide a way to directly probe quantum chaotic dynamics through analyzing population dynamics in individual potential wells.

Deep time-recurrence features

In this study, the notion of recurrence in chaos and nonlinear dynamics is formulated as a new method for deep feature extraction from complex data. This feature type can enhance the learning power of a state-of-the-art approach in artificial intelligence using time series or sequential data. The deep time-recurrence features are derived using the fuzzy recurrence algorithm and the iterative procedure of convolution, non-linear transformation, and down-sampling. Experimental results obtained from using a public database of healthy and pathological voice signals show that the proposed features can significantly improve the classification performance of long short-term memory networks.

Photovoltaic Systems Based on Average Current Mode Control: Dynamical Analysis and Chaos Suppression by Using a Non-Adaptive Feedback Outer Loop Controller

This paper deals with the modeling and theoretical study of an average-current-mode-controlled photovoltaic power conversion chain. It should be noted that current mode control is a superior scheme for controlling DC–DC power electronic converters for photovoltaic applications. Bifurcation diagrams, largest Lyapunov exponents, Floquet theory, and time series are used to study the dynamics of the system. The theoretical results show the existence of subharmonic oscillations and period-1 oscillations in the system. The results of the numerical simulations showed that when the battery voltage at the output of the converter is fixed and ramp amplitude is taken as a control parameter, the photovoltaic power system exhibits the phenomenon of period doubling leading to chaotic dynamics. Furthermore, bifurcation diagrams showed that both the critical value of ramp amplitude for the occurrence of border collision bifurcation and the critical value of ramp amplitude for the occurrence of period-1 in the proposed system increased with the value of the battery terminal voltage. The numerical results are in accordance with the theoretical ones. Finally, an external control based on a non-adaptive controller having a sinusoidal function as a target is applied to the overall system for the suppression of chaotic behavior.

Dynamics research and chaos identification of rigid-flexible coupling multi-link mechanism with irregular wear clearances

Dynamics research and chaos identification of rigid-flexible coupling multi-link mechanism with irregular wear clearances

Spin Chaos Dynamics in Classical Random Dipolar Interactions

The stochastic nature of magnetization dynamics of dipole–dipole interactions described by the Landau–Lifshitz–Gilbert equation without considering the Gilbert damping parameter is investigated. It is shown that the occurrence of the complex dynamic states depends on the spatial anisotropy of interactions on one hand and the lattice geometry on the other. It is observed from the higher-order moments of the magnetization fluctuations that two significant dynamical regimes, regular and chaos, may be obtained depending on the perturbation strength. Relying on the Hurst exponent obtained by the standard deviation principle, the correlation and persistence of the magnetization fluctuations are analyzed. The results also exhibit a transition from an anti-correlated to a positively correlated system as the relevant parameters of the system vary.

Out-of-time-order correlator for the van der Waals potential

The quantum-to-classical correspondence is often quantified in dynamics by the out-of-time-order correlator (OTOC). In chaotic systems, the OTOC is expected to grow exponentially at early time, characteristic of a Lyapunov exponent; however, exponential growth can also occur for integrable systems. Here we investigate the OTOC for realistic diatomic molecular potentials in one degree of freedom, finding that the OTOC can grow exponentially near the dissociation energy of the molecule. Further, this dynamics is tied to the classical dynamics of the atoms at the outer classical turning point of the potential. These results should serve to guide and interpret dynamical chaos in more complex molecules.

Wormholes from heavy operator statistics in AdS/CFT

We construct higher dimensional Euclidean AdS wormhole solutions that reproduce the statistical description of the correlation functions of an ensemble of heavy CFT operators. We consider an operator which effectively backreacts on the geometry in the form of a thin shell of dust particles. Assuming dynamical chaos in the form of the ETH ansatz, we demonstrate that the semiclassical path integral provides an effective statistical description of the microscopic features of the thin shell operator in the CFT. The Euclidean wormhole solutions provide microcanonical saddlepoint contributions to the cumulants of the correlation functions over the ensemble of operators. We finally elaborate on the role of these wormholes in the context of non-perturbative violations of bulk global symmetries in AdS/CFT.

Quantum Chaos and Level Dynamics

We review the application of level dynamics to spectra of quantally chaotic systems. We show that the statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics, such as level avoided-crossing distributions, level slope distributions, or level curvature distributions. We show both the aspects of universality in these distributions and their limitations. We concentrate in some detail on measures imported from the quantum information approach such as the fidelity susceptibility, and more generally, geometric tensor matrix elements. The possible open problems are suggested.

Dynamical chaos in nonlinear Schrödinger models with subquadratic power nonlinearity.

We devise an analytical method to deal with a class of nonlinear Schrödinger lattices with random potential and subquadratic power nonlinearity. An iteration algorithm is proposed based on the multinomial theorem, using Diophantine equationsand a mapping procedure onto a Cayley graph. Based on this algorithm, we are able to obtain several hard results pertaining to asymptotic spreading of the nonlinear field beyond a perturbation theory approach. In particular, we show that the spreading process is subdiffusive and has complex microscopic organization involving both long-time trapping phenomena on finite clusters and long-distance jumps along the lattice consistent with Lévy flights. The origin of the flights is associated with the occurrence of degenerate states in the system; the latter are found to be a characteristic of the subquadratic model. The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border, above which the field can spread to long distances on a stochastic process and below which it is Anderson localized similarly to a linear field.

Chaos Generation in Opto‐Mechanical Coupling System Assisted by Two‐Level Atoms

AbstractChaos is important in nonlinear science and promotes the development of fundamental studies, such as neural networks, extreme event statistics, and electron transport. In this paper, a theoretical scheme for generating dynamical chaos in a Fabry–Perot cavity with two‐level atoms is investigated. Through the injection of atoms, controllable chaos of the cavity and mechanical oscillator is achieved simultaneously by the external laser field. The trajectory and the maximal Lyapunov exponent that characterize the properties of the chaos could be optimized by adjusting the coupling constant, driving field, injection of atoms, the frequency of the cavity, and the frequency of the mechanical oscillator. This study provides a new idea to manipulate the cavity and mechanical chaos assisted by two level atoms. It is hoped that the results presented can benefit controllable chaos generation and its applications.

Chaos generated in a semiconductor microcavity.

The dynamics of chaos in quantum systems has attracted much interest in connection with the fundamental aspects of quantum mechanics. We study the chaotic dynamics of both the excitonic mode and the cavity mode in a microcavity containing a quantum well driven by an external field. We investigate how the chaotic dynamics is influenced by the frequencies of the exciton and the cavity, the coupling constant between the exciton and cavity, the Coulomb interaction between excitons, and the response of the exciton to the cavity and the external field. We show that chaos can be generated synchronously in both the cavity and the excitonic mode by choosing appropriate parameters. Moreover, this kind of chaos can be controlled by the coupling constant, the strength of the interaction between excitons, the external field, the response of the excitons to the cavity, and the detuning between the cavity field and the excitonic field. The present study may have applications in chaos-based neural networks and extreme event statistics.

Chaos and pole-skipping in a simply spinning plasma

We study the relationship between many-body quantum chaos and energy dynamics in holographic quantum field theory states dual to the simply-spinning Myers-Perry-AdS5 black hole. The enhanced symmetry of such black holes allows us to provide a thorough examination of the phenomenon of pole-skipping, that is significantly simpler than a previous analysis of quantum field theory states dual to the Kerr-AdS4 solution. In particular we give a general proof of pole-skipping in the retarded energy density Green’s function of the dual quantum field theory whenever the spatial profile of energy fluctuations satisfies the shockwave equation governing the form of the OTOC. Furthermore, in the large black hole limit we are able to obtain a simple analytic expression for the OTOC for operator configurations on Hopf circles, and demonstrate that the associated Lyapunov exponent and butterfly velocity are robustly related to the locations of a family of pole-skipping points in the energy response. Finally, we note that in contrast to previous studies, our results are valid for any value of rotation and we are able to numerically demonstrate that the dispersion relations of sound modes in the energy response explicitly pass through our pole-skipping locations.

Experimental Investigation of a Relative Transmission Scheme on Chaotic Radio Pulses

The practical feasibility of a wireless relative transmission scheme based on chaotic radio pulses is demonstrated. New components necessary for the implementation of this scheme have been developed. A prototype of a transmission system in the frequency range of 200–500 MHz was created on which experiments were carried out on the transmission of binary information. The measurement results correspond to the previously obtained theoretical and computational estimates on the main properties and characteristics of a new transmission scheme that uses dynamic chaos as an information carrier.

Problems of modeling the stability of the financial market as a dynamic system

Subject. The article addresses the stable functioning of the financial market and its protection against financial crises as the main indicator of financial system’s stability. It considers the history of the issue, enabling to conclude that financial markets are built mainly on the principle of unstable equilibrium in contrast to the more stable equilibrium underlying the commodity markets and industrial production. Objectives. The article attempts to compare well-known stochastic models with dynamic and chaotic systems. Methods. The study employs stochastic modeling (autoregressive conditional heteroscedasticity (ARCH) and generalized autoregressive conditional heteroscedasticity (GARCH) models), investigates methods and approaches to solving some types of differential stochastic equations, in particular, the Ito and Fokker-Planck-Kolmogorov equations. Results. Financial markets are considered within the theory of dynamic systems as an example of a non-linear system. It is extremely difficult to predict the behavior of such a system, precisely because of the non-linearity, which is reduced to random and chaotic processes. Through mathematical transformations, the paper shows that solutions are reduced to multidimensional stochastic volatility models. Conclusions. Stochastic volatility models, despite their relative theoretical elaboration and practical applicability, can lead to dynamic chaos, when there is a vector of asset return, the conditional covariance matrix of which changes over time.

Роль информационного фактора в моделировании устойчивости финансового рынка

The information function of the financial market plays a key role in the pricing of financial assets. As the importance of information rises, it becomes more expensive and its value begins to exceed the value of the market assets themselves. This gives grounds for including the information factor as a variable not only in the pricing model of financial assets, but also in the financial market as a whole. Information acts as an argument for a non-linear function of return, price and risk level. The stable functioning of the financial market today is of paramount importance for the global financial system and the development of national economies. Is the stock market secondary or does it affect real economic activity? The article touches upon the potential effects of financial markets, which follow from the informational role of market prices. It is shown that taking into account the feedback effect from market prices to the real economy significantly changes our understanding of the pricing process, information content of prices and trading behavior of speculators. The paper considers linear martingale and nonlinear conditionally Gaussian models. In practice, they are not enough to reflect the asymmetric effects of external influences (exogenous factors). For this reason, it is proposed to use fractal Brownian models along with them. At the same time, one should take into account the degree of information content of the price itself, the reflexivity of price information, i.e. the ability of prices to form market expectations and the psychological factor leading to non-linearity and dynamic chaos.

Dynamics of coupled quasiperiodic generator and Rossler system

The interaction of a system with quasi-periodic autonomous dynamics and a chaotic system (Rossler system) is considered. The behavior of Lyapunov exponents is studied to identify possible types of system dynamics: chaos with additional zero Lyapunov exponents, three-frequency and two-frequency quasi-periodic regimes, periodic oscillations and the mode of oscillation death. Keywords: quasi-periodic oscillations, dynamical chaos, Rossler system, Lyapunov exponents.

Ultra-wideband chaos generator with selected inertia in the microwave range

An original scheme for constructing an ultra-wideband single-transistor generator of noise-like oscillations of the microwave range of wavelengths was proposed. The generator contains an inertial converter of the output signal of a nonlinear amplifier with positive feedback, the signal of which modulates the supply voltage of the active element (transistor). An experimental model of a chaotic signal generator based on a powerful domestic transistor 2T982A-2 operating in a small signal mode was created. The frequency band of generated noise oscillations with a power spectrum irregularity of 5 dB occupied the frequency range from 2.3 to 7.4 GHz with an integrated power of 5,mW with an average spectral density of noise oscillations of 10-6 W/MHz. The generator efficiency is 1%. Keywords: powerful bipolar transistor, ultra-wideband spectrum, dynamic chaos, generator with selected inertia.

Stability of equilibrium points of equation of regulatory mechanisms of cardiac activity

The article presents a mathematical model of regulatory mechanisms of cardiac activity in the form of system of functional-differential equations with delay arguments. With the use of reduction and scaling methods, the system of equations is reduced to the form of a functional-differential equation with delay argument. The equation was qualitatively analyzed. Equilibrium points are revealed and their stability is analyzed. As a result of a qualitative analysis, it was revealed that the mathematical model can reflect various modes of regulatory mechanisms of cardiac activity in normal conditions and in case of anomalies, the modes such as stationary, auto-oscillating, dynamic chaos, “black hole” and falling state.

Two-dimensional discrete-time laser model with chaos and bifurcations

<abstract><p>We explore the local dynamical characteristics, chaos and bifurcations of a two-dimensional discrete laser model in $ \mathbb{R}_+^2 $. It is shown that for all $ a $, $ b $, $ c $ and $ p $, model has boundary fixed point $ P_{0y}(0, \frac{p}{c}) $, and the unique positive fixed point $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $ if $ p > \frac{b c}{a} $. Further, local dynamical characteristics with topological classifications for the fixed points $ P_{0y}(0, \frac{p}{c}) $ and $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $ have explored by stability theory. It is investigated that flip bifurcation exists for the boundary fixed point $ P_{0y}(0, \frac{p}{c}) $, and also there exists a flip bifurcation if parameters vary in a small neighborhood of the unique positive fixed point $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $. Moreover, it is also explored that for the fixed point $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $, laser model undergoes a Neimark-Sacker bifurcation, and in the meantime stable invariant curve appears. Numerical simulations are implemented to verify not only obtain results but also exhibit complex dynamics of period $ -2 $, $ -3 $, $ -4 $, $ -5 $, $ -8 $ and $ -9 $. Further, maximum lyapunov exponents along with fractal dimension are computed numerically to validate chaotic behavior of the laser model. Lastly, feedback control method is utilized to stabilize chaos exists in the model.</p></abstract>