Evidence Of Chaotic Behavior Research Articles

A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability

In nonlinear dynamics, there is a continuous exploration of introducing systems with evidence of chaotic behavior. The presence of nonlinearity within system equations is crucial, as it allows for the emergence of chaotic dynamics. Given that quadratic terms represent the simplest form of nonlinearity, our study focuses on introducing a novel chaotic system characterized by only quadratic nonlinearities. We conducted an extensive analysis of this system’s dynamical properties, encompassing the examination of equilibrium stability, bifurcation phenomena, Lyapunov analysis, and the system’s basin of attraction. Our investigations revealed the presence of eight unstable equilibria, the coexistence of symmetrical strange repeller(s), and the potential for multistability in the system.

Evidence for Chaotic Behavior during the Yielding of a Soft Particle Glass.

Materials comprised of deformable particles such as microgels and concentrated emulsions and foams display complex rheological behavior that includes a yielding transition from an elastic solid to viscous fluid. Most studies of this class of soft matter involve shear flows, and only a handful report both shear and normal stresses. We present measurements of the shear stress and two normal stress differences for a microgel subjected to constant shear rate flows. The shear stress evolves through the yield point in a manner indicative of simple yield stress fluid behavior. Prior to yielding, the normal stress differences are immeasurable; beyond the yield point, they evolve in a reproducibly chaotic manner.

Harmonic oscillator kicked by spin measurements: A Floquet-like system without a classical analog

We present a kicked harmonic oscillator where the impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom and not by the canonical quantization of a time-dependent Hamiltonian. The ancilla is dynamically entangled with the oscillator position, while the background Hamiltonian remains static. The dynamics of this system is determined in closed analytical form, allowing for the evaluation of a properly defined Loschmidt echo, ensemble averages, and phase-space portraits. As in the case of standard Floquet systems, we observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidence of chaotic behavior, however, not originating from any classically chaotic system.

Detecting Chaotic Behavior in Agricultural Exchange-traded Funds

<p>This study investigates the chaos effect of agricultural exchange-traded funds (ETFs) using Brock, Dechert, and Scheinkman test, rescaled range analysis, and correlation dimension analysis. The standardized residuals from generalized autoregressive conditional heteroskedasticity models are fitted into eight ETFs and examined in each case for evidence of chaotic behavior. This study also examines whether or not the ETFs are consistent with the chaos effect based on the underlying random data with trend-reinforcing series. Research results outline the financial insights for the agricultural ETF field of investment forecasting to eliminate trading emotions, while pursuing considerable profitable experience for investors.</p>

Detecting Chaotic Behavior in Agricultural Exchange-traded Funds

<p>This study investigates the chaos effect of agricultural exchange-traded funds (ETFs) using Brock, Dechert, and Scheinkman test, rescaled range analysis, and correlation dimension analysis. The standardized residuals from generalized autoregressive conditional heteroskedasticity models are fitted into eight ETFs and examined in each case for evidence of chaotic behavior. This study also examines whether or not the ETFs are consistent with the chaos effect based on the underlying random data with trend-reinforcing series. Research results outline the financial insights for the agricultural ETF field of investment forecasting to eliminate trading emotions, while pursuing considerable profitable experience for investors.</p>

Evidence for chaotic behaviour in pulsar spin-down rates

We present evidence for chaotic dynamics within the spin-down rates of 17 pulsars originally presented by Lyne et al. Using techniques that allow us to re-sample the original measurements without losing structural information, we have searched for evidence of a strange attractor in the time series of frequency derivatives for each of the 17 pulsars. We demonstrate the effectiveness of our methods by applying them to a component of the Lorenz and R\"ossler attractors that were sampled with similar cadence to the pulsar time series. Our measurements of correlation dimension and Lyapunov exponent show that the underlying behaviour appears to be driven by a strange attractor with approximately three governing non-linear differential equations. This is particularly apparent in the case of PSR B1828$-$11 where a correlation dimension of 2.06\pm0.03 and a Lyapunov exponent of $(4.0\pm0.3)\times10^{-4}$ inverse days were measured. These results provide an additional diagnostic for testing future models of this behaviour.

Evidence of Chaotic Behavior in Noise From Industrial Process

Usually, in dealing with the dynamical behavior of noise from an industrial process (NFIP), random or even white noise is assumed to describe it. However, since white noise is just an ideal model in mathematics and can hardly exist in an industrial process, this assumption seriously hinders the successful application of classical control theory in practice. For this reason, nonlinear time series analysis is used to analyze NFIP in an attempt to capture the signature of chaos. The chaotic behavior is apparent in NFIP due to the presence of finite and non-integer correlation dimension, and the minimum number of macroscopic variables required to model NFIP dynamics is obtained. These results indicate that NFIP is deterministic and high-dimensional chaos but not random or white noise and, in the future, might lead the way towards the direct solution of prediction and modeling of NFIP and a series of changes to the traditional algorithms in the control field may appear

Period-doubling events in the light curve of R Cygni: Evidence for chaotic behaviour

A detailed analysis of the century long visual light curve of the long-period Mira star R Cygni is presented and discussed. The data were collected from the publicly available databases of the AFOEV, the BAAVSS and the VSOLJ. The full light curve consists of 26655 individual points obtained between 1901 and 2001. The light curve and its periodicity were analysed with help of the O-C diagram, Fourier analysis and time-frequency analysis. The results demonstrate the limitations of these linear methods. The next step was to investigate the possible presence of low-dimensional chaos in the light curve. For this, a smoothed and noise-filtered signal was created from the averaged data and with the help of time delay embedding, we have tried to reconstruct the attractor of the system. The main result is that R Cygni shows such period-doubling events that can be interpreted as being caused by a repetitive bifurcation of the chaotic attractor between a period 2T orbit and chaos. The switch between these two states occurs in a certain compact region of the phase space, where the light curve is characterized by ∼1500-day long transients. The Lyapunov spectrum was computed for various embedding parameters confirming the chaotic attractor, although the exponents suffer from quite high uncertainty because of the applied approximation. Finally, the light curve is compared with a simple one zone model generated by a third-order differential equation which exhibits well-expressed period-doubling bifurcation. The strong resemblance is another argument for chaotic behaviour. Further studies should address the problem of global flow reconstruction, including the determination of the accurate Lyapunov exponents and dimension.

Effect of aggregation on chaotic time series

Modeling the variability of daily streamflows has received less analysis than those of monthly or annual streamflows. Since daily streamflows are affected by individual rainstorms, characterizing their features is more complicated. In this work, we analyze the complex behavior of daily streamflows and search for evidence of deterministic nonlinear dynamics. However, there is no evidence of chaotic behavior in the investigated streamflows. We also investigate the effect of aggregation process on chaotic time series. We suggest that the lack of evidence for nonlinear determinism in daily streamflows may be due to such aggregation process.

Arc root dynamics in high power plasma torches — Evidence of chaotic behavior

Although plasma torches have been commercially available for about 50 years, areas such as plasma gun design, process efficiency, reproducibility, plasma stability, torch lives etc. have remained mostly unattended. Recent torch developments have been focusing on the basic understanding of the plasma column and its dynamics inside the plasma torch, the interaction of plasma jet and the powders, the interaction of the plasma jet with surroundings and the impingement of the jet on the substrate. Two of the major causes of erratic and poor performance of a variety of thermal plasma processes are currently identified as the fluctuations arising out of the arc root movement on the electrodes inside the plasma torch and the fluid dynamic instabilities arising out of entrainment of the air into the plasma jet. This paper reviews the current state of understanding of these fluctuations as well as the dynamics of arc root movement in plasma torches. The work done at the author’s laboratory on studying the fluctuations in arc voltage, arc current, acoustic emissions and optical emissions are also presented. These fluctuations are observed to be chaotic and interrelated. Real time monitoring and controlling the arc instabilities through chaos characterization parameters can greatly contribute to the understanding of electrode erosion as well as improvement of plasma torch lifetime.

Nonlinear analysis and prediction of river flow time series

In this paper we consider the problem of nonlinear modelling the discharge time series of a river in order to study the forecasting ability of a nonlinear approach. To this aim, we first check for some evidence of chaotic behaviour in the dynamics by considering a set of different procedures (phase portrait of the attractor, correlation dimension, the largest Lyapunov exponent, DVS diagram). Their joint application to our data allows us not to exclude the presence of a nonlinear deterministic dynamics of chaotic type. Secondly, we consider two kinds of nonlinear predictors: a univariate predictor, which is based only on the information of the discharges times series and a multivariate one, which also takes into account the information coming from rainfall data. By comparing these predictors with a linear predictor, we can conclude that nonlinear river flow modelling is an effective method to improve prediction in a statistically significant way. Copyright © 2000 John Wiley & Sons, Ltd.

Temporally-explicit models of fire and forest

Pollen and charcoal data from varved sediments of Lake Ahvenainen, southern Finland, were examined through ordination analyses to determine temporal groupings of vegetation. The ordination `continually' changed throughout the pollen profile, indicating nonequilibrium system dynamics. However, temporal associations that were stationary existed during the history of vegetation change at Lake Ahvenainen, and these temporal associations were nested in a hierarchy. Weighted averaging regression and calibration were used to model the relationship between fire and vegetation within each temporal association. Fire was significantly related to the vegetation for nearly all temporal associations. Community dynamics within temporal associations were examined with cross-correlation analysis. Taxa were correlated with fire occurrence (charcoal fragments) within the temporal associations and classic successional recovery was confirmed. In addition, two temporal associations showed evidence of chaotic behavior. The long-term pollen-charcoal analysis supported three theories of system dynamics: (1) nonequilibrium long-term dynamics, (2) hierarchical structuring of temporally stationary associations, and (3) chaotic dynamics in stationary associations. These theories are not necessarily contradictory, but are scale dependent.

Observations of Bifurcation and Chaos in Plant Physiological Responses to Light

Although some theoretical predictions have been made, no experimental evidence of chaotic behaviour in plant physiological responses has been reported. Here we present observations of period- doubling and tripling in higher plants. For leaf bioelectric and temperature responses of maize, tomato, and burweed plants to rhythmical light, two different routes to chaos were found experimentally. One was via successive period-doubling and the other via the formation of intermittently chaotic oscillations from a subharmonic synchronisation. Because these effects appeared in intact plants, under conditions close to those found in nature, they may have wide significance, including for plant phylogenesis.

Evidence of chaotic behavior in computer simulations of fracture processes

Although the science of fracture mechanics has had considerable success in using continuum mechanics to predict fracture stress distributions and the approximate fracture path in groups of identical samples, a great amount of uncertainty is always present in the behavior of a single sample. It has been generally accepted that this lack of predictability is the result of an incomplete knowledge of the state of flaws on a sample surface coupled with limitations in fracture mechanics models. In the simulation of fracture in amorphous silica, the stress-strain behavior during fracture and the structure of the fracture paths are ultimately dependent on individual atomic motions and all aspects of the structure. This is a hallmark of chaotic behavior, indicating that the characteristics of fracture in materials can be predicted only in general terms, regardless of the precision used to define the initial configurations.

Evidence for chaotic behaviour in seismic wave scattering

Scattering of seismic waves by lithospheric heterogeneities produces seismic coda which typically look random. Consequently stochastic modelling methods are usually applied to these coda [1–6]. Here, we introduce a technique, based on previous work [7], for evaluating the predictability of time‐series data as an indicator of underlying determinism. When analyzed using this method both earthquake and explosive source seismic coda display strong short term predictability which is not consistent with a random generation mechanism.

Evidence for chaotic behavior in driven ventricles

Toad ventricles were externally driven by periodic pulses while monophasic action potential (MAP) signals were recorded in seven excised and seven in situ ventricles. As the frequency was slowly increased in steps, the stimulated tissue displayed several dynamic characteristics. Hierarchies of periodic behavior, like phase-locking and period-doubling sequences leading to chaos, were observed. Results showed that subharmonic bifurcations (order one and two) and chaotic-like behavior may systematically occur in the MAP signal within a definite frequency interval in the 1:1 phase locking regime. The chaotic, or more cautiously expressed, chaotic-like behavior is characterized by the power spectrum, the autocorrelation function, the Poincaré map, and the reconstructed 2-D phase portrait. It is concluded that (a) bifurcations of order one and two and the characteristic irregular behavior are evidences of local universal chaotic dynamics in cardiac tissue; (b) there are no qualitative differences in the dynamics of the in situ and excised ventricles; and (c) fibrillation seems to be related to chaotic behavior, but whether they are similar or equivalent phenomena still remains to be seen.

Resonant laser-induced desorption: classical and adiabatic quantum models

We report results of model calculations aimed at understanding the phenomenon of resonant laser-induced desorption. The calculations consider a diatomic molecule with a harmonic internal vibration adsorbed to a substrate in an end-on configuration with a van der Waals-type binding potential. Using the adiabatic (Born–Oppenheimer) approximation, we calculate quantum mechanically the change in the adsorption potential produced when the internal vibration is excited. Within this approximation, elastic tunneling transitions from bound to continuum states do not occur. The same problem is treated classically by direct numerical integration of the nonlinear classical equations of motion, both with and without damping. The exact classical results confirm the quantum adiabatic approximation. No evidence for chaotic behavior is found.