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Models for simulating some aspects of neural intelligence are presented and discussed. Special attention is given to terminal neurodynamics as a particular architecture of terminal dynamics suitable for modeling information flows. Applications of terminal chaos to information fusion as well as to planning and modeling coordination among neurons in biological systems are disussed.
This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.
The CHAOS and Thermal Sciences Laboratory (CaTs) at James Madison University evolved into a noteworthy effort to increase minority representation in the sciences and mathematics. Serving ten students and faculty directly, and nearly 50 students indirectly, CaTs, through recruitment efforts, workshops, mentoring programs, tutorial services and research and computational laboratories, fulfilled its intent to initiate an academically enriched research program aimed at strengthening the academic and self-actualization skills of undergraduate students with potential to pursue doctoral study in the sciences. The stated goal of the program was to increase by 5% the number of enrolled mathematics and science students into the program. Success far exceeded the program goals by producing 100% graduation rate of all supported recipients during its tenure, with 30% of the students subsequently in pursuit of graduate degrees. Student retention in the program exceeded 90% and faculty participation exceeded the three members involved in mentoring and tutoring, gaining multi-disciplinary support. Aggressive marketing of the program resulted in several paid summer internships and commitments from NASA and an ongoing relationship with CHROME, a nationally recognized organization which focuses on developing minority students in the sciences and mathematics. Success of the program was only limited by the limited fiscal resources at NASA which resulted in phasing out of the program.
Level, bench-like platforms in the interior of the Gorgonum Chaos basin appear to be shorelines associated with an ancient lake. These shorelines, however, seem to lack the typical features of shorelines associated with wave and current transport and erosion, such as crescentic embayments, spits, barrier islands, and wave-cut cliffs. Rather, the lakefacing platform edges are commonly rounded and cumulate in planform, often evenly encircling presumed islands. We interpret these shorelines to have been formed by outward growth in a quiescent environment, possibly in ice-covered bodies of water and possibly, in part, as chemical precipitates.
Multispectral imaging of Europa s surface by Galileo s Solid State Imaging (SSI) camera has revealed two major surface color units, which appear as white and red-brown regions in enhanced color images of the surface (see figure). The Galileo Near- Infrared Mapping Spectrometer (NIMS) experiment suggests that the whitish material is icy, almost pure water ice, while the spectral signatures of the reddish regions are dominated by a non-ice material. Two endmember models have been proposed for the composition of the non-ice material: magnesium sulfate hydrates [1] and sulfuric acid and its byproducts [2]. There is also debate concerning whether the origin of this non-ice material is exogenic or endogenic [3].Goals: The key questions this work addresses are: 1) Is the non-ice material exogenic or endogenic in origin? 2) Once emplaced, is this non-ice material primarily modified by exogenic or endogenic processes? 3) Is the non-ice material within ridges, bands, chaos, and lenticulae the same non-ice material across all such geological features? 4) Does the distribution of the non-ice material provide any evidence for or against any of the various models for feature formation? 5) To what extent do the effects of scattered light in SSI images change the spectral signatures of geological features?
Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.
It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices. Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.
A proposed approach to control of noise and chaos in dynamic systems would supplement conventional methods. The approach is based on fictitious forces composed of expectations governed by Fokker-Planck or Liouville equations that describe the evolution of the probability densities of the controlled parameters. These forces would be utilized as feedback control forces that would suppress the undesired diffusion of the controlled parameters. Examples of dynamic systems in which the approach is expected to prove beneficial include spacecraft, electronic systems, and coupled lasers.
The primary objective of this work is to develop an approach for multifidelity uncertainty quantification and to lay the framework for future design under uncertainty efforts. In this study, multifidelity is used to describe both the fidelity of the modeling of the physical systems, as well as the difference in the uncertainty in each of the models. For computational efficiency, a multifidelity surrogate modeling approach based on non-intrusive polynomial chaos using the point-collocation technique is developed for the treatment of both multifidelity modeling and multifidelity uncertainty modeling. Two stochastic model problems are used to demonstrate the developed methodologies: a transonic airfoil model and multidisciplinary aircraft analysis model. The results of both showed the multifidelity modeling approach was able to predict the output uncertainty predicted by the high-fidelity model as a significant reduction in computational cost.
The goal of this overview talk on information-theoretic aspects of scrambling and chaos is to connect "out-of-time-ordered correlators" (OTOC) with as many "information-theoretic" quantities as we can, in hopes of better understanding what the OTOC actually measures. Recently published papers on this topic will include but not be limited to Styliaris, et al., PRL 126, 030601 (2021); Zanardi and Anand, PRA 103, 06224 (2021); and Anand and Zanardi, Quantum 6, 746 (2022).
Spatio-temporal evolution, of large-amplitude Alfven waves, is investigated by means of their characteristic evolution equations as well as by MHD simulations.
The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.
Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiality are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equation of motion, and then at the level of the equations of motion themselves.
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Numerical experiments on two-dimensional thermosolutal convection reveal oscillations in the form of traveling, standing, modulated, and chaotic waves. Transitions between these wave forms and steady convection are investigated and compared with theory. Such rich nonlinear behavior is possible in fluid layers of wide horizontal extent, and provides an explanation for waves observed in recent laboratory experiments with binary fluid mixtures.
Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.
Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiability are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equations of motion, and then at the level of the equations of motion themselves.
Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.