Visualizing the logistic map with a microcontroller

The logistic map is one of the simplest nonlinear dynamical systems that clearly exhibit the route to chaos. In this paper, we explored the evolution of the logistic map using an open-source microcontroller connected to an array of light emitting diodes (LEDs). We divided the one-dimensional interval $[0,1]$ into ten equal parts, and associated and LED to each segment. Every time an iteration took place a corresponding LED turned on indicating the value returned by the logistic map. By changing some initial conditions of the system, we observed the transition from order to chaos exhibited by the map.Comment: LaTeX, 6 pages, 3 figures, 1 listin

Effects of non-denumerable fixed points in finite dynamical systems

The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point that a point on the fixed point in the phase space should remain there forever, for, a fixed point can evolve as well! Under such considerations one can argue that a free-kicked football should be non-chaotic.Comment: This paper is a replaced version to modify the not-so-true claim, made unknowingly in the earlier version, of being first to propose the peculiar dynamical systems as described in the paper. With respect to the original workers, we present here our original finding

Age- and Gender-Specific Normative Data of Grip and Pinch Strength in a Healthy Adult Swiss Population

Assessment of hand strength is used in a wide range of clinical settings especially during treatment of diseases affecting the function of the hand. This investigation aimed to determine age- and gender-specific reference values for grip and pinch strength in a normal Swiss population with special regard to old and very old subjects as well as to different levels of occupational demand. Hand strength data were collected using a Jamar dynamometer and a pinch gauge with standard testing position, protocol and instructions. Analysis of the data from 1023 tested subjects between 18 and 96 years revealed a curvilinear relationship of grip and pinch strength to age, a correlation to height, weight and significant differences between occupational groups. Hand strength values differed significantly from those of other populations, confirming the thesis that applying normative data internationally is questionable. Age- and gender-specific reference values for grip and pinch strength are presented

On positive solutions and the Omega limit set for a class of delay differential equations

This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\leq 0$ such that the solution is positive for all time $t>0$. The condition is "optimal". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\omega$ limit set of this dynamical system, which can provide informations about the long time behavior of positive solutions of the delay differential equation.Comment: 15 pages, 2 figure

Oscillons: an encounter with dynamical chaos in 1953?

We present evidences that Ben F. Laposky (1914-2000) might have been the first person who created a family of nonlinear analog circuits that allowed him to observe chaotic attractors and other trademarks of nonlinear science as early as 1953.Comment: accepted to Chao

Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics

We experimentally observe the nonlinear dynamics of an optoelectronic time-delayed feedback loop designed for chaotic communication using commercial fiber optic links, and we simulate the system using delay differential equations. We show that synchronization of a numerical model to experimental measurements provides a new way to assimilate data and forecast the future of this time-delayed high-dimensional system. For this system, which has a feedback time delay of 22 ns, we show that one can predict the time series for up to several delay periods, when the dynamics is about 15 dimensional.Comment: 10 pages, 4 figure

Value of Irrigation Water with Alternative Input Prices, Product Prices and Yield Levels: Texas Coastal Bend, Cross Timbers, Deep East, Edwards Aquifer, El Paso, Gulf Coast, Lower South Central, Rolling Plains, Trans Pecos and Winter Garden Regions

Agriculture is a major income generating sector of the Texas economy. Irrigated agriculture is an important part of Texas agriculture and an "adequate" water supply is important in maintaining a viable agriculture. Irrigation water is important both as a means of increasing the overall production of agricultural commodities and to stabilize farm income from commodities because of the high (year to year) variability of rainfall in most agricultural areas of Texas. Current interest in the value of irrigation water in agricultural production stems in part from rapid change in prices paid for farm inputs and prices received for farm products. The past two years have been a period of abrupt and large increases in prices. Prices of some farm products have risen to record levels; because of the energy crisis and the rapid rate of inflation, prices of fertilizer and fuel have at least doubled, and the price of other farm inputs have risen substantially. These price changes, in absolute and relative terms, make past studies of the value of irrigation water no longer meaningful or applicable. This study was undertaken to determine the value of irrigation water under 1974 price levels and relationships, and for prices that might be reasonably expected in the future. In this report, estimates are presented of the value of irrigation water at irrigation levels typically used on major crops (one percent or more of cropped land area based on 1969 TWDB inventory) produced in the Coastal Bend, Cross Timbers, Deep East Texas, Edwards Aquifer, E1 Paso, Lower and Upper Gulf Coast, Lower South Central, Rolling Plains I and II, Trans-Pecos and Winter Garden regions. The original contract (TWB 14-40034) did not specify several of the regions included in this report; e.g., Cross Timbers, Deep East Texas, E1 Paso and Rolling Plains. However, the data were available and insignificant additional costs of both time and funds were required to make the report comprehensive. Combining this report with the materials in Texas Water Resources Institute Technical Report Number 58, submitted August of 1974 yields analyses of all irrigated crops in all producing regions of Texas. Estimates of the value of irrigation water under alternative product prices, production costs, and yield levels are presented. This allows the reader to observe the "sensitivity" of the "ability-to-pay" for irrigation water to changing economic conditions (i.e., changing input and output prices)

Probability of local bifurcation type from a fixed point: A random matrix perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectra is considered both numerically and analytically using previous work of Edelman et. al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion is not general, e.g. real random matrices with Gaussian elements with a large positive mean and finite variance.Comment: 21 pages, 19 figure

Quantifying chaos for ecological stoichiometry

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincareacute return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing delta(1). However, for higher values of delta(1) the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter zeta) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model

A Model for Estimating Demand for Irrigation Water on the Texas High Plains

With rapidly changing conditions in production agriculture, the need for highly flexible and quickly applicable methods of analysis is emphasized. The purpose of this study was to develop such a model for a homogeneous production region in the Texas High Plains. A linear programming model was constructed whereby crop or input prices are readily adjustable. In addition, limitations on quantities of inputs available can easily be evaluated. The model contains cotton, grain sorghum, corn, wheat and soybeans. Inputs that can be evaluated include irrigation water, natural gas, diesel, nitrogen fertilizer and herbicides. The primary focus of this work was to estimate the demand for irrigation water in the study area. The model was applied using alternative crop prices and input prices. Assuming average crop prices, current input prices and only variable costs of production, as the price of water was increased wheat shifted from irrigated to dryland production, then grain sorghum, cotton, corn and soybeans, in that order. The price of water was $71.75 per acre foot plus current pumping cost when all land shifted to dryland production. The same analysis, except variable and fixed costs both included, gave similar results relative to the sequence of crops that shift to dryland production as the price of water was increased. However, the shifts occurred at much lower water prices; i.e., at$24.47 per acre foot plus current pumping costs, all land had shifted to dryland production. This suggests that over the long run, irrigation in the Texas High Plains is quite sensitive to the price of energy used in pumping water. Further, there are strong implications relative to farmer's "ability to pay" for water imported to the High Plains from other regions. In this report, several scenarios including low, high and average crop prices and average and high input prices were evaluated