Nonlinear stiffness, Lyapunov exponents, and attractor dimension

I propose that stiffness may be defined and quantified for nonlinear systems using Lyapunov exponents, and demonstrate the relationship that exists between stiffness and the fractal dimension of a strange attractor: that stiff chaos is thin chaos.Comment: See home page http://lec.ugr.es/~julya

Preliminary Evaluation of a Dodder Anthracnose Fungus from China as a Mycoherbicide for Dodder Control in the US

Dodder (Cuscuta spp.) is a noxious, parasitic, annual weed throughout most of the United States. A fungus used to control it in China was imported under permit for studies with U.S. dodder species in containment. The fungus, Colletotrichum gloeosporioides, sporulated on liquid and solid media at room temperature. Conidia from 7-12 day old cultures were diluted to 3.5 to 7 X 16⁶ spores ml^-1 for host range inoculations. Germination on water agar at 24 hrs was higher at 28 than 30 or 24 C. Inoculated plants were exposed to dew periods of 12-1 4 hrs at 24 or 28 C, then transferred to growth chambers with 1 2-hr photoperiods at constant temperatures of 24, 28, and 32C. Dodder species were severely diseased but rarely killed. Symptoms were most severe on native collections of Cuscuta campestris after 4 to 5 days incubation when this species on periwinkle seedlings was inoculated with 3.5 to 7 X 10⁵ spores ml^-1 . Cuscuta cuspidata, C. pentagona, and C. campestris from a California seedlot were also tested under optimum conditions for disease. The C. campestris from California was the most susceptible. Inoculation of 16 species in eight plant families revealed no other host except sweet potato which developed a necrotic fleck. This research indicates a need for strain improvement prior to field tests

Fuzzy Control of Chaos

We introduce the idea of the fuzzy control of chaos: we show how fuzzy logic can be applied to the control of chaos, and provide an example of fuzzy control used to control chaos in Chua's circuit

Some First Results for Noncooperative Pregames : Social Conformity and Equilibrium in Pure Strategies.

We introduce the framework of noncooperative pregames and demonstrate that for all games with sufficiently many players, there exists approximate (E) Nash equilibria in pure strategies. Moreover, an equilibrium can be selected with the property that most players choose the same strategies as all other players with similar attributes. More precisely, there is an integer K, depending on E but not on the number of players so that any sufficiently large society can be partitioned into fewer than K groups, or cultures, consisting of similar players, and all players in the same group play the same pure strategy. In ongoing research we are extending the model to cover a broader class of situations, including incomplete information.GAMES ; INFORMATION ; STRATEGIC PLANNING

Tidal estimation in the Pacific with application to SEASAT altimetry

The techniques for computing the eigenfunctions of the velocity potential (Proudman functions) set out in Sanchez, et al. (1986) in relation to the Atlantic-Indian Oceans are here applied to the Pacific Ocean, using a 6x6 degree grid of 510 points (455 points for the associated stream functions). Normal modes are computed from the first Proudman functions and have natural periods from 43.9h downward. Tidal syntheses are derived from these modes by direct application of the (frictionless) dynamic equations and by least-squares fitting of Proudman functions to the dynamically interpolated tide-gauge data of Schwiderski (1983). The modes contributing the most energy to the principal harmonic tidal constituents are different in the two computations: their natural periods are typically in the range of 9 to 16h for semidiurnal, and 14 to 43h for diurnal tides. The rms of fit for the Proudman functions is, in all cases, better than the corresponding value for the same number of spherical harmonics

Three-frequency resonances in dynamical systems

We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental device (an electronic oscillator). We compare the hierarchies of three-frequency resonances we find in each of these systems. All three show similar qualitative behaviour, suggesting the existence of generic features in the parameter-space organization of three-frequency resonances.Comment: See home page http://lec.ugr.es/~julya

Burridge-Knopoff Models as Elastic Excitable Media

We construct a model of an excitable medium with elastic rather than the usual diffusive coupling. We explore the dynamics of elastic excitable media, which we find to be dominated by low dimensional structures, including global oscillations, period-doubled pacemakers, and propagating fronts. We suggest that examples of elastic excitable media are to be found in such diverse physical systems as Burridge-Knopoff models of frictional sliding, electronic transmission lines, and active optical waveguides

Universality in Three-Frequency Resonances

We investigate the hierarchical structure of three-frequency resonances in nonlinear dynamical systems with three interacting frequencies. We hypothesize an ordering of these resonances based on a generalization of the Farey tree organization from two frequencies to three. In experiments and numerical simulations we demonstrate that our hypothesis describes the hierarchies of three-frequency resonances in representative dynamical systems. We conjecture that this organization may be universal across a large class of three-frequency systems