A general class of predation models with multiplicative Allee effect

A class of models of predator–prey interaction with Allee effect on the prey population is presented. Both the Allee effect and the functional response are modelled in the most simple way by means of general terms whose conveniently chosen mathematical properties agree with, and generalise, a number of concrete Leslie–Gower-type models. We show that this class of models is well posed in the sense that any realistic solution is bounded and remains non-negative. By means of topological equivalences and desingularization techniques, we find specific conditions such that there may be extinction of both species. In particular, the local basin boundaries of the origin are found explicitly, which enables one to determine the extinction or survival of species for any given initial condition near this equilibrium point. Furthermore, we give conditions such that an equilibrium point corresponding to a positive steady state may undergo saddle-node, Hopf and Bogdanov–Takens bifurcations. As a consequence, we are able to describe the dynamics governed by the bifurcated limit cycles and homoclinic orbits by means of carefully sketched bifurcation diagrams and suitable illustrations of the relevant invariant manifolds involved in the overall organisation of the phase plane. Finally, these findings are applied to concrete model vector fields; in each case, the particular relevant functions that define the conditions for the associated bifurcations are calculated explicitly.     

Delayed fluorescence in perhydrotriphenylene-oligothiophene inclusion compounds: evidence for molecular oxygen-related excited States

Delayed emission from α-terthiophene (3T) and α-quinquethiophene (5T) in a perhydrotriphenylene (PHTP) host is investigated. Delayed fluorescence for the lowest singlet excited state of 3T and 5T is detected at both low (80 K) and room temperatures. In addition, at low temperature, phosphorescence from 3T is observed with a lifetime of ～100 μs. Comparison of the dependence of delayed fluorescence and phosphorescence on excitation intensity and time shows that delayed fluorescence does not originate from triplet--triplet annihilation. A dependence of the delayed fluorescence on atmospheric pressure indicates that it originates, at least partially, from complexes of photoexcited oligothiophene and molecular oxygen O(2).     

Dechlorane Plus in eggs of two gull species (Larus michahellis and Larus audouinii) from the southwestern Mediterranean Sea

Dechlorane Plus (DP) and some of its possible degradation products were measured in eggs from the yellow-legged gull (Larus michahellis) and Audouin's gull (Larus audouinii) from a protected area in the southwestern Mediterranean Sea. Statistically significant differences were found between both gull species, with yellow-legged gull eggs showing the highest average total DP concentration (209?pg/g wet weight). According to stable nitrogen and carbon isotope values, variations in DP concentrations in the gull species studied are explained by foraging behavior and diet rather than by the trophic position. Both DP stereoisomers were quantified in all the samples studied, and a slight enrichment of the anti-DP could have occurred in both species. The quantification of anti-[DP-1Cl] only in ～58?% of yellow-legged gulls support the hypothesis of a species-dependent factor influencing the bioaccumulation and/or biotransformation of Dechlorane-related compounds. This study reports on the first measurements of Dechlorane-related compounds in biota from the North African continent, contributing to the knowledge about DP environmental fate and distribution. In the light of our results, more research on differences in species-dependent bioaccumulation and biotransformation capabilities as well as ecological effects is encouraged in future Dechlorane-related compound studies.     

Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems

This paper proposes a procedure by which it is possible to synthesize Rossler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.     

Testing for intracycle determinism in pseudoperiodic time series

A determinism test is proposed based on the well-known method of the surrogate data. Assuming predictability to be a signature of determinism, the proposed method checks for intracycle (e.g., short-term) determinism in the pseudoperiodic time series for which standard methods of surrogate analysis do not apply. The approach presented is composed of two steps. First, the data are preprocessed to reduce the effects of seasonal and trend components. Second, standard tests of surrogate analysis can then be used. The determinism test is applied to simulated and experimental pseudoperiodic time series and the results show the applicability of the proposed test.     

Closed-loop suppression of chaos in nonlinear driven oscillators

Summary This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.This work has been supported by CNPq (Brazil) under Grant 200597/90-6 and SERC (UK) under Grant GR/H 35286.