Nonlinear time-periodic models of the longitudinal flight dynamics of desert locusts Schistocerca gregaria

Previous studies of insect flight control have been statistical in approach, simply correlating wing kinematics with body kinematics or force production. Kinematics and forces are linked by Newtonian mechanics, so adopting a dynamics-based approach is necessary if we are to place the study of insect flight on its proper physical footing. Here we develop semi-empirical models of the longitudinal flight dynamics of desert locusts Schistocerca gregaria. We use instantaneous force–moment measurements from individual locusts to parametrize the nonlinear rigid body equations of motion. Since the instantaneous forces are approximately periodic, we represent them using Fourier series, which are embedded in the equations of motion to give a nonlinear time-periodic (NLTP) model. This is a proper mathematical generalization of an earlier linear-time invariant (LTI) model of locust flight dynamics, developed using previously published time-averaged versions of the instantaneous force recordings. We perform various numerical simulations, within the fitted range of the model, and across the range of body angles used by free-flying locusts, to explore the likely behaviour of the locusts upon release from the tether. Solutions of the NLTP models are compared with solutions of the nonlinear time-invariant (NLTI) models to which they reduce when the periodic terms are dropped. Both sets of models are unstable and therefore fail to explain locust flight stability fully. Nevertheless, whereas the measured forces include statistically significant harmonic content up to about the eighth harmonic, the simulated flight trajectories display no harmonic content above the fundamental forcing frequency. Hence, manoeuvre control in locusts will not directly reflect subtle changes in the higher harmonics of the wing beat, but must operate on a coarser time-scale. A state-space analysis of the NLTP models reveals orbital trajectories that are impossible to capture in the LTI and NLTI models, and inspires the hypothesis that asymptotic orbital stability is the proper definition of stability in flapping flight. Manoeuvre control on the scale of more than one wing beat would then consist in exciting transients from one asymptotically stable orbit to another. We summarize these hypotheses by proposing a limit-cycle analogy for flapping flight control and suggest experiments for verification of the limit-cycle control analogy hypothesis

Atividade alelopática de substâncias químicas isoladas do Capim-Marandu e suas variações em função do pH Allelopathic activity of chemical substances isolated from Brachiaria brizantha cv. Marandu and their variations in function of pH

Este trabalho teve por objetivos isolar, identificar e caracterizar a atividade alelopática de substâncias químicas produzidas pela Brachiaria brizantha cv. Marandu e determinar as variações na atividade dessas substâncias em função da variação do pH da solução. A atividade alelopática foi realizada em bioensaios de germinação e desenvolvimento da radícula e do hipocótilo, utilizando as plantas daninhas malícia (Mimosa pudica) e mata-pasto (Senna obtusifolia) como receptoras. Os efeitos do pH foram analisados na faixa de 3,0 a 9,0. Os triterpenos pentacíclicos friedelina e epifriedelinol isolados da parte aérea de B. brizantha apresentaram baixa atividade inibitória na germinação de sementes e no desenvolvimento da radícula e do hipocótilo das duas plantas daninhas. As duas substâncias apresentaram comportamento diferenciado em relação à variação do pH da solução, com inibições mais marcantes em relação à planta daninha mata-pasto.<br>This work aimed to isolate, identify and determine the allelopathic activity of the chemical substances produced by Brachiaria brizantha cv. Marandu and to verify the effects of the pH in the solution on the activity of these compounds. The allelopathic activity was evaluated based on germination bioassays and radicle and hypocotyl growth using the species 'malícia' (Mimosa pudica) and 'mata-pasto' (Senna obtusifolia) as receptors. The effect of pH was analyzed in a range from 3.0 to 9.0. The pentacyclic triterpenes friedelin and epifriefelinol isolated from the shoots of B. brizantha showed a low inhibitory activity against seed germination and radicle and hypocotyl growth of the two receptor plants evaluated. The pentacyclic triterpenes friedelin and epifrifelinol presented differentiated behaviors in relation to the pH variation in the solution, with stronger inhibition activity against the weed 'mata-pasto'