Regular and chaotic vibration in a piezoelectric energy harvester

We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0–1 test. The appearance of chaotic vibrations reduces the level of harvested energy

Persistence of Pollination Systems

Pollination systems are composed of flowering plants and flower visitors, en- gaging into mutualistic interactions. However, the flower visitors include true pollinators, which pollinate the flower by visiting it through the legitimate way, and also by cheaters, which use the flower′s resources (e.g. nectar and pollen) without pollinating it or been just marginally efficient on pollination. On the one hand, plants have different flower structures, as shallow and tubu- lar flowers, which can provide some protection agains the cheaters effects or higher efficiency when visited by pollinators. Even though cheaters can dam- age flowers, there is evidence that cheaters can have a positive effect on the pollination service. In fact, the existence of cheaters decreases the amount of reward provided by plants in a given environment. Therefore, pollinators travel further in order to visit more flowers or even spend a longer time in each flower to collect enough resources. It increases the cross-pollination rate and the pollination success, especially to auto-incompatible plant species. The presence of cheaters in these systems represent a delicate trade-off when mutualistic interactions when cheaters effects are taken into account. In this work, we are interested to understand how pollination systems allow the per- sistent coexistence of the two types of visitors and plants. We developed a mean field analytical model relying on game theory, with a bipartite network of two kinds of plants (shallow and tubular flowers) and two kinds of visitors (pollinators and cheaters). Our analytical and numerical results confirm the presence of metastable states of persistent coexistence of the above-mentioned visitors and plants. In order to better describe additional real-world features of pollination systems (i.e. the spatial distribution of flowers, the depletion of resources, and the crossing pollination effect) we also implement an agent- based model. In this case, we observed coexistence of the two visitors and two plants when we included the space. We are still studying the agent- based mode approach to understand, for instance, how spatial structures (as the ones resulting from mankind actions) can affect pollination systems