Turing Patterns for a Nonlocal Lotka–Volterra Cooperative System

This paper is devoted to investigating the pattern dynamics of Lotka–Volterra cooperative system with nonlocal effect and finding some new phenomena. Firstly, by discussing the Turing bifurcation, we build the conditions of Turing instability, which indicates the emergence of Turing patterns in this system. Then, by using multiple scale analysis, we obtain the amplitude equations about different Turing patterns. Furthermore, all possible pattern structures of the model are obtained through some transformation and stability analysis. Finally, two new patterns of the system are given by numerical simulation.

Multiple-Scale Analysis of a Tunable Bi-Stable Piezoelectric Energy Harvester

This paper presents the theoretical modeling and multiple-scale analysis of a novel piezoelectric energy harvester composed of a metal cantilever beam, piezoelectric films, and an axial preload spring at the moveable end. The harvester experiences mono- and bi-stable regimes as the stiffness of preload spring increases. The governing equations are derived with two high-order coupling terms induced by the axial motion. The literature shows that these high-order coupling terms lead to tedious calculations in the stability analysis of solutions. This work introduces an analytical strategy and the implementation of the multiple-scale method for the harvester in either the mono- or bi-stable status. Numerical simulations are performed to verify the analytical solutions. The influence of the electrical resistance, excitation level, and the spring pre-deformation on the voltage outputs and dynamics are investigated. The spring pre-deformation has a slight influence on the energy harvesting performance of the mono-stable system, but a large effect on that of the bi-stable system.

Multiple-Scale Analysis of a Novel Piezoelectric Energy Harvester With a Tunable Potential Function

Publisher’s Note: This paper was selected for publication in ASME Letters in Dynamic Systems and Control. https://www.asmedigitalcollection.asme.org/lettersdynsys/article/doi/10.1115/1.4046961/1082714/Multiple-Scale-Analysis-of-a-Tunable-Bi-Stable