Search Results
Analysis of an operator-differential model for magnetostrictive energy harvesting
We present a model of, and analysis of an optimization problem for, a magnetostrictive harvesting device which converts mechanical energy of the repetitive process such as vibrations of the smart material to electrical energy that is then supplied to an electric load. The model combines a lumped differential equation for a simple electronic circuit with an operator model for the complex constitutive law of the magnetostrictive material. The operator based on the formalism of the phenomenological Preisach model describes nonlinear saturation effects and hysteresis losses typical of magnetostrictive materials in a thermodynamically consistent fashion. We prove well-posedness of the full operatordifferential system and establish global asymptotic stability of the periodic regime under periodic mechanical forcing that represents mechanical vibrations due to varying environmental conditions. Then we show the existence of an optimal solution for the problem of maximization of the output power with respect to a set of controllable parameters (for the periodically forced system). Analytical results are illustrated with numerical examples of an optimal solution.
Memory and adaptive behaviour in population dynamics: Anti-predator behaviour as a case study
Memory enables to forecast future on the basis of experience, and thus, in some form, is principally important for the development of flexible adaptive behaviour by animal communities. To model memory, in this paper we use the concept of hysteresis, which mathematically is described by the Preisach operator. As case study, we consider anti-predator adaptation in the classic Lotka-Volterra predator-prey model. Despite its simplicity, the model allows to naturally incorporate essential features of an adaptive system and memory. Our analysis and simulations show that a system with memory can have a continuum of equilibrium states with non-trivial stability properties.