This paper presents a comprehensive numerical analysis of a nonlinear energy harvesting system utilizing magnetic interactions and piezoelectric transducers. The primary objective of the study was to evaluate the influence of varying magnetic pole configurations and excitation parameters on the system's energy efficiency. For the configuration exhibiting the most favorable energy properties, a detailed dynamic analysis was conducted, considering the presence of coexisting solutions and regions of chaotic excitation. Special emphasis was placed on an original identification procedure for multiple Poincaré sections, based on partitioning phase coordinate sequences into even and odd sets. The analysis revealed complex phenomena, such as transient chaos and the coexistence of multiple stable periodic orbits, which – under specific initial conditions – offer significantly higher energy effectiveness than standard solutions. The results confirmed that the optimal magnet configuration ensures stable energy harvesting over a wide frequency range, while the number of excited multiple Poincaré sections is significantly determined by the cyclic variation of the potential.
In this paper, we propose a nonlinear kinetic model of the dynamics of social opinions that takes into account the manipulation of fake news. The model includes both a nonlinear term describing the change of opinions between agents and the linear term of the influence of fake news manipulation on opinion formation. The latter term is modeled throughout an external term. We perform a preliminary theoretical analysis of the model. Furthermore, some numerical simulations show the behavior of solutions in the change of opinions, depending on the particular scenario taking into account, i.e., parameters of the system and initial conditions. In particular, polarization effects are observed according to what is expected from real-world situations.
