MEMS-Based Atomic Force Microscope: Nonlinear Dynamics Analysis and Its Control

In this chapter, we explore a mathematical modelling that describes the nonlinear dynamic behavior of atomic force microscopy (AFM). We propose two control techniques for suppressing the chaotic motion of the system. The proposed model considers the interatomic interactions between the analyzed sample and the cantilever. These acting forces are van der Waals type, and we add a mathematical term that is a simple approximation to the viscoelasticity that possibly occurs in biological samples. We analyzed the behavior of the initial conditions of the proposed mathematical model, which showed a degree of complexity of the basins of attraction that were detected by entropy and uncertainty parameter, both detect if the basins have a fractal behavior. Numerical results showed that the nonlinear dynamic behavior has chaotic regions with the Lyapunov exponent, bifurcation diagram, and the Poincaré map. And, we propose two control techniques to suppress the chaotic movement of the AFM cantilever. First technique is the optimal linear feedback control (OLFC), which does not consider the nonlinearities of mathematical model. On the other hand, the control state dependent Riccati equation (SDRE) considers the nonlinearities of mathematical model. Both control techniques for a desired periodic orbit proved to be efficient

Analysis and chaos control of a four-dimensional magnetohydrodynamic model with hyperchaotic solutions

In this paper, the dynamical behavior of a four-dimensional magnetohydrodynamic model, consisting of a generalized Lorenz model, is investigated. A nonlinear dynamical analysis is performed using Lyapunov exponents and bifurcation diagrams, focusing on the chaotic and hyperchaotic behaviors associated with the bifurcation parameter $$\left( k_{1} \right)$$ that couples the equations of fluid displacement to the induced magnetic field. The State-dependent Riccati Equation (SDRE) and the Optimal Linear Feedback Control (OLFC) techniques are considered to design the state feedback control system that stabilizes the system to a previously defined orbit. The performance of the control systems are compared showing that the OLFC presents better results

Mitochondrial Biogenesis and Function in Arabidopsis†

Mitochondria represent the powerhouse of cells through their synthesis of ATP. However, understanding the role of mitochondria in the growth and development of plants will rely on a much deeper appreciation of the complexity of this organelle. Arabidopsis research has provided clear identification of mitochondrial components, allowed wide-scale analysis of gene expression, and has aided reverse genetic manipulation to test the impact of mitochondrial component loss on plant function. Forward genetics in Arabidopsis has identified mitochondrial involvement in mutations with notable impacts on plant metabolism, growth and development. Here we consider the evidence for components involved in mitochondria biogenesis, metabolism and signalling to the nucleus