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Bifurcation analysis of torsional micromirror actuated by electrostatic forces

Taghizadeh M., Mobki H.

Archives of Mechanics

2014

Vol. 66, nr 2

95--111

In this paper, static and dynamic behavior of an electrostatically actuated torsional micro-actuator is studied. The microactuator is composed of a micromirror and two torsional beams, which are excited with two electrodes. Unlike in the traditional microactuators, the electrostatic force is exerted to both sides of micromirror, so the model is exposed to a DC voltage applied from the ground electrodes. The static governing equation of the torsional microactuator is derived and the relation between rotation angle and the driving voltage is determined. Local and global bifurcation analysis is performed, considering torsional characteristics of the micro-beams. By solving static deflection equation, the fixed points of the actuator are obtained. Critical values of the applied voltage leading to qualitative changes in the microactuator behavior through a saddle-node or pitchfork bifurcations for different spatial condition are obtained. Furthermore, the effects of different gap and electrode sizes as well as beam lengths on the dynamic behavior are investigated. It is shown that an increase of the applied voltage leads the structure to an unstable condition by undergoing saddle-node and pitchfork bifurcations when the voltages ratio is zero and one, respectively.

Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response

Chen Q., Teng Z., Hu Z.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 2

247--261

The dynamics of a discrete-time predator–prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations in period-2, 4, 8, 16, quasi-periodic orbits, an attracting invariant circle, an inverse period-doubling bifurcation from the period-32 orbit leading to chaos and a boundary crisis, a sudden onset of chaos and a sudden disappearance of the chaotic dynamics, attracting chaotic sets and non-attracting sets. We also observe that when the prey is in chaotic dynamics the predator can tend to extinction or to a stable equilibrium. Specifically, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control.