Complex Dynamical Behaviors of a Typical Linkage-Slider Structure

Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators

“…We consider a typical linkage-slider structure [12,15] whose simplified diagram is shown in Figure 1. e oscillation of the slider is governed by the following equation:…”

“…Since oscillators are well known to have the complex dynamical behavior in the neighborhood of the main resonance, in this section we follow our previous work [12] and consider that the motion appears to be in the vicinity of the primary resonance.…”

“…Global bifurcation often leads to the erosion of safe basin [28] and chaos [12,18]. We wonder if the heteroclinic bifurcation in system (2) may cause the two types of initial-sensitive phenomena simultaneously.…”

“…Razzak [11] proposed a new noble modi ed method to obtain the approximate solution of strongly nonlinear oscillator systems with a rational force and an irrational one. Qin and Shang [12] applied the average method directly to get the approximate periodic solutions semi-analytically in the vibrating system of a linkage slider under an irrational tensile force. Amer et al [13] used the Poincare method of small parameter to achieve the asymptotic solutions of a three-dimensional system of a gyrostat for the case of irrational frequencies.…”