An inverted pendulum with multibranching view as self-controlled system: Modelling and vibration absorber capacity

The design and performance evaluation of a self-controlled system are investigated. An autonomous set of pendulums with different branches is considered. A mathematical model is derived, and the damping mechanism due to the transfer of energy between the central column and its attached branches is pointed out. The case of earthquake loads has been tested. Dynamics study shows that the energy received by the central column is distributed to the different branches, leading to a self-vibration control of the system. It is also found that one can increase the damping ratio according to the physical characteristics of the structure. This is a good candidate for earthquake protection of mechanical structures.

Dynamical Stability of Bulk Viscous Isotropic and Homogeneous Universe

In this paper, we study the phase space portrait of homogeneous and isotropic universe by taking different coupling functions between dark energy models and bulk viscous dark matter. The dimensionless quantities are introduced to establish an autonomous set of equations. To analyze the stability of the cosmos, we evaluate critical points and respective eigenvalues for different dynamical quantities. For bulk viscous matter and radiation in tachyon coupled field, these points show stable evolution when γ ≫ δ but accelerated expansion of the universe for δ > 1 9 . The stability of the universe increases for some stationary points which may correspond to the late-time expansion for the coupled phantom field.

QUENCHING LORENZIAN CHAOS

How fluctuations can be eliminated or attenuated is a matter of general interest in the study of steadily-forced dissipative nonlinear dynamical systems. Here, we extend previous work on "nonlinear quenching" [Hide, 1997] by investigating the phenomenon in systems governed by the novel autonomous set of nonlinear ordinary differential equations (ODE's) [Formula: see text], ẏ=-xzq+bx-y and ż=xyq-cz (where (x, y, z) are time(t)-dependent dimensionless variables and [Formula: see text], etc.) in representative cases when q, the "quenching function", satisfies q=1-e+ey with 0≤e≤1. Control parameter space based on a,b and c can be divided into two "regions", an S-region where the persistent solutions that remain after initial transients have died away are steady, and an F-region where persistent solutions fluctuate indefinitely. The "Hopf boundary" between the two regions is located where b=bH(a, c; e) (say), with the much studied point (a, b, c)=(10, 28, 8/3), where the persistent "Lorenzian" chaos that arises in the case when e=0 was first found lying close to b=bH(a, c; 0). As e increases from zero the S-region expands in total "volume" at the expense of F-region, which disappears altogether when e=1 leaving persistent solutions that are steady throughout the entire parameter space.