Synchronization behaviors of coupled systems composed of hidden attractors

Based on a class of chaotic system composed of hidden attractors, in which the equilibrium points are described by a circular function, complete synchronization between two identical systems, pattern formation and synchronization of network is investigated, respectively. A statistical factor of synchronization is defined and calculated by using the mean field theory, the dependence of synchronization on bifurcation parameters discussed in numerical way. By setting a chain network, which local kinetic is described by hidden attractors, synchronization approach is investigated. It is found that the synchronization and pattern formation are dependent on the coupling intensity and also the selection of coupling variables. In the end, open problems are proposed for readers’ extensive guidance and investigation.

Experimental Kinematics of a Special Shape Actuator

This paper investigates the kinematical behavior of a polymer based star-shaped actuator, able to produce mechanical work through the shape memory effect, that allows a significant shape variations on the application of an external stimulus. The adopted material is a semicrystalline network based on poly(ε-caprolactone) crosslinked by thermal curing; the material was adopted due to its fast recovery process when heated close to the melting temperature and the high recovery degree, and, due to its good biocompatibility, it may suitable for biomedical application. The original, or “permanent”, material shape is that of a cylindrical annulus, which is set in a “temporary” configuration as a six spikes star. The temporary shape is fixed through a thermo-mechanical program, involving deformation above melting temperature and cooling under fixed strain and carried out by means of an ad-hoc designed fixture. By heating the deformed specimen above the melting temperature, the system is able to recover the original cylindrical shape realizing a motion and a mechanical power. This peculiar response, consisting in a progressive radial expansion activated by temperature, may be considered for application as self-expanding stenting device triggered by the human body temperature. The shape of the system, that changes during the transformation, can be described as a two dimensional temporal function that represents the mean line of the section of the cylindrical annulus (perpendicular to the height of the annulus). This temporal function is a combination of a circular function and of a modified rhodoneal function and, after a proper calibration through experimental tests, is used to evaluate the kinematics of the system. The function is able to describe adequately the shape evolution experimentally displayed by the samples, with a very good agreement at the starting and final instants of the transformation, while the accuracy during the transformation is acceptable for the proposed application.