Action-reaction based parameters identification and states estimation of flexible systems

This work attempts to identify and estimate flexible system's parameters and states by a simple utilization of the Action-Reaction law of dynamical systems. Attached actuator to a dynamical system or environmental interaction imposes an action that is instantaneously followed by a dynamical system reaction. The dynamical system's reaction carries full information about the dynamical system including system parameters, dynamics and externally applied forces that arise due to system interaction with the environment. This in turn implies that the dynamical system's reaction can be considered as a natural feedback as it carries full coupled information about the dynamical system. The idea is experimentally implemented on a dynamical system with three flexible modes, then it can be extended to more complicated structures with infinite modes

The conflict triad dynamical system

A dynamical model of the natural conflict triad is investigated. The conflict interacting substances of the triad are: some biological population, a living resource, and a negative factor (e.g., infection diseases). We suppose that each substance is multi-component. The main coexistence phases for substances are established: the equilibrium point (stable state), the local cyclic orbits (attractors), the global periodic oscillating trajectories, and the evolution close to chaotic. The bifurcation points and obvious thresholds between phases are exhibited in the computer simulations

Dynamical versus diffraction spectrum for structures with finite local complexity

It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as ergodic Delone dynamical systems, both via suitable embeddings. The connection is rather well understood when the spectrum is pure point, where the two spectral notions are essentially equivalent. In general, however, the dynamical spectrum is richer. Here, we consider (uniquely) ergodic systems of finite local complexity and establish the equivalence of the dynamical spectrum with a collection of diffraction spectra of the system and certain factors. This equivalence gives access to the dynamical spectrum via these diffraction spectra. It is particularly useful as the diffraction spectra are often simpler to determine and, in many cases, only very few of them need to be calculated.Comment: 27 pages; some minor revisions and improvement