Self-synchronization and controlled synchronization

An attempt is made to give a general formalism for synchronization in dynamical systems encompassing most of the known definitions and applications. The proposed set-up describes synchronization of interconnected systems with respect to a set of functionals and captures peculiarities of both self-synchronization and controlled synchronization. Various illustrative examples are give

Motion of Gas Bubbles and Rigid Particles in Vibrating Fluid-Filled Volumes

AbstractMotion of gas bubbles and rigid particles in an oscillating fluid is of fundamental interest for the theory of various widely used technological processes, in particular, for the flotation process. Therefore, many studies have been concerned with this problem, some of those being undertaken by eminent scientists. The main remarkable effects are heavy particles rising and light particles (gas bubbles) sinking in vibrating fluid's volume, and asynchronous self-induced vibration of emerging air cushion.In the authors’ recent papers, the problem has been solved by means of the concept of vibrational mechanics and the method of direct separation of motions; experimental studies have been also conducted. The present paper generalizes and supplements these studies. A special attention is given to the analysis of motion of bubbles and light rigid particles, whose sizes are small in comparison with the amplitude of external excitation; motion of larger (compressible) bubbles is also considered in the paper. It is shown that at certain parameters of external excitation such particles and bubbles will sink in the fluid, corresponding conditions are formulated

Self-synchronization and controlled synchronization of dynamical systems

A general definition of synchronization of dynamical systems is given capturing features of both self-synchronized systems and systems synchronized by means of control. It has been demonstrated for important special cases of "master-slave" and coupled systems that synchronizing control may be designed using feedback linearization or passification methods

Detecting local synchronization in coupled chaotic systems

We introduce a technique to detect and quantify local functional dependencies between coupled chaotic systems. The method estimates the fraction of locally syncronized configurations, in a pair of signals with an arbitrary state of global syncronization. Application to a pair of interacting Rossler oscillators shows that our method is capable to quantify the number of dynamical configurations where a local prediction task is possible, also in absence of global synchronization features

Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

Synchronization of coupled limit cycles

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte