Synchronization Of Nonlinear Oscillators Research Articles

Mathematical modelling, nonlinear dynamics, bifurcation, synchronization and control of mechanisms driven by power supply

The special issue entitled “Mathematical modelling, nonlinear dynamics, bifurcation, synchronization and control of mechanisms driven by power supply,” published by The European Physical Journal: Special Topics (EPJST), aims to bring into discussion works involving nonlinear and dynamic and chaotic behaviors, which are frequently found in mechanical and electromechanical systems, nonlinear circuits, and biologically inspired systems, stimulating the integration of findings on the nonlinear dynamics that can be observed in various systems in the physical sciences and engineering. This special issue presents 27 papers concerning the dynamics and control of flexible structure systems, nonideal systems, energy harvesting problems, and vibration absorbers. In addition, the papers address problems involving chaos control of nonlinear oscillations, phase-locked loops, synchronization of nonlinear oscillators, dynamics of bio-inspired and biostructural systems, nonlinear methods, and nonlinear circuits.

Realization of synchronization of nonlinear oscillators under intermittent coupling controlled by pulse signal

Based on the Lyapunov stability theory, an improved Lyapunov function scheme is used to understand the complete synchronization of hyperchaotic systems by imposing pulse linear coupling on the response system. According to this scheme, the controller begins to control the response system in a period when the output error variables are increasing; otherwise, the controller turns off. The distribution of conditional Lyapunov exponent versus coupling intensity, and the synchronization cost (averaged power consumption of controller) is calculated, respectively. By designing an exponential type of Lyapunov function, it is found that complete synchronization could be realized between two Chen hyperchaotic systems and two 4-dimensional LC hyperchaotic systems. Our numerical results are consistent with the previous theoretical discussion.

Optimal Control and Stochastic Synchronization of Phase Oscillators

Synchronization of oscillations is a phenomenon prevalent in natural, social, and engineering systems, such as neural circuitry in the brain, sleep cycles in biology, semiconductor lasers in physics, and periodic vibrations in mechanical engineering. The ability to control synchronization of oscillating systems then has important research and clinical implications, for example, for the study of brain functions. In this paper, we study optimal control and synchronization of nonlinear oscillators described by the phase model. We consider both deterministic and stochastic cases, in which we derive open-loop controls that create desired synchronization patterns and devise feedback controls that maximize the steady-state synchronization probability of coupled oscillators in the presence of shared and unshared noisy stimuli modeled by the Brownian motion.

Synchronization in nonlinear oscillators with conjugate coupling

In this work, we investigate the synchronization in oscillators with conjugate coupling in which oscillators interact via dissimilar variables. The synchronous dynamics and its stability are investigated theoretically and numerically. We find that the synchronous dynamics and its stability are dependent on both coupling scheme and the coupling constant. We also find that the synchronization may be independent of the number of oscillators. Numerical demonstrations with Lorenz oscillators are provided.

Experimental observation of complete and anticipation synchronization of heterogeneous oscillators using a common dynamical environment

Complete and anticipation synchronization of nonlinear oscillators from different origins is attempted experimentally. This involves coupling these heterogeneous oscillators to a common dynamical environment. Initially, this phenomenon was studied using two parameter mismatched Chua circuits. Subsequently, three different timeseries: a) x variable of the Lorenz oscillator b) the X-component of Earth’s magnetic field and c) per-day temperature variation of the Region Santa Cruz in Mumbai, India are environmentally coupled, under the master-slave scenario, with a Chua circuit. Our results indicate that environmental coupling is a potent tool to provoke complete and anticipation synchronization of heterogeneous oscillators from distinct origins.

An experimental study on synchronization of nonlinear oscillators with Huygens' coupling

In this experimental study, phase synchronization is studied in pairs of nonlinear oscillators coupled through a movable support. In particular, the dynamics of two discontinuous mass-spring-damper oscillators and the dynamics of the classical Huygens' pendulum clocks are considered. In both systems the individual oscillators are self-sustained. It is shown that in both cases, the oscillators exhibit in-phase and anti-phase synchronization. All experiments are executed on a new experimental setup consisting of two controllable mass-spring-damper oscillators coupled through an elastically supported rigid bar. The results suggest, that the synchronized motion observed by Christiaan Huygens around 1650 in a pair of pendulum clocks mounted on a flexible support, in many cases can also be observed when the pendulum clocks are replaced by other self-sustained nonlinear oscillators.

Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables.

When a dynamical system is investigated from a time series, one of the most challenging problems is to obtain a model that reproduces the underlying dynamics. Many papers have been devoted to this problem but very few have considered the influence of symmetries in the original system and the choice of the observable. Indeed, it is well known that there are usually some variables that provide a better representation of the underlying dynamics and, consequently, a global model can be obtained with less difficulties starting from such variables. This is connected to the problem of observing the dynamical system from a single time series. The roots of the nonequivalence between the dynamical variables will be investigated in a more systematic way using previously defined observability indices. It turns out that there are two important ingredients which are the complexity of the coupling between the dynamical variables and the symmetry properties of the original system. As will be mentioned, symmetries and the choice of observables also has important consequences in other problems such as synchronization of nonlinear oscillators. (c) 2002 American Institute of Physics.

On the Parallel Between Learning and Evolution

On the Parallel Between Learning and Evolution