Predict-prevent control method for perturbed excitable systems

We present a control method based on two steps: prediction and prevention. For prediction we use the anticipated synchronization scheme, considering unidirectional coupling between excitable systems in a master-slave configuration. The master is the perturbed system to be controlled, meanwhile the slave is an auxiliary system which is used to predict the master's behavior. We demonstrate theoretically and experimentally that an efficient control may be achieved.Comment: 4 pages, 5 figure

Thermodynamic limit of the first-order phase transition in the Kuramoto model

In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter $K_c$. We obtain the asymptotic dependence of the order parameter above criticality: $r-r_c \propto (K-K_c)^{2/3}$. For a finite population, we demonstrate that the population size $N$ may be included into a self-consistency equation relating $r$ and $K$ in the synchronized state. We analyze the convergence to the thermodynamic limit of two alternative schemes to set the natural frequencies. Other frequency distributions different from the uniform one are also considered.Comment: 6 page

Multiobjective synchronization of coupled systems

Copyright @ 2011 American Institute of PhysicsSynchronization of coupled chaotic systems has been a subject of great interest and importance, in theory but also various fields of application, such as secure communication and neuroscience. Recently, based on stability theory, synchronization of coupled chaotic systems by designing appropriate coupling has been widely investigated. However, almost all the available results have been focusing on ensuring the synchronization of coupled chaotic systems with as small coupling strengths as possible. In this contribution, we study multiobjective synchronization of coupled chaotic systems by considering two objectives in parallel, i. e., minimizing optimization of coupling strength and convergence speed. The coupling form and coupling strength are optimized by an improved multiobjective evolutionary approach. The constraints on the coupling form are also investigated by formulating the problem into a multiobjective constraint problem. We find that the proposed evolutionary method can outperform conventional adaptive strategy in several respects. The results presented in this paper can be extended into nonlinear time-series analysis, synchronization of complex networks and have various applications

Detection of synchronization from univariate data using wavelet transform

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.Comment: 10 pages, 9 figure

Anti-phase synchronization of phase-reduced oscillators using open-loop control

In this letter, we present an elegant method to build and maintain an anti-phase configuration of two nonlinear oscillators with different natural frequencies and dynamics described by the sinusoidal phase-reduced model. The anti-phase synchronization is achieved using a common input that couples the oscillators and consists of a sequence of square pulses of appropriate amplitude and duration. This example provides a proof of principle that open-loop control can be used to create desired synchronization patterns for nonlinear oscillators, when feedback is expensive or impossible to obtain

Revisiting the models of vibration screening process

This talk presents two approaches for modeling of the vibration screening process. The first approach is analytical. It models the screening process as a diffusion of undersize fraction taking into account the special term for vibration separation (the Brazil nut effect). The talk provides a solution of the corresponding partial differential equation. The solution in turn allows estimation of the screening performance dependence on both deterministic and stochastic factors as well as evaluation of the factors dominance conditions. The talk presents simple evaluation formulae for the screening process performance. The second approach is based on a simulation model. The model deals with monolayer dynamics. Embodying traditional concepts of vibration transportation, the approach introduces some novel techniques of evaluation of the effect of the granular particles shape. Taking into account the particle shape factor may significantly improve the modeling precision for nonspherical particles

Rare events – rare attractors; formalization and examples

Analogy between attractors in nonlinear dynamics, called “rare attractors” by M.V. Zakrzhevsky and his colleagues [1] and emergencies, such as natural and technogenic catastrophes as well as downfalls caused by risky economic policies and strategies has been discussed. Examples of rare but technically significant attractors in nonlinear dynamics have been give

Experimental Study of the Effect of External Signal on Microwave Oscillations in a Nonrelativistic Electron Beam with Virtual Cathode

The effect of an external harmonic signal on the characteristics of microwave generation in a nonrelativistic electron beam with virtual cathode (VC) formed in a static retarding electric field (low-voltage vircator system) has been experimentally studied. A significant increase in the vircator generation power is observed when the frequency of the external signal is close to the frequency of VC oscillations. At large detunings, a broadband chaotic generation is observed.Comment: 3 pages, 2 figure

Controlled Synchronization of One Class of Nonlinear Systems under Information Constraints

Output feedback controlled synchronization problems for a class of nonlinear unstable systems under information constraints imposed by limited capacity of the communication channel are analyzed. A binary time-varying coder-decoder scheme is described and a theoretical analysis for multi-dimensional master-slave systems represented in Lurie form (linear part plus nonlinearity depending only on measurable outputs) is provided. An output feedback control law is proposed based on the Passification Theorem. It is shown that the synchronization error exponentially tends to zero for sufficiantly high transmission rate (channel capacity). The results obtained for synchronization problem can be extended to tracking problems in a straightforward manner, if the reference signal is described by an {external} ({exogenious}) state space model. The results are applied to controlled synchronization of two chaotic Chua systems via a communication channel with limited capacity.Comment: 8 pages, 2 figure