1,582 research outputs found
Complex partial synchronization patterns in networks of delay-coupled neurons
We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators
We describe a flexible and modular delayed-feedback nonlinear oscillator that
is capable of generating a wide range of dynamical behaviours, from periodic
oscillations to high-dimensional chaos. The oscillator uses electrooptic
modulation and fibre-optic transmission, with feedback and filtering
implemented through real-time digital-signal processing. We consider two such
oscillators that are coupled to one another, and we identify the conditions
under which they will synchronize. By examining the rates of divergence or
convergence between two coupled oscillators, we quantify the maximum Lyapunov
exponents or transverse Lyapunov exponents of the system, and we present an
experimental method to determine these rates that does not require a
mathematical model of the system. Finally, we demonstrate a new adaptive
control method that keeps two oscillators synchronized even when the coupling
between them is changing unpredictably.Comment: 24 pages, 13 figures. To appear in Phil. Trans. R. Soc. A (special
theme issue to accompany 2009 International Workshop on Delayed Complex
Systems
Dynamics of Oscillators Coupled by a Medium with Adaptive Impact
In this article we study the dynamics of coupled oscillators. We use
mechanical metronomes that are placed over a rigid base. The base moves by a
motor in a one-dimensional direction and the movements of the base follow some
functions of the phases of the metronomes (in other words, it is controlled to
move according to a provided function). Because of the motor and the feedback,
the phases of the metronomes affect the movements of the base while on the
other hand, when the base moves, it affects the phases of the metronomes in
return.
For a simple function for the base movement (such as in which is the velocity of the base,
is a multiplier, is a proportion and and
are phases of the metronomes), we show the effects on the dynamics of the
oscillators. Then we study how this function changes in time when its
parameters adapt by a feedback. By numerical simulations and experimental
tests, we show that the dynamic of the set of oscillators and the base tends to
evolve towards a certain region. This region is close to a transition in
dynamics of the oscillators; where more frequencies start to appear in the
frequency spectra of the phases of the metronomes
Synchronization of coupled neural oscillators with heterogeneous delays
We investigate the effects of heterogeneous delays in the coupling of two
excitable neural systems. Depending upon the coupling strengths and the time
delays in the mutual and self-coupling, the compound system exhibits different
types of synchronized oscillations of variable period. We analyze this
synchronization based on the interplay of the different time delays and support
the numerical results by analytical findings. In addition, we elaborate on
bursting-like dynamics with two competing timescales on the basis of the
autocorrelation function.Comment: 18 pages, 14 figure
Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators
We consider networks of delay-coupled Stuart-Landau oscillators. In these
systems, the coupling phase has been found to be a crucial control parameter.
By proper choice of this parameter one can switch between different synchronous
oscillatory states of the network. Applying the speed-gradient method, we
derive an adaptive algorithm for an automatic adjustment of the coupling phase
such that a desired state can be selected from an otherwise multistable regime.
We propose goal functions based on both the difference of the oscillators and a
generalized order parameter and demonstrate that the speed-gradient method
allows one to find appropriate coupling phases with which different states of
synchronization, e.g., in-phase oscillation, splay or various cluster states,
can be selected.Comment: 8 pages, 7 figure
Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling
In this work a robust exponential function based controller is designed to
synchronize effectively a given class of Chua's chaotic systems. The stability
of the drive-response systems framework is proved through the Lyapunov
stability theory. Computer simulations are given to illustrate and verify the
method.Comment: 12 pages, 18 figure
Synchronization and prediction of chaotic dynamics on networks of optoelectronic oscillators
The subject of this thesis is the exploration of chaotic synchronization for novel applications including time-series prediction and sensing. We begin by characterizing the nonlinear dynamics of an optoelectronic time-delayed feedback loop. We show that synchronization of an accurate numerical model to experimental measurements provides a way to assimilate data and forecast the future of deterministic chaotic behavior. Next, we implement an adaptive control method that maintains isochronal synchrony for a network of coupled feedback loops when the interaction strengths are unknown and time-varying. Control signals are used as real-time estimates of the variations present within the coupling paths. We analyze the stability of synchronous solutions for arbitrary coupling topologies via a modified master stability function that incorporates the adaptation response dynamics. Finally, we show that the master stability function, which is derived from a set of linearized equations, can also be experimentally measured using a two-node network, and it can be applied to predict the convergence behavior of large networks
Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey
This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany
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