162 research outputs found
Accelerating dynamics of collective attention
The impacts of technological development on social sphere lack strong empirical foundation. Here the authors presented quantitative analysis of the phenomenon of social acceleration across a range of digital datasets and found that interest appears in bursts that dissipate on decreasing timescales and occur with increasing frequency
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 Tuning of Feedback Gain in Time-Delayed Feedback Control
We demonstrate that time-delayed feedback control can be improved by
adaptively tuning the feedback gain. This adaptive controller is applied to the
stabilization of an unstable fixed point and an unstable periodic orbit
embedded in a chaotic attractor. The adaptation algorithm is constructed using
the speed-gradient method of control theory. Our computer simulations show that
the adaptation algorithm can find an appropriate value of the feedback gain for
single and multiple delays. Furthermore, we show that our method is robust to
noise and different initial conditions.Comment: 7 pages, 6 figure
Control of unstable steady states by time-delayed feedback methods
We show that time-delayed feedback methods, which have successfully been used
to control unstable periodic ortbits, provide a tool to stabilize unstable
steady states. We present an analytical investigation of the feedback scheme
using the Lambert function and discuss effects of both a low-pass filter
included in the control loop and non-zero latency times associated with the
generation and injection of the feedback signal.Comment: 8 pages, 11 figure
Controlling unstable chaos: stabilizing chimera states by feedback
Copyright © 2014 American Physical SocietyWe present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it loses its attractivity. Similar to classical delayed feedback control, the scheme is noninvasive, however only in an appropriately relaxed sense considering the chaotic regime as a statistical equilibrium displaying random fluctuations as a finite size effect. We demonstrate the control scheme for so-called chimera states, which are coherence-incoherence patterns in coupled oscillator systems. The control makes chimera states observable close to coherence, for small numbers of oscillators, and for random initial conditions.Engineering and Physical Sciences Research Council (EPSRC
Coherence resonance in a network of FitzHugh-Nagumo systems: interplay of noise, time-delay and topology
We systematically investigate the phenomena of coherence resonance in
time-delay coupled networks of FitzHugh-Nagumo elements in the excitable
regime. Using numerical simulations, we examine the interplay of noise,
time-delayed coupling and network topology in the generation of coherence
resonance. In the deterministic case, we show that the delay-induced dynamics
is independent of the number of nearest neighbors and the system size. In the
presence of noise, we demonstrate the possibility of controlling coherence
resonance by varying the time-delay and the number of nearest neighbors. For a
locally coupled ring, we show that the time-delay weakens coherence resonance.
For nonlocal coupling with appropriate time-delays, both enhancement and
weakening of coherence resonance are possible
Controlling cluster synchronization by adapting the topology
We suggest an adaptive control scheme for the control of zero-lag and cluster
synchronization in delay-coupled networks. Based on the speed-gradient method,
our scheme adapts the topology of a network such that the target state is
realized. It is robust towards different initial condition as well as changes
in the coupling parameters. The emerging topology is characterized by a
delicate interplay of excitatory and inhibitory links leading to the
stabilization of the desired cluster state. As a crucial parameter determining
this interplay we identify the delay time. Furthermore, we show how to
construct networks such that they exhibit not only a given cluster state but
also with a given oscillation frequency. We apply our method to coupled
Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in
an expansion of systems close to a Hopf bifurcation. The successful and robust
control of this generic model opens up possible applications in a wide range of
systems in physics, chemistry, technology, and life science
Loss of synchronization in complex neuronal networks with delay
We investigate the stability of synchronization in networks of delay-coupled
excitable neural oscillators. On the basis of the master stability function
formalism, we demonstrate that synchronization is always stable for excitatory
coupling independently of the delay and coupling strength. Superimposing
inhibitory links randomly on top of a regular ring of excitatory coupling,
which yields a small-world-like network topology, we find a phase transition to
desynchronization as the probability of inhibitory links exceeds a critical
value. We explore the scaling of the critical value in dependence on network
properties. Compared to random networks, we find that small-world topologies
are more susceptible to desynchronization via inhibition.Comment: 6 pages, 4 figure
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