484 research outputs found
Achieving synchronization in arrays of coupled differential systems with time-varying couplings
In this paper, we study complete synchronization of the complex dynamical
networks described by linearly coupled ordinary differential equation systems
(LCODEs). The coupling considered here is time-varying in both the network
structure and the reaction dynamics. Inspired by our previous paper [6], the
extended Hajnal diameter is introduced and used to measure the synchronization
in a general differential system. Then we find that the Hajnal diameter of the
linear system induced by the time-varying coupling matrix and the largest
Lyapunov exponent of the synchronized system play the key roles in
synchronization analysis of LCODEs with the identity inner coupling matrix. As
an application, we obtain a general sufficient condition guaranteeing directed
time-varying graph to reach consensus. Example with numerical simulation is
provided to show the effectiveness the theoretical results.Comment: 22 pages, 4 figure
Semi-passivity and synchronization of diffusively coupled neuronal oscillators
We discuss synchronization in networks of neuronal oscillators which are
interconnected via diffusive coupling, i.e. linearly coupled via gap junctions.
In particular, we present sufficient conditions for synchronization in these
networks using the theory of semi-passive and passive systems. We show that the
conductance-based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the
popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a
semi-passivity property, i.e. that is the state trajectories of such a model
remain oscillatory but bounded provided that the supplied (electrical) energy
is bounded. As a result, for a wide range of coupling configurations, networks
of these oscillators are guaranteed to possess ultimately bounded solutions.
Moreover, we demonstrate that when the coupling is strong enough the
oscillators become synchronized. Our theoretical conclusions are confirmed by
computer simulations with coupled \HR and \ML oscillators. Finally we discuss
possible "instabilities" in networks of oscillators induced by the diffusive
coupling
Massive MIMO is a Reality -- What is Next? Five Promising Research Directions for Antenna Arrays
Massive MIMO (multiple-input multiple-output) is no longer a "wild" or
"promising" concept for future cellular networks - in 2018 it became a reality.
Base stations (BSs) with 64 fully digital transceiver chains were commercially
deployed in several countries, the key ingredients of Massive MIMO have made it
into the 5G standard, the signal processing methods required to achieve
unprecedented spectral efficiency have been developed, and the limitation due
to pilot contamination has been resolved. Even the development of fully digital
Massive MIMO arrays for mmWave frequencies - once viewed prohibitively
complicated and costly - is well underway. In a few years, Massive MIMO with
fully digital transceivers will be a mainstream feature at both sub-6 GHz and
mmWave frequencies. In this paper, we explain how the first chapter of the
Massive MIMO research saga has come to an end, while the story has just begun.
The coming wide-scale deployment of BSs with massive antenna arrays opens the
door to a brand new world where spatial processing capabilities are
omnipresent. In addition to mobile broadband services, the antennas can be used
for other communication applications, such as low-power machine-type or
ultra-reliable communications, as well as non-communication applications such
as radar, sensing and positioning. We outline five new Massive MIMO related
research directions: Extremely large aperture arrays, Holographic Massive MIMO,
Six-dimensional positioning, Large-scale MIMO radar, and Intelligent Massive
MIMO.Comment: 20 pages, 9 figures, submitted to Digital Signal Processin
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