Related papers: Theory of synchronisation and pattern formation on…
There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques…
Synchronization problem for linear coupled networks is a hot topic in recent decade. However, until now, some confused concepts and results still puzzle people. To avoid further misleading researchers, it is necessary to point out these…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…
Shared resources synchronization is a well studied problem, in both shared memory environment or distributed memory environment. Many synchronization mechanisms are proposed, with their own way to reach certain consistency level. This…
We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the…
We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to met demand, the requirement for simultaneous availability of resources means that a network may…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
Synchronization phenomena on networks have attracted much attention in studies of neural, social, economic, and biological systems, yet we still lack a systematic understanding of how relative synchronizability relates to underlying network…
We study the problem of clock synchronization in a networked system with arbitrary starts for all nodes. We consider a synchronous network of $n$ nodes, where each node has a local clock that is an integer counter. Eventually, clocks must…
In this paper, the fixed-time cluster synchronization problem for complex networks via pinning control is discussed. Fixed-time synchronization has been a hot topic in recent years, which means that the network can achieve synchronization…
The time-dependent vulnerability of synchronized states is shown for a complex network composed of electronic circuits. We demonstrate that disturbances to the local dynamics of network units can produce different outcomes to…
In this contribution we give an overview over recent work on the theory of interacting neural networks. The model is defined in Section 2. The typical teacher/student scenario is considered in Section 3. A static teacher network is…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.
Network systems are one of the most active research areas in the engineering community as they feature a paradigm shift from centralized to distributed control and computation. When dealing with network systems, a fundamental challenge is…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…