相关论文: Visibility of heteroclinic networks

We define observability and detectability for linear switching systems as the possibility of reconstructing and respectively of asymptotically reconstructing the hybrid state of the system from the knowledge of the output for a suitable…

Network systems and their control are highly important and appear in a variety of applications, including vehicle platooning and formation con- trol. Especially vehicle platoons are highly investigated and an interesting problem that arises…

We are offering a particular interpretation (well within the range of experimentally and theoretically accepted notions) of neural connectivity and dynamics and discuss it as the data-and-process architecture of the visual system. In this…

In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…

In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…

Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…

Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…

The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…

In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and…

Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…

We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…

The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on…

We study heteroclinic networks in $\mathbb{R}^4$, made of a certain type of simple robust heteroclinic cycle. In simple cycles all the connections are of saddle-sink type in two-dimensional fixed-point spaces. We show that there exist only…

Much has been said about observability in system theory and control; however, it has been recently that observability in complex networks has seriously attracted the attention of researchers. This paper examines the state-of-the-art and…

Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by…

Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…

Object permanence is the concept that objects do not suddenly disappear in the physical world. Humans understand this concept at young ages and know that another person is still there, even though it is temporarily occluded. Neural networks…

The connection between network topology and stability remains unclear. General approaches that clarify this relationship and allow for more efficient stability analysis would be desirable. Inspired by chemical reaction networks, I…