适应与自组织系统

In this article, we discuss some of the recent developments in applying machine learning (ML) techniques to nonlinear dynamical systems. In particular, we demonstrate how to build a suitable ML framework for addressing two specific…

Consensus algorithms on networks have received increasing attention in recent years for various applications ranging from animal flocking to multi-vehicle co-ordination. Building on the established model for second-order consensus of…

Networks of limit cycle oscillators can show intricate patterns of synchronization such as splay states and cluster synchronization. Here we analyze dynamical states that display a continuum of seemingly independent splay clusters. Each…

In this paper, we continue the discussion on database classifiers constructed with networks of interacting chemical oscillators. In our previous papers we demonstrated that a small, regular network of oscillators can predict if three random…

The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchronization in large oscillator networks.…

Several complex systems can be modeled as large networks in which the state of the nodes continuously evolves through interactions among neighboring nodes, forming a high-dimensional nonlinear dynamical system. One of the main challenges of…

In this article, I develop a formal model of free will for complex systems based on emergent properties and adaptive selection. The model is based on a process ontology in which a free choice is a singular process that takes a system from…

We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…

In this study, we investigate how specific micro interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erd\"os-R\'enyi networks and an…

While criticality is widely observed in neural networks, its underlying neural mechanism is not known well. We consider a network of $N$ excitatory leaky integrated and fire (LIF) neurons that reside on a regular lattice with periodic…

We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…

Two fundamental issues surrounding research on Zipf's law regarding city sizes are whether and why this law holds. This paper does not deal with the latter issue with respect to why, and instead investigates whether Zipf's law holds in a…

Volunteered geographic information (VGI), one of the most important types of user-generated web content, has been emerging as a new phenomenon. VGI is contributed by numerous volunteers and supported by web 2.0 technologies. This chapter…

Phase oscillator systems with global sine-coupling are known to exhibit low-dimensional dynamics. In this paper, such characteristics are extended to phase oscillator systems driven by Cauchy noise. The low-dimensional dynamics solution…

The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…

Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…

Observability can determine which recorded variables of a given system are optimal for discriminating its different states. Quantifying observability requires knowledge of the equations governing the dynamics. These equations are often…

Strange nonchaotic attractors (SNAs) have been identified and studied in the literature exclusively in quasiperiodically driven nonlinear dynamical systems. It is an interesting question to ask whether they can be identified with other…

In this article, we investigate the dynamical robustness in a network of relaxation oscillators. In particular, we consider a network of diffusively coupled Van der Pol oscillators to explore the aging transition phenomena. Our…

In this paper, a methodology inspired on bond and site percolation methods is applied to the estimation of the resilience against failures in power grids. Our approach includes vulnerability measures with both dynamical and structural…