相关论文: Forecasting transitions in systems with high dimen…

We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…

The myriad microscopic interactions among the individual organisms that constitute an ecological system collectively give rise, at the macroscopic scale, to evolutionary trends. The ability to detect the directionality of such trends is…

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g. by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a…

Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…

Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…

Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…

We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…

Understanding systems level behaviour of many interacting agents is challenging in various ways, here we'll focus on the how the interaction between components can lead to hierarchical structures with different types of dynamics, or…

Models of complex dynamical systems like the Earth's climate often involve large numbers of uncertain parameters. Comprehensive exploration of the parameter space is typically prohibitive due to excessive computational costs. Systematic…

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…

We study the Tangled Nature model of macro evolution and demonstrate that the co-evolutionary dynamics produces an increasingly correlated core of well occupied types. At the same time the entire configuration of types becomes increasing…

Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…

We show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold,…

Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering…

We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…

We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…

When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…