Related papers: Recurrence Plots for the Analysis of Complex Syste…
Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems are now routinely used as evidence for low dimensional chaos . Extracting accurate dynamical information…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
In this paper, we elaborate over the well-known interpretability issue in echo state networks. The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques taken from research on complex systems.…
Traditional methods in educational research often fail to capture the complex and evolving nature of learning processes. This chapter examines the use of complex systems theory in education to address these limitations. The chapter covers…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
Physics has been transforming our view of nature for centuries. While combining physical knowledge with computational approaches has enabled detailed modeling of physical systems' evolution, understanding the emergence of patterns and…
In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed…
We show that, under suitable assumptions, Poincare recurrences of a dynamical system determine its topology in phase space. Therefore, dynamical systems with the same recurrences are topologically equivalent.
The development of science has been transforming man's view towards nature for centuries. Observing structures and patterns in an effective approach to discover regularities from data is a key step toward theory-building. With increasingly…
We introduce a novel time-energy uncertainty relation within the context of restarts in monitored quantum dynamics. Initially, we investigate the concept of ``first hitting time'' in quantum systems using an IBM quantum computer and a…
Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while sometimes chaotic,…
We present an analytical description of the distribution of diagonal lines in Recurrence Plots (RPs) for white noise and chaotic systems, and find that the latter one is linked to the correlation entropy. Further we identify two scaling…
The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can…