Related papers: Quantifying the irregularity of a time series
In this paper, we use Time Scale Calculus (TSC) to formulate and solve pharmacokinetic models exploring multiple dose dynamics. TSC is a mathematical framework that allows the modeling of dynamical systems comprising continuous and discrete…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Given two time series, can one tell, in a rigorous and quantitative way, the cause and effect between them? Based on a recently rigorized physical notion namely information flow, we arrive at a concise formula and give this challenging…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise…
An order parameter, termed the maximal row correlation, is proposed for classical spin systems. Monte Carlo simulations on various Potts models suggest that this order parameter is applicable to a broad range of spin systems, including…
A celebrated and controversial hypothesis conjectures that some biological systems --parts, aspects, or groups of them-- may extract important functional benefits from operating at the edge of instability, halfway between order and…
Poincare's classification of the dynamics of homeomorphisms of the circle is one of the earliest, but still one of the most elegant, classification results in dynamical systems. Here we generalize this to quasiperiodically forced circle…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
Time series motif discovery has been a fundamental task to identify meaningful repeated patterns in time series. Recently, time series chains were introduced as an expansion of time series motifs to identify the continuous evolving patterns…
We present a novel approach to learn the formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a statistical dynamical model of the system which…
Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is…
Periodically-driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins leads to complicated dynamics. Hence, it is of interest to understand what constraints such dynamics…
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…
Atmospheric flows exhibit fluctuations of all scales (space -time) ranging from turbulence (millimeters-seconds) to climate (thousands of kilometers-years). The apparently random fluctuations however exhibit long-range spatio-temporal…
A major challenge of interdisciplinary description of complex system behaviour is whether real systems of higher complexity levels can be understood with at least the same degree of objective, "scientific" rigour and universality as…
Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in…
Our current understanding of brain rhythms is based on quantifying their instantaneous or time-averaged characteristics. What remains unexplored, is the actual structure of the waves -- their shapes and patterns over finite timescales. To…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…