Related papers: Statistical complexity of the quasiperiodical damp…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…
We quantify nonlinear interactions between coupled complex processes, when the system is subject to noise and not all its components are measurable. Our method is applicable even when the system cannot be continuously monitored over time,…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
We consider a pendulum with vertically oscillating support and time-dependent damping coefficient which varies until reaching a finite final value. The sizes of the corresponding basins of attraction are found to depend strongly on the full…
Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
The universal concept of complexity by the dynamic redundance paradigm and the ensuing concept of extended dynamic fractality (physics/9806002) are applied here to higher levels of complexity corresponding to living systems. After recalling…
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more…
In this paper we introduce the idea of probability in the definition of Sequential Dynamical Systems, thus obtaining a new concept, Probabilistic Sequential System. The introduction of a probabilistic structure on Sequential Dynamical…
We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped…