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We derive a trace formula for the splitting-weighted density of states suitable for chaotic potentials with isolated symmetric wells. This formula is based on complex orbits which tunnel through classically forbidden barriers. The theory is…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
Depending on initial conditions, individual finite time trajectories of dynamical systems can have very different chaotic properties. Here we present a numerical method to identify trajectories with atypical chaoticity, pathways that are…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only…
Investigating the network stability or synchronization dynamics of multi-agent systems with time delays is of significant importance in numerous real-world applications. Such investigations often rely on solving the transcendental…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of…
Time-fluctuating signals are ubiquitous and diverse in many physical, chemical, and biological systems, among which random telegraph signals (RTSs) refer to a series of instantaneous switching events between two discrete levels from…
It has been long recognized that the task of semiclassical evaluation of quantum spectra for the classically nonintegrable systems is fundamentally more complex than for the classically integrable ones. Below it is argued that the quantum…
In this paper, we study the chaotic behavior of a discrete-time linear inclusion.
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable…
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
We show how a simple scheme of symbolic dynamics distinguishes a chaotic from a random time series and how it can be used to detect structural relationships in coupled dynamics. This is relevant for the question at which scale in complex…
Quantum trajectories defined in the de Broglie--Bohm theory provide a causal way to interpret physical phenomena. In this Letter, we use this formalism to analyze the short time dynamics induced by unstable periodic orbits in a classically…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
We derive a Gutzwiller-type trace formula for quantum chaotic systems that accounts for both particle spin precession and discrete geometrical symmetries. This formula generalises previous results that were obtained either for systems with…
We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then…
Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical…