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Self-adjusting, or adaptive systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these…
This article provides a self-contained comprehensive review of the phenomenon of synchronization in dynamical systems, with a particular focus on chaotic systems in both continuous-time and discrete-time contexts. Synchronization, initially…
This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…
Chaotic dynamics have emerged as a versatile resource for neuromorphic and probabilistic computing, enabling high-dimensional nonlinear processing and classical analogues of quantum randomness. Exploiting chaos for computation requires…
In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for…
The complexity of quantum evolutions can be understood by examining their dispersion in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this dispersion [V. Balasubramanian et…
In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced that sensitively probes phase space localization properties of eigenstates. It is based on a system's response to varying an external…
In this chapter we present a new approach to the study of manifestations of chaos in real complex system. Recently we have achieved the following result. In real complex systems the informational measure of chaotic chatacter (IMC) can serve…
We present a new method for locating unstable periodic points of one dimensional chaotic maps. This method is based on order statistics. The densities of various maxima of the iterates are discontinuous exactly at unstable periodic points…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
Wave chaotic systems underpin a wide range of research activities, from fundamental studies of quantum chaos via electromagnetic compatibility up to more recently emerging applications like microwave imaging for security screening, antenna…
We show that the recently introduced operator fidelity metric provides a natural tool to investigate the cross-over to quantum chaotic behaviour. This metric is an information-theoretic measure of the global stability of a unitary evolution…
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective.…
This study redefines the analysis of Devaney chaos in multiple mappings from a set-valued perspective and introduces new conditions to characterize their chaotic behavior. As an innovative advancement, we develop computational algorithms to…
Statistical measures of chaos have long been used in the study of chaotic dynamics in the framework of the interacting boson model. The use of large number of bosons renders additional studies of chaos possible, that can provide a direct…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…