Related papers: Nonlinear Dynamics in Complexity Quantification
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [Phys. Rev. Lett. 120, 084102 (2018)] and quasiperiodically [Phys. Rev. E 107, 014205 (2023)] time-varying delay. Compared to…
Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the…
We consider the unsteady regimes of an acoustically-driven jet that forces a recirculating flow through successive reflections on the walls of a square cavity. The specific question being addressed is to know whether the system can sustain…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It…
A data-driven chaos indicator concept is introduced to characterize the degree of chaos for nonlinear dynamical systems. The indicator is represented by the prediction accuracy of surrogate models established purely from data. It provides a…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
A recent quasiclassical description of a tunneling universe model is shown to exhibit chaotic dynamics by an analysis of fractal dimensions in the plane of initial values. This result relies on non-adiabatic features of the quantum…
Detection and identification of nonlinearity is a task of high importance for structural dynamics. Detecting nonlinearity in a structure, which has been designed to operate in its linear region, might indicate the existence of damage.…
We derive a locally projective noise reduction scheme for nonlinear time series using concepts from deterministic dynamical systems, or chaos theory. We will demonstrate its effectiveness with an example with known deterministic dynamics…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Chaos is usually referred to the sensitivity to initial conditions in which the nonlinearity plays a crucial role. Beyond such a mathematical description, the understanding of the underlying physical origin of the chaos is still not very…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
Deterministic chaos permits a precise notion of a "perfect measurement" as one that, when obtained repeatedly, captures all of the information created by the system's evolution with minimal redundancy. Finding an optimal measurement is…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
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…
This is an extended discussion of Ref.[1], presenting a nonlinear dynamical model of quantum collapse, with randomness emerging from self-generated noise. Here we focus on a few issues: 1) the way chaos theory explains "deterministic but…
Chaos is a fundamental phenomenon in nonlinear dynamics, manifesting as irregular and unpredictable behavior across various physical systems. Among the diverse routes to chaos, intermittent chaos is a distinct transition pathway,…