Chaos In Complex Systems Research Articles

Out of time order correlation of the Hubbard model with random local disorder.

The out-of-time-order correlator (OTOC) serves as a powerful tool for investigating quantum information spreading and chaos in complex systems. We present a method employing non-equilibrium dynamical mean-field theory and coherent potential approximation combined with diagrammatic perturbation on the Schwinger-Keldysh contour to calculate the OTOC for correlated fermionic systems subjected to both random disorder and electron interaction. Our key finding is that random disorder enhances the OTOC decay in the Hubbard model for the metallic phase in the weakly interacting limit. However, the current limitation of our perturbative solver restricts the applicability to weak interaction regimes.

The Primacy of Doubt: From Quantum Physics to Climate Change, How the Science of Uncertainty Can Help Us Understand Our Chaotic World

The Primacy of Doubt: From Quantum Physics to Climate Change, How the Science of Uncertainty Can Help Us Understand Our Chaotic World

Exploring transitions to chaos in complex systems

Exploring transitions to chaos in complex systems

Chasing chaos by improved identification of suitable embedding dimensions and lags.

The detection of an underlying chaotic behavior in experimental recordings is a longstanding issue in the field of nonlinear time series analysis. Conventional approaches require the assessment of a suitable dimension and lag pair to embed a given input sequence and, thereupon, the estimation of dynamical invariants to characterize the underlying source. In this work, we propose an alternative approach to the problem of identifying chaos, which is built upon an improved method for optimal embedding. The core of the new approach is the analysis of an input sequence on a lattice of embedding pairs whose results provide, if any, evidence of a finite-dimensional, chaotic source generating the sequence and, if such evidence is present, yield a set of equivalently suitable embedding pairs to embed the sequence. The application of this approach to two experimental case studies, namely, an electronic circuit and magnetoencephalographic recordings of the human brain, highlights how it can make up a powerful tool to detect chaos in complex systems.

Topological characterization and early detection of bifurcations and chaos in complex systems using persistent homology.

Early detection of bifurcations and chaos and understanding their topological characteristics are essential for safe and reliable operation of various electrical, chemical, physical, and industrial processes. However, the presence of non-linearity and high-dimensionality in system behavior makes this analysis a challenging task. The existing methods for dynamical system analysis provide useful tools for anomaly detection (e.g., Bendixson-Dulac and Poincare-Bendixson criteria can detect the presence of limit cycles); however, they do not provide a detailed topological understanding about system evolution during bifurcations and chaos, such as the changes in the number of subcycles and their positions, lifetimes, and sizes. This paper addresses this research gap by using topological data analysis as a tool to study system evolution and develop a mathematical framework for detecting the topological changes in the underlying system using persistent homology. Using the proposed technique, topological features (e.g., number of relevant k-dimensional holes, etc.) are extracted from nonlinear time series data which are useful for deeper analysis of the system behavior and early detection of bifurcations and chaos. When applied to a Logistic map, a Duffing oscillator, and a real life Op-amp based Jerk circuit, these features are shown to accurately characterize the system dynamics and detect the onset of chaos.

Suppressing or inducing chaos in a model of robot arms and mechanical manipulators

We study the problems of suppressing or inducing chaotic dynamics in a simple model of robot arms and mechanical manipulators, assuming that the unperturbed systems possess multiple non-transverse homoclinic and/or heteroclinic orbits depending on the model parameters. Based on the Melnikov method and numerical computations for Melnikov integrals, fixed points, and turning points, we obtain conditions for chaos suppression and generation. We prove that the initial phase difference Ψ plays an important role in suppressing or inducing chaos in complex systems. Our results indicate that these methods of controlling or inducing chaos can be easily applied to many systems in natural science and engineering.