相关论文: Detecting bifurcations in dynamical systems with C…

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing…

Traditionally, computation of Lyapunov exponents has been the marque method for identifying chaos in a time series. Recently, new methods have emerged for systems with both known and unknown models to produce a definitive 0--1 diagnostic.…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

In topological data analysis (TDA), persistence diagrams have been a succesful tool. To compare them, Wasserstein and Bottleneck distances are commonly used. We address the shortcomings of these metrics and show a way to investigate them in…

We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical…

We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…

Energy level statistics of a bounded quantum system, whose classical dynamical system exhibits bifurcations, is investigated using the two-point correlation function (TPCL), which at the bifurcation points exhibits periodic spike…

In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the…

We study bifurcation behavior in periodic perturbations of two-dimensional symmetric systems exhibiting codimension-two bifurcations with a double eigenvalue when the frequencies of the perturbation terms are small. We transform the…

We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…

We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot based analysis for…

The qualitative study of dynamical systems using bifurcation theory is key to understanding systems from biological clocks and neurons to physical phase transitions. Data generated from such systems can feature complex transients, an…

Aeroelastic flutter represents a critical nonlinear instability arising from the coupling between structural elasticity and unsteady aerodynamics. In deterministic settings, flutter onset is associated with bifurcations of invariant sets…

Machining processes are most accurately described using complex dynamical systems that include nonlinearities, time delays, and stochastic effects. Due to the nature of these models as well as the practical challenges which include…

Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two…

Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…

The goal of this paper is to show how to produce a piece of rigorous bifurcation diagram of periodic orbits for an ODE. We study the Rossler system, one of the textbook examples of ODEs generating nontrivial dynamics, for the parameter…

Bifurcations in dynamical systems characterize qualitative changes in the system behavior. Therefore, their detection is important because they can signal the transition from normal system operation to imminent failure. While standard…

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…