Related papers: Application of the SALI chaos detection method to …
This paper deals with the gradient-based extremum seeking control for multivariable maps under actuator saturation. By exploiting a polytopic embedding of the unknown Hessian, we derive a LMI-based synthesis condition to ensure that the…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
We compare three methods for computing invariant Lyapunov exponents (LEs) in general relativity. They involve the geodesic deviation vector technique (M1), the two-nearby-orbits method with projection operations and with coordinate time as…
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
The regular or chaotic dynamics of an analytical realistic three dimensional model composed of a spherically symmetric central nucleus, a bar and a flat disk is investigated. For describing the properties of the bar we introduce a new…
The transition from order to chaos has been a major subject of research since the work of Poincare, as it is relevant in areas ranging from the foundations of statistical physics to the stability of the solar system. Along this transition,…
Using new integral field observations of 106 galaxies in three nearby clusters we investigate how the intrinsic scatter of the Fundamental Plane depends on the way in which the velocity dispersion and effective radius are measured. Our…
We study the regular or chaotic nature of orbits in a 3D potential describing a triaxial galaxy surrounded by a spherical dark halo component. Our numerical calculations show, that the percentage of chaotic orbits decreases exponentially,…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
In chaotic dynamical systems, a number of rare trajectories with low level of chaoticity are embedded in chaotic sea, while extraordinary unstable trajectories can exist even in weakly chaotic regions. In this study, a quantitative method…
We present a frequency-domain method for computing the sensitivities of time-averaged quantities of chaotic systems with respect to input parameters. Such sensitivities cannot be computed by conventional adjoint analysis tools, because the…
The chaotic low energy region of the Fermi-Ulam simplified accelerator model is characterised by use of scaling analysis. It is shown that the average velocity and the roughness (variance of the average velocity) obey scaling functions with…
We introduce a computationally efficient and accurate reduced order modelling approach for the optimization of spatiotemporally chaotic systems. The proposed method combines quantized local reduced order modelling with adjoint-based…
We present a scalable and effective multi-agent safe motion planner that enables a group of agents to move to their desired locations while avoiding collisions with obstacles and other agents, with the presence of rich obstacles,…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…
Recently, we have demonstrated that our approach is a highly effective tool while analysing complex phenomena existing in networks of coupled nonlinear systems. In the present article we present the results of our investigations into a…
Owing to the pioneering work of Contopoulos, a strongly barred galaxy is known to have irregular orbits in the vicinity of the bar. By definition, irregular orbits can not be represented by action-angle tori everywhere in phase space. This…
We consider a $2$-dimensional autonomous system subject to a $1$-periodic perturbation, i.e. $$ \dot{\vec{x}}=\vec{f}(\vec{x})+\epsilon\vec{g}(t,\vec{x},\epsilon),\quad \vec{x}\in\Omega .$$ We assume that for $\epsilon=0$ there is a…
This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…
Recent surface anomaly detection methods excel at identifying structural anomalies, such as dents and scratches, but struggle with logical anomalies, such as irregular or missing object components. The best-performing logical anomaly…