Related papers: Symmetry Groups of Basins of Attraction in Equivar…
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which…
In this paper, we study geometric properties of basins of attraction of monotone systems. Our results are based on a combination of monotone systems theory and spectral operator theory. We exploit the framework of the Koopman operator,…
In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in…
We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. Such systems have been proposed for use in nonlinear computing and have been applied to classification problems in bioinformatics. We describe some…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the…
In many applications one is interested in finding the stability regions (basins of attraction) of some stationary states (attractors). In this paper we show that one cannot compute, in general, the basins of attraction of even very regular…
The basin of attraction is the set of initial points that will eventually converge to some attracting set. Its knowledge is important in understanding the dynamical behavior of a given dynamical system of interest. In this work, we address…
The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the pseudo-Newtonian planar circular restricted three-body problem, where the primaries have equal masses. The parametric variation…
We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and…
We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the system flow. The input to the method is…
Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most…
We consider a system of two identical linearly coupled Lorenz oscillators, presenting synchro- nization of chaotic motion for a specified range of the coupling strength. We verify the existence of global synchronization and…
We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…
In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This problem is rather common especially in population dynamics models. Precisely, a particular solution of a…
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…
We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orbits of a given dynamical system. We develop theory for it…
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…
The present work deals with the recently introduced restricted six body-problem with square configuration. It is determined that the total number of libration points are twelve and twenty for the mass parameter $0< \mu < 0.25$. The…