相关论文: Finding similarity of orbits between two discrete …
The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical…
Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
In previous study [1], we proposed a new physical law applicable to both particle and thermodynamical systems. Additionally, we introduced a physical definition of chaos and self-organization. In the present work, we extend this novel…
We describe collective-move Monte Carlo algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional Monte Carlo simulations…
We present here a new method which applies well ordered symbolic dynamics to find unstable periodic and non-periodic orbits in a chaotic system. The method is simple and efficient and has been successfully applied to a number of different…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M \in \mathbb{Q}^{d \times d}$, an initial vector…
The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a…
In the pattern formation problem, robots in a system must self-coordinate to form a given pattern, regardless of translation, rotation, uniform-scaling, and/or reflection. In other words, a valid final configuration of the system is a…
Sharkovskii proved that the existence of a periodic orbit in a one-dimensional dynamical system implies existence of infinitely many periodic orbits. We obtain an analog of Sharkovskii's theorem for periodic orbits of shear homeomorphisms…
Unidirectionally coupled Lorenz systems in which the drive possesses a chaotic attractor and the response admits two stable equilibria in the absence of the driving is under investigation. It is found that double chaotic attractors coexist…
The main focus of this paper is to explore how much similarity between two stochastic differential systems. Motivated by the conjugate theory of stochastic dynamic systems, we study the relationship between two systems by finding…
Homoclinic and heteroclinic orbits provide a skeleton of the full dynamics of a chaotic dynamical system and are the foundation of semiclassical sums for quantum wave packet, coherent state, and transport quantities. Here, the homoclinic…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
An order parameter, termed the maximal row correlation, is proposed for classical spin systems. Monte Carlo simulations on various Potts models suggest that this order parameter is applicable to a broad range of spin systems, including…
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…
We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…