Related papers: Finding similarity of orbits between two discrete …

Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…

We study the dynamical regimes that emerge from the strongly coupling between two Chua's circuits with parameters mismatch. For the region around the perfect synchronous state we show how to combine parameter diversity and coupling in order…

Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…

We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…

We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…

Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…

Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…

Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid version of Pontryagin's maximum principle was presented.…

Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…

Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…

The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical…

The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…

The deep learning revolution has spurred a rise in advances of using AI in sciences. Within physical sciences the main focus has been on discovery of dynamical systems from observational data. Yet the reliability of learned surrogates and…

This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…

Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…

We study generalized indicators of sensitivity to initial conditions and orbit complexity in topological dynamical systems. The orbit complexity is a measure of the asymptotic behavior of the information that is necessary to describe the…

Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…

We formulate, for continuous-time dynamical systems, a sufficient condition to be a gradient-like system, i.e. that all bounded trajectories approach stationary points and therefore that periodic orbits, chaotic attractors, etc. do not…

We present an algorithm for obtaining an optimal control policy for hybrid dynamical systems in cluttered environments. To the best of our knowledge, this is the first attempt to have a locally optimal solution for this specific problem…