相关论文: On the Existence and Uniqueness of Poincar\'e Maps…

We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both…

In this paper, we consider sufficient conditions for an invariant double circle to occur in a one parameter discrete dynamical systems on a cylinder.

New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…

This paper introduces the \textit{truncator} map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify…

The problem of orbital stabilization of underactuated mechanical systems with one passive degree-of-freedom (DOF) is revisited. Virtual holonomic constraints are enforced using a continuous controller; this results in a dense set of closed…

The problem of nonprehensile manipulation of a stick in three-dimensional space using intermittent impulsive forces is considered. The objective is to juggle the stick between a sequence of configurations that are rotationally symmetric…

Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous works on the analysis of sampled-data, impulsive and switched systems have only been shown to be…

The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…

This paper focuses on the equilibria and their regions of attraction for continuous-time nonlinear dynamical systems. The classical Poincar\'e--Hopf Theorem from differential topology is used to derive a result on a sufficient condition on…

Analytical perturbations of the Euler top are considered. The perturbations are based on the Poisson structure for such a dynamical system, in such a way that the Casimir invariants of the system remain invariant for the perturbed flow. By…

Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…

Without involving bounce events, a Poincar\'e section associated with the axes is found to give a map on the annulus for the diamagnetic Kepler problem. Symbolic dynamics is then established based on the lift of the annulus map. The…

A high dimensional dynamical system is often studied by experimentalists through the measurement of a relatively low number of different quantities, called an observation. Following this idea and in the continuity of Boshernitzan's work,…

Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We…

We consider time-invariant nonlinear $n$-dimensional strongly $2$-cooperative systems, that is, systems that map the set of vectors with up to weak sign variation to its interior. Strongly $2$-cooperative systems enjoy a strong…

A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…

In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a…

A degenerate dynamical system is characterized by a state-dependent multiplier of the time derivative of the state in the time evolution equation. It can give rise to Hamiltonian systems whose symplectic structure possesses a non-constant…

A generalization of the Poincar\'{e}-Hopf index theorem applicable to hybrid dynamical systems is obtained. For the hybrid systems considered, guard sets are not assumed to be smooth; distinct "modes" are not assumed to have constant…

This paper reviews a paper from 1906 by J. Henri Poincar\'e on statistical mechanics with a background in his earlier work and notable connections to J. Willard Gibbs. Poincar\'e's paper presents important ideas that are still relevant for…