Glutsyuk, A. A. Netay, I. V.
Published in
Journal of Dynamical and Control Systems

The paper deals with a three-parameter family of special double confluent Heun equations that was introduced and studied by V. M. Buchstaber and S. I. Tertychnyi as an equivalent presentation of a model of overdamped Josephson junction in superconductivity. The parameters are l,λ,μ∈ℝ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{was...

Favez, J.-Y. Mullhaupt, Ph. Srinivasan, B. Bonvin, D.
Published in
Journal of Dynamical and Control Systems

The bifurcation of the attraction region for planar systems with one stable and one unstable pole under a saturated linear state feedback is considered. The attraction region can have either an unbounded hyperbolic shape or be bounded by a limit cycle. An analytical condition, under which either of these boundary shapes occurs, is given with a form...

Lokutsievskiy, L. V. Zelikin, M. I.
Published in
Journal of Dynamical and Control Systems

Simple natural proofs of all known results regarding the aerodynamic Newton problem are obtained. Additional new theorems and new promising formulas in terms of Hessian measures are found.

Ortiz-Bobadilla, L. Rosales-González, E. Voronin, S. M.
Published in
Journal of Dynamical and Control Systems

We consider germs of holomorphic vector fields in (ℂn,0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\mathbb {C}^{n},0)$\end{document}, n ≥ 3, with non-isolated sing...

Ali, Entisar Abdul-Latif Charlot, Grégoire
Published in
Journal of Dynamical and Control Systems

We consider specific sub-Finslerian structures in the neighborhood of 0 in ℝ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {R}^{2}$\end{document}, defined by f...

Choi, Woocheol Ponge, Raphaël
Published in
Journal of Dynamical and Control Systems

In this paper, we attempt to give a systematic account on privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant a manifold with a distinguished filtration of subbundles of the tangent bundle which is compatible with the Lie bracket of vector fields. This paper lies down the background for its sequ...

Arai, Tatsuya
Published in
Journal of Dynamical and Control Systems

In the second paragraph of Definition 2.4, we defined elements x and y to be asymptotic if for any U ∈ 𝓤 and any {Gi | i ∈ ℕ} ∈ 𝓖, there exists k ∈ ℕ such that (gx,gy) ∈ U for each g ∈ G∖Gk. However, this definition is incorrect, because it holds that x and y are asymptotic if and only if x = y.

Glutsyuk, A. A.
Published in
Journal of Dynamical and Control Systems

In 1973, B. Josephson received a Nobel Prize for discovering a new fundamental effect concerning a Josephson junction,—a system of two superconductors separated by a very narrow dielectric: there could exist a supercurrent tunneling through this junction. We will discuss the model of the overdamped Josephson junction, which is given by a family of ...

Xu, Fei Yang, Xue Li, Yong Liu, Moxin
Published in
Journal of Dynamical and Control Systems

In this paper, we prove that every Newton affine-periodic system admits an affine-periodic solution via the lower and upper solutions method and the homotopy invariance of Leray-Schauder degree. Furthermore, we give some specific examples about oscillators to illustrate our main results.

Breitenbach, Tim Borzì, Alfio
Published in
Journal of Dynamical and Control Systems

A sequential quadratic Hamiltonian (SQH) method for solving control-constrained parabolic optimal control problems with continuous and discontinuous non-convex cost functionals is investigated. The solution to these problems is characterised by the Pontryagin’s maximum principle, which is also the starting point for the development of a sequential ...