Related papers: A Dynamical Systems Approach to The Fourth Painlev…
We define a hierarchy of dynamic relaxed gas spheres as solutions of the Poisson equation coupled to a hierarchy of approximations of the Liouville equation leading, when this equation is satisfied, to the well-known isothermal gas spheres…
Poles of solutions to the Painleve-I equation are intimately related to the theory of the cubic anharmonic oscillator. In particular, poles of integrale tritronquee are in 1-1 correspondence with cubic oscillators that admit the…
We introduce a holistic framework for the analysis, approximation and control of the trajectories of hybrid dynamical systems which display event-triggered discrete jumps in the continuous state. We begin by demonstrating how to explicitly…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the…
The general equations of motion for ocean dynamics are presented and the waves supported by the (inviscid, unforced) linearized system with respect to a state of rest are derived. The linearized dynamics sustains one zero frequency mode…
In this paper, we study the existence of bifurcation of a van der Pol-Duffing oscillator with quintic terms and its quasi-periodic solutions by means of qualitative and bifurcation theories. Firstly, we analyze the autonomous system and…
In this work, supersymmetric quantum mechanics will be used to obtain complex solutions to Painleve IV equation with real parameters. We will also focus on the properties of the associated Hamiltonians, i.e. the algebraic structure, the…
This article deals with the asymptotic behavior of fourth order differential equation where the coefficients are perturbations of linear constant coefficient equation. We introduce a change of variable and deduce that the new variable…
Four 4-dimensional Painlev\'e-type equations are obtained by isomonodromic deformation of Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, the Sasano system, and the sixth matrix Painlev\'e system.…
Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically off a boundary curve. The state of the system is given by two numbers: one describing the location along the curve where the bounce occurs, and…
For a class of $(N+1)$-dimensional systems of differential delay equations with a cyclic and monotone negative feedback structure, we construct a two-dimensional invariant manifold, on which phase curves spiral outward towards a bounding…
Two classes of time-periodic systems of ordinary differential equations with a small nonnegative parameter, those with fast and slow time, are studied. Right-hand sides of these systems are three times continuously differentiable with…
The numerical simulation of convection-dominated transient transport phenomena poses significant computational challenges due to sharp gradients and propagating fronts across the spatiotemporal domain. Classical discretization methods often…
In this paper, we investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the…
A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…
With this paper we extend our studies [1] on polarized beams by distilling tools from the theory of principal bundles. Four major theorems are presented, one which ties invariant fields with the notion of normal form, one which allows one…
The dynamics of moving solids with unilateral contacts are often modeled by assuming rigidity, point contacts, and Coulomb friction due to the simplicity of these models. The canonical example of a rigid rod with one endpoint slipping in…
This article aims to derive equations of motion for dynamical systems with angular momentum on Finsler geometries. To this end, we apply Souriau's Principle of General Covariance, which is a geometrical framework to derive diffeomorphism…
In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the…