Related papers: Families of periodic delay orbits
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices trace each other on a common closed orbit.
The PID controller parameters can be adjusted in such a manner that it gives the desired frequency response and the results are found using the Bodes integral formula in order to adjust the slope of the nyquist curve in a desired manner.…
We consider parametrized families of linear retarded functional differential equations (RFDEs) projected onto finite-dimensional invariant manifolds, and address the question of versality of the resulting parametrized family of linear…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
We consider a broad matrix parameterized family of pseudo-differential calculi, containing the usual Shubin's family of pseudo-differential calculi, parameterized by real numbers. We show that continuity properties in the framework of…
Using a novel electronic implementation of a well-known time-delayed system, the Mackey-Glass (MG) system, we investigate the organization of the trajectories in the phase space, and classify the coexisting solutions, both, in observations…
We study the problem of desingularizing coassociative conical singularities via gluing, allowing for topological and analytic obstructions, and discuss applications. This extends the author's earlier work on the unobstructed case. We…
We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain…
In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the…
In this paper we use the deformation procedure introduced in former work on deformed defects to investigate several new models for real scalar field. We introduce an interesting deformation function, from which we obtain two distinct…
Determining the space of free discrete two generator groups of M\"obius transformations is an old and difficult problem. In this paper we show how to construct large balls of full dimension in this space. To do this, we begin with a marked…
This paper considers a class of delay differential equations with unimodal feedback and describes the structure of certain unstable sets of stationary points and periodic orbits. These unstable sets consist of heteroclinic connections from…
Orthogonal polynomials in two variables on cubic curves are considered, including the case of elliptic curves. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal…
We propose a curvature-based approach for choosing good values for the time-delay parameter $\tau$ in delay reconstructions. The idea is based on the effects of the delay on the geometry of the reconstructions. If the delay is chosen too…
The renormalization method which is a type of perturbation method is extended to a tool to study weakly nonlinear time-delay systems. For systems with order-one delay, we show that the renormalization method leads to reduced systems without…
A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the…
We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast…
In this article, we study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when…
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we…