Related papers: The Orbit Problem for Parametric Linear Dynamical …
Characterizing existence or not of periodic orbit is a classical problem and it has both theoretical importance and many real applications. Here, several new criterions on nonexistence of periodic orbits of the planar dynamical system $\dot…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contract. A contraction metric does not require knowledge of the…
The character of motion for the three-dimensional circular restricted three-body problem with oblate primaries is investigated. The orbits of the test particle are classified into four types: non-escaping regular orbits around the…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of $2\times 2$ matrices for the whole hierarchy, we construct the…
We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…
Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this…
We prove that either there exists at least one hamilton periodic orbit in a given energy close smooth hypersurface or there exist at least two hamilton periodic orbits in a near-by energy close smooth hypersurface. More general results also…
Our work is motivated by the challenges presented in preparing arrays of atoms for use in quantum simulation. The recently-developed process of loading atoms into traps results in approximately half of the traps being filled. To consolidate…
The article is devoted to the existence of solutions of a certain system of quadratic integral equations in H^1(R, R^N). We show the existence of a perturbed solution by using a fixed point technique in the Sobolev space on the real line.
The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether…
We study the Levenberg-Marquardt (L-M) method for solving the highly nonlinear and ill-posed inverse problem of identifying the Robin coefficients in elliptic and parabolic systems. The L-M method transforms the Tikhonov regularized…
Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters…
In this paper, we mainly study the robust stability of linear continuous systems with parameter uncertainties, a more general kind of uncertainties for system matrices is considered, i.e., entries of system matrices are rational functions…
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…
We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann…
We investigate the geodesic structure of realistic static and spherically symmetric spacetimes embedding neutron stars in metric $f(R)$ gravity, focusing on the quadratic Starobinsky model $f(R)=aR^2$ with $a<0$. Neutron-star solutions are…
The framework of decision-making, modeled as a Markov Decision Process (MDP), typically assumes a single objective. However, practical scenarios often involve tradeoffs between multiple objectives. We address this in the Linear Quadratic…