Related papers: On the Poisson Stability to Study a Fourth-Order D…
The exact solution to the Einstein equations that represents a static axially symmetric source deformed by an internal quadrupole is considered. By using the Poincare section method we numerically study the geodesic motion of test…
This paper discusses stability and robustness properties of a recently proposed observer algorithm for linear time varying systems. The observer is based on the approximation and subsequent modification of the non-negative Lyapunov…
For a model system defined as combination of sequentially applied continuous transformations of a sphere, the question of arrangement of the parameter space around the domain of existence of the Plykin-type attractor is considered. Results…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
We present a method for determining the local stability of equilibrium points of conservative generalizations of the Lotka-Volterra equations. These generalizations incorporate both an arbitrary number of species -including odd-dimensional…
In this paper, we develop a framework for the discretization of a mixed formulation of quasi-reversibility solutions to ill-posed problems with respect to Poisson's equations. By carefully choosing test and trial spaces a formulation that…
This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The…
We consider a stabilization problem for a piezoelectric system. We prove an exponential stability result under some Lions geometric condition. Our method is based on an identity with multipliers that allows to show an appropriate…
In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering has been introduced for the periodic Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the nonlinear…
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…
Recently, energetic variational approach was employed to derive models for non-isothermal electrokinetics by Liu et. al \cite{Liu-Wu-Liu-CMS2018}. In particular, the Poisson-Nernst-Planck-Fourier (PNPF) system for the dynamics of $N$-ionic…
An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps,…
In this paper we study the asymptotic behavior of nonoscillatory solutions for high order differential equations of Poincar\'e type. We introduce two new and more weak than classical hypotheses on the coefficients, which implies a well…
This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing the fixed point operator associated with the…
Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
For a probability measure preserving dynamical system $(\mathcal{X},f,\mu)$, the Poincar\'e Recurrence Theorem asserts that $\mu$-almost every orbit is recurrent with respect to its initial condition. This motivates study of the statistics…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…