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In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
Motivated by networked systems, stochastic control, optimization, and a wide variety of applications, this work is devoted to systems of switching jump diffusions. Treating such nonlinear systems, we focus on stability issues. First…
This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…
Mathematical models of glucose, insulin, and pancreatic $\beta$-cell mass dynamics are essential for understanding the physiological basis of type 2 diabetes. This paper investigates the Topp model's discrete-time dynamics to represent…
The potential energy of a system in stable equilibrium has a minimum value. This property is used to derive a formula that is useful in determi- nation of stability of a floating body. It is found that a floating body is in stable…
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…
This paper is devoted to the stability analysis of a classical three-field formulation of Biot's consolidation model where the unknown variables are the displacements, fluid flux (Darcy velocity), and pore pressure. Specific…
The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we analyze the stability of a system under distribution…
This paper considers the stability of tidal equilibria for planetary systems in which stellar rotation provides a significant contribution to the angular momentum budget. We begin by applying classic stability considerations for two bodies…
In this letter, we analytically investigate the sensitivity of stability index to its dependent variables in general power systems. Firstly, we give a small-signal model, the stability index is defined as the solution to a semidefinite…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
With the increasing penetration of Inverter-Based Resources (IBRs) and their impact on power system stability and operation, the concept of stability-constrained optimization has drawn significant attention from researchers. In order to…
In this work, the null controllability problem for a linear system in $\ell^2$ is considered, where the matrix of a linear operator describing the system is an infinite matrix with $\lambda\in \mathbb R$ on the main diagonal and 1s above…
We have studied in this paper, the stability of dynamical system in $f(R)$ gravity. We have considered the $f(R)$ $\gamma$-gravity and explored its dynamical analysis. We found six critical points among which only one describes an universe…