Related papers: Jacobi Stability Analysis for Systems of ODEs Usin…
It is well-known that in an m-machine power system where each machine is represented by a second-order differential equation, the Jacobian of the system equation contains (m-1) pairs of conjugate eigenvalues and two real eigenvalues,…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
Evidence of signatures associated with cryptographic modes of operation is established. Motivated by some analogies between cryptographic and dynamical systems, in particular with chaos theory, we propose an algorithm based on Lyapunov…
We conduct a comprehensive investigation into the dynamics of gradient descent using large-order constant step-sizes in the context of quadratic regression models. Within this framework, we reveal that the dynamics can be encapsulated by a…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
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…
Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved. Moreover, the…
Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in particular -- for the $L^2$ setting -- on the absence of…
In this manuscript we study algebraic and analytic properties of the sequence of monic polynomials orthogonal with respect to a Jacobi differential operator. A fluid dynamics model for source points location of a flow of an incompressible…
Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and…
We consider a nonlinear variational wave equation that models the dynamics of the director field in nematic liquid crystals with high molecular rotational inertia. Being derived from an energy principle, energy stability is an intrinsic…
Explicit Runge-Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial semidiscretisations can be used to obtain systems…
The Riccati equation method is used to establish some new stability criteria for systems of two linear first-order ordinary differential equations. It is shown that two of these criteria in the two dimensional case imply the Routh -…
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In analog to the classical probability measure for Markovian processes, we show that the set of invariant…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The…
We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…
Preliminary results of our investigations on solving indefinite qua\-dra\-tic programs by dynamical systems are given. First, dynamical systems corresponding to two fundamental DC programming algorithms to deal with indefinite quadratic…
In this work we revisit the geometric approach to chaos in Hamiltonian dynamics, by means of the Jacobi-Levi-Civita equation (JLCE). We inspect numerically two low-dimensional dynamical systems; show that, along chaotic orbits, the…