Related papers: On 2D integro-differential systems. Stability and …
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
Using older and recent results on the integrability of two-dimensional (2d) dynamical systems, we prove that the results obtained in a recent publication concerning the 2d generalized Ermakov system can be obtained as special cases of a…
Two-dimensional case in the theory of dynamical systems admitting the normal shift differs crucially from multidimensional case. Features of two-dimensional case are gathered and studied in this thesis.
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…
The multidimensional ($n$-D) systems described by Roesser model are presented in this paper. These $n$-D systems consist of discrete systems and continuous fractional order systems with fractional order $\nu$, $0<\nu<1$. The stability and…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
We prove stability for a coefficient determination problem for a two velocity 2x2 system of hyperbolic PDEs in one space dimension.
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and…
We review, restate, and prove a result due to Kaushal and Korsch [Phys. Lett. A 276, 47 (2000)] on the complete integrability of two-dimensional Hamiltonian systems whose Hamiltonian satisfies a set of four linear second order partial…
We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…
This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set…