Related papers: The hypocoercivity index for the short time behavi…

The focus of this work is on local stability of a class of nonlinear ordinary differential equations (ODE) that describe limits of empirical measures associated with finite-state weakly interacting N-particle systems. Local Lyapunov…

In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it…

We propose the new generalization of linear stationary dynamical systems with discrete time $t\in\mathbb{Z}$ to the case $t\in\nspace{Z}{N}$. The dynamics of such a system can be reproduced by means of its associated multiparametric…

We study out-of-time order correlators (OTOCs) of the form $\langle\hat A(t)\hat B(0)\hat C(t)\hat D(0)\rangle$ for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small…

This paper studies the problem of state estimation for linear time-invariant descriptor systems in their most general form. The estimator is a system of ordinary differential equations (ODEs). We introduce the notion of partial causal…

Out-of-time-order correlators (OTOC) being explored as a measure of quantum chaos, is studied here in a coupled bipartite system. Each of the subsystems can be chaotic or regular and lead to very different OTOC growths both before and after…

We address the long time behaviour of weakly interacting diffusive particle systems on the d-dimensional torus. Our main result is to show that, under certain regularity conditions, the weak error between the empirical distribution of the…

We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive…

Second-order continuous-time dissipative dynamical systems with viscous and Hessian driven damping have inspired effective first-order algorithms for solving convex optimization problems. While preserving the fast convergence properties of…

We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling…

We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their $L^2$ algebraic decay. Some of these inequalities have not been…

The aim of this article is to construct solutions to second order in time stochastic partial differential equations and to show hypocoercivity of the corresponding transition semigroups. More generally, we analyze non-linear…

For N-dimensional (ND) static quadratic map, we present a time-delay approach to gradient-based extremum seeking (ES) both, in the continuous and, for the first time, the discrete domains. As in the recently introduced (for 2D maps in the…

We study the stability of a vector field associated to a nearly-integrable Hamiltonian dynamical system to which a dissipation is added. Such a system is governed by two parameters, named the perturbing and dissipative parameters, and it…

We present an index for the local sensitivity of spatiotemporal structures in coupled oscillatory systems based on the asymptotic scaling of local-in-space, finite-time Lyapunov Exponents. For a system of nonlocally-coupled R\"{o}ssler…

In this article, we study the long-time behavior of a finite-volume discretization for a nonlinear kinetic reaction model involving two interacting species. Building upon the seminal work of [Favre, Pirner, Schmeiser, ARMA, 2023], we extend…

Reference [1] established an index theory for a class of linear selfadjoint operator equations covering both second order linear Hamiltonian systems and first order linear Hamiltonian systems as special cases. In this paper based upon this…

It is well known that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is well approximated by the associated averaged system, called slow system. Each resonance is…

The basic tool of classical results by Malkin and Melnikov on bifurcation of periodic solutions from nondegenerate cycles of autonomous systems with periodic perturbations is an implicit function theorem. In this paper the Poincare index is…

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…