Related papers: The hypocoercivity index for the short time behavi…
Even if a linear system of ordinary differential equations has a globally attracting equilibrium at the origin, small disturbances from the equilibrium may lead to large transient excursions before the system stabilizes. This…
This paper considers the problem of finite dimensional output feedback H-infinity control for a class of nonlinear spatially distributed processes (SDPs) described by highly dissipative partial differential equations (PDEs), whose state is…
The present article considers stability of the solutions to nonlinear and nonautonomous compartmental systems governed by ordinary differential equations (ODEs). In particular, compartmental systems with a right-hand side that can be…
Dynamical systems driven by a general L\'evy stable noise are considered. The inertia is included and the noise, represented by a generalised Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive…
In this paper, we provide a result of exponential stability for several dissipative linear kinetic equations with heavy-tailed equilibria. The approach, inspired by the so-called $L^2$-hypocoercivity method, is robust enough to provide…
We consider the problem of Arnold's diffusion for nearly integrable isochronous Hamiltonian systems. We prove a shadowing theorem which improves the known estimates for the diffusion time. We also develop a new method for measuring the…
We study the uniform-in-time weak propagation of chaos for the consensus-based optimization (CBO) method on a bounded searching domain. We apply the methodology for studying long-time behaviors of interacting particle systems developed in…
The out-of-time-order correlator (OTOC), recently analyzed in several physical contexts, is studied for low-dimensional chaotic systems through semiclassical expansions and numerical simulations. The semiclassical expansion for the OTOC…
In this study we consider unconditionally non-oscillatory, high order implicit time marching based on time-limiters. The first aspect of our work is to propose the high resolution Limited-DIRK3 (L-DIRK3) scheme for conservation laws and…
We show dissipative spatial solitons in nonlinear optical micro-resonators in which the refractive index is laterally modulated. In addition to "normal" and "staggered" dissipative solitons, similar to those in spatially modulated…
This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…
Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic evolution of a local observable repeats itself at an integer multiple of the driving…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…
In this paper, we study the hypocoercivity for a class of linear kinetic equations with both transport and degenerately dissipative terms. As concrete examples, the relaxation operator, Fokker-Planck operator and linearized Boltzmann…
Dissipative quantum systems are sometimes phenomenologically described in terms of a non-hermitian hamiltonian $H$, with different left and right eigenvectors forming a bi-orthogonal basis. It is shown that the dynamics of waves in open…
We are concerned with discretisations of the classical Kolmogorov equation by a standard space-time discontinuous Galerkin method. {The} Kolmogorov equation serves as simple, yet rich enough in the present context, model problem for a wide…
We employ weak hypocoercivity methods to study the long-term behavior of operator semigroups generated by degenerate Kolmogorov operators with variable second-order coefficients, which solve the associated abstract Cauchy problem. We prove…
The paper is considered with the dissipative theory and feedback control under the framework of dissipation with the supply rate is the inner product of input u and the derivation of output y for the linear/nonlinear time-invariant input…
The recurrence-based divergence quantifier ($DIV$), traditionally applied to dissipative systems, is shown here to be an effective finite-time chaos indicator for conservative dynamics. We benchmark its performances against the…