相关论文: Asymptotic Dynamical Difference between the Nonloc…
Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in two flavours: a \emph{kinematic} non-locality -- arising from…
In this article, we study the global dynamics of a discrete two dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this…
When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…
Basing on the increasing evidence for the cosmological relevance of the local Hubble flow, we consider a simple analytical cosmological model for the Local Universe. This is a non-Friedmann model with a non-uniform static space-time. The…
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations containing a compact spatial heterogeneity. While one-dimensional…
In a fully inhomogeneous, anisotropic cosmological simulation performed by solving Einstein's equations with numerical relativity, we find a local measurement of the effective Hubble parameter differs by less than 1\% compared to the global…
We study homoclinic orbits of the Swift-Hohenberg equation near a Hamiltonian-Hopf bifurcation. It is well known that in this case the normal form of the equation is integrable at all orders. Therefore the difference between the stable and…
Local and global persistence exponents associated with zero temperature quenched dynamics of two dimensional XY model and three dimensional Heisenberg model have been estimated using numerical simulations. We have used the method of block…
The range of existence and the properties of two essentially different chaotic attractors found in a model of nonlinear convection-driven dynamos in rotating spherical shells are investigated. A hysteretic transition between these…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
In some pattern-forming systems, for some parameter values, patterns form with two wavelengths, while for other parameter values, there is only one wavelength. The transition between these can be organised by a codimension-three point at…
We study the asymptotic dynamics of open quantum systems in the Heisenberg picture. We find an explicit expression for the attractor subspace and the dynamics that takes place in it. We present the relationship between the attractor…
We complete our previous derivation, at the sixth post-Newtonian (6PN) accuracy, of the local-in-time dynamics of a gravitationally interacting two-body system by giving two gauge-invariant characterizations of its complementary…
The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schr\"odinger (HNLS) equation is discussed. Based on analytical and extensive numerical simulations an approximate…
The paper is devoted to establishing relationships between global and local monotonicity, as well as their maximality versions, for single-valued and set-valued mappings between finite-dimensional and infinite-dimensional spaces. We first…
Time-dependent Hamiltonian dynamics is derived for a curve (molecular strand) in $\mathbb{R}^3$ that experiences both nonlocal (for example, electrostatic) and elastic interactions. The dynamical equations in the symmetry-reduced variables…
In this paper we study the geometry of the attractors of holomorphic maps with an irrationally indifferent fixed point. We prove that for an open set of such holomorphic systems, the local attractor at the fixed point has Hausdorff…
In this paper, the dynamical heteroclinic orbit and attractor have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviates the fine tuning problem in cosmological dynamical system…
The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…