相关论文: Heteroclinic orbits, mobility parameters and stabi…

In this paper we analyze the heteroclinic cycle and the Hopf bifurcation of a generic dynamical system with the symmetry of the group $\mathbf{Q}_8,$ constructed via a Cayley graph. While the Hopf bifurcation is similar to that of a…

We discuss a hopping model of electrons between idealized molecular sites with local orbital degeneracy and dynamical Jahn-Teller effect, for crystal field environments of sufficiently high symmetry. For the Mott-insulating case (one…

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and…

We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, the proof, based on variational methods, relies on a…

At a finite temperature, the stable equilibrium states of a coupled two-component superfluid with the same mass in both non-rotating and rotating cases can be obtained by studying its real time dynamics via holography, the equilibrium state…

We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a…

We study main bifurcations of multidimensional diffeomorphisms having a non-transversal homoclinic orbit to a saddle-node fixed point. On a parameter plane we build a bifurcation diagram for single-round periodic orbits lying entirely in a…

We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…

Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…

We study a Langevin equation for a particle moving in a periodic potential in the presence of viscosity $\gamma$ and subject to a further external field $\alpha$. For a suitable choice of the parameters $\alpha$ and $\gamma$ the related…

We study a third-order nonlinear ordinary differential equation whose solutions, under certain specific conditions, are individual pulses. These correspond to homoclinic orbits in the phase space of the equation and we study the possible…

We study a non-reciprocal version of Model B, as the continuum theory for non-reciprocal particle mixtures. In contrast to non-reciprocal Cahn-Hilliard models, it is important in this context to consider the dependence of mobility…

Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…

We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary…

Insects and birds are often faced by opposing requirements for agile and stable flight. Here, we explore the interplay between aerodynamic effort, maneuverability, and stability in a model system that consists of a $\Lambda$-shaped flyer…

The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…

Hysteresis and the non-equilibrium dynamic phase transition in thin magnetic films subject to an oscillatory external field have been studied by Monte Carlo simulation. The model under investigation is a classical Heisenberg spin system…

We study radial oscillations of hybrid non-rotating neutron stars composed by a quark matter core and hadronic external layers. At first, we physically deduce the junction conditions that should be imposed between two any phases in these…

We drive a d-dimensional Heisenberg magnet using a spatially anisotropic current of mobile particles or heat. The continuum Langevin equation is analyzed using a dynamical renormalization group, stability analysis and numerical simulations.…

We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings…