Related papers: Dissecting a resonance wedge on heteroclinic bifur…
We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. We find four fundamental rogue waves can emerge for second-order vector RW in the coupled system, in contrast to the high-order ones…
A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…
An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal…
Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to demonstrate these…
Heteroclinic connections between two distinct hyperbolic periodic orbits in conservative systems are important in a wide range of applications. On the other hand, it is theoretically challenging to find large amplitude connections from…
Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a…
We study Langevin dynamics of $N$ Brownian particles on two-dimensional Riemannian manifolds, interacting through pairwise potentials linear in geodesic distance with quenched random couplings. These \emph{frustrated Brownian particles}…
We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distributon in a special topology to a piecewise constant process…
We consider autonomous Lagrangian systems with two degrees of freedom, having an hyperbolic equilibrium of saddle-saddle type (that is the eingenvalues of the linearized system about the equilibrium are $\pm \lambda_1, \pm \lambda_2 $,…
In this paper, we investigate the ground state of two-dimensional disordered cylinders which contain spinless, interacting electrons using the Hartree-Fock approximation. Calculations of the deviation of the polarization from uniformity…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
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,…
It is shown that the incorporation of linear sink/source terms in the three-wave resonance interaction model results in the time dependence of the wave amplitudes, which could exhibit the properties of a strange attractor. This finding…
We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome cavity resonator that owe their shape and character entirely to the Goos-Haenchen effect. The V-shaped modes, which have purely TE or TM polarization, are well…
Gyroscopic metamaterials --- mechanical structures composed of interacting spinning tops --- have recently been found to support one-way topological edge excitations. In these structures, the time reversal symmetry breaking that enables…
Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…
We examine a 2DOF Hamiltonian system, which arises in study of first-order mean motion resonance in spatial circular restricted three-body problem "star-planet-asteroid", and point out some mechanisms of chaos generation. Phase variables of…
The separating and reattaching turbulent flow past a rectangular cylinder is studied to describe how small and large scales contribute to the sustaining mechanism of the velocity fluctuations. The work is based on the Anisotropic…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…
We present a group theoretical study of the symmetry-broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking…