Recently both shear turbulence and isotropic turbulence have been investigated by means of unstable periodic orbits. These orbits are embedded in a high dimensional chaotic attractor that represents the turbulent flow. In both cases, the periodic motion can be shown to bear a strong similarity to the turbulent motion. Therefore we can learn about the nature of turbulence by studying the periodi...

In this paper the dynamics of an autonomous mathematical models COVID-19 depending on a real parameter bifurcation, is controlled by switching periodically value. For purpose Parameter Switching (PS) algorithm used. With technique, it proved that every attractor considered system can be numerically approximated and, therefore, determined to evolve along, e.g., stable periodic motion or chaotic ...

Numerical bifurcation analysis, and in particular two-parameter continuation, is used consort with numerical simulation to reveal complicated dynamics the Mackey-Glass equation for moderate values of delay close onset chaos. In a cusp periodic orbits resulting branches folds effectively partition parameter space into regions where different behaviours are seen. The leads directly bistability be...

Flux dynamics in an annular long Josephson junction is studied. Three main topics are covered. The first is chaotic flux dynamics and its prediction via Melnikov integrals. It turns out that DC current bias cannot induce chaotic flux dynamics, while AC current bias can. The existence of a common root to the Melnikov integrals is a necessary condition for the existence of chaotic flux dynamics. ...

The 2D incompressible Boussinesq system with partial or fractional dissipation have recently attracted considerable attention. In this paper, we study the Cauchy problem for the 2D Boussinesq system in a periodic domain with fractional vertical dissipation in the subcritical case, and we prove the global well-posedness of strong solutions. Based on this, we also discuss the existence of the glo...

Chaotic attractors contain unstable periodic orbits of any desired period (this is shown in chapter 22 for Axiom A attractors). Furthermore, for an ergodic attractor we know that any trajectory will eventually come arbitrarily close to any of these orbits. This offers the opportunity for controlling chaos: when the chaotic orbit approaches the unstable periodic orbit of interest it can be attra...

Numerical method for detection of unstable periodic orbits on attractors of nonlinear dynamical systems is proposed. This method requires the similar techniques as the data assimilation does. This fact facilitates its implementation for geophysical models. Some low-period orbits of the Lorenz model have been calculated explicitely. The orbits encoding and application of symbolic dynamics is use...

<p style='text-indent:20px;'>We establish a smoothing result for the generalized KdV (gKdV) on torus with polynomial non-linearity, damping, and forcing that matches level gKdV at <inline-formula><tex-math id="M1">\begin{document}$ H^1 $\end{document}</tex-math></inline-formula>. As consequence, we existence of global attractor this equation as well its compactness...