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Dependence of hidden attractors on non-linearity and Hamilton energy in a class of chaotic system

Ge Zhang, Chunni Wang, Ahmed Alsaedi, Jun Ma, Guodong Ren (2018)

Kybernetika

Non-linearity is essential for occurrence of chaos in dynamical system. The size of phase space and formation of attractors are much dependent on the setting of nonlinear function and parameters. In this paper, a three-variable dynamical system is controlled by different nonlinear function thus a class of chaotic system is presented, the Hamilton function is calculated to find the statistical dynamical property of the improved dynamical systems composed of hidden attractors. The standard dynamical...

Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions

David Hoff (2001)

Journées équations aux dérivées partielles

We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time, more rapidly for larger acoustic speeds and smaller...

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