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Lyapunov function for cosmological dynamical system

Szydłowski M., Krawiec A.

Demonstratio Mathematica

2017

Vol. 50, nr 1

51--55

We prove the asymptotic global stability of the de Sitter solution in the Friedmann-Robertson-Walker conservative and dissipative cosmology. In the proof we construct a Lyapunov function in an exact form and establish its relationship with the first integral of dynamical system determining evolution of the flat Universe. Our result is that de-Sitter solution is asymptotically stable solution for general form of equation of state p = p(p, H), where dependence on the Hubble function H means that the effect of dissipation are included.

First integrals of evolution systems and nonlinear stability of stationary solutions for the ideal atmospheric, oceanic, hydrodynamical and plasma models

Gordin V.

Journal of Technical Physics

1998

Vol. 39, no 2

213-219

First integrals of the systems of nonlinear equations governing the behaviour of atmospheric, oceanic and MHD plasma models are determined. The Lyapunov stability conditions for the solutions under small initial disturbances are analyzed. \