Dynamical properties of a nonlinear Kuramoto–Sivashinsky growth equation

Some Dynamical Properties for a Class of Nonlinear Difference Equation

In this paper, the global behavior for a class of nonlinear difference equation is considered, mainly for the global asymptotical stability of zero equilibrium with attractive basin, the existence of unbounded solutions, the existence of period two solutions, and the existence of oscillatory solutions, etc. Our results extend and generalize the known ones.

Dynamical Properties in a Fourth-Order Nonlinear Difference Equation

The rule of trajectory structure for fourth-order nonlinear difference equation xn 1 x a n−2 xn−3 / x a n−2xn−3 1 , n 0, 1, 2, . . . , where a ∈ 0, 1 and the initial values x−3, x−2, x−1, x0 ∈ 0,∞ , is described clearly out in this paper. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4 , 3−, ...

Dynamical Properties for a Relaxation Scheme Applied to a Weakly Damped Non Local Nonlinear Schrödinger Equation

We apply a semi-discrete in time relaxation scheme to a weakly damped forced nonlinear Schrödinger system. This provides us with a discrete infinite-dimensional dynamical system. We prove the existence of a global attractor for this dynamical system.

A Nonlinear Differential-difference Equation of Growth.

Spatial Analyticity on the Global Attractor for the KuramotoSivashinsky Equation

For the Kuramoto Sivashinsky equation with L-periodic boundary conditions we show that the radius of space analyticity on the global attractor is lowersemicontinuous function at the stationary solutions, and thereby deduce the existence of a neighborhood in the global attractor of the set of all stationary solutions in which the radius of analyticity is independent of the bifurcation parameter ...