Using the three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD) scheme is proposed to solve the time-dependent Schrödinger equation. First, the high-order symplectic framework for discretizing Schrödinger equation is described. Then the numerical stability and dispersion analyses are provided for the FDT...

In this paper, we investigate the finite-time synchronization problem of a novel hyperchaotic complex-variable system which generates 2-, 3and 4-scroll attractors. Based on the finite-time stability theory, two control strategies are proposed to realize synchronization of the novel hyperchaotic complex-variable system in finite time. Finally, two numerical examples have been provided to illustr...

Abstract: This paper studies adaptive cluster synchronization of uncertain complex dynamical networks in finite time. Based on Lyapunov stability theorem and the finite-time control techniques, a useful criteria is established to guarantee the realization of adaptive cluster synchronization in finite time. Finally, a numerical example is given to illustrate the effectiveness and correctness of ...

Fixed-time and finite-time stabilities of non-linear systems are investigated using the introduced notions sub- sup-homogeneity. These concepts allow to be analyzed homogeneity, even if they do not admit homogeneous approximations. Finite-time fixed-time stability properties can established homogeneity degree sup-homogeneous extensions.

This paper examines finite-time stability of homogeneous systems. The main result is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity.