The paper dwells on the problems of stability of dynamical systems on a time scale. The paper is divided into the following sections: local existence and uniqueness, dynamic inequalities, existence of extremal solutions, comparison results, linear variation of parameters, nonlinear variation of parameters, global existence and stability, comparison theorems, stability criteria, etc.

Genes influence the expression of each other through a complex, nonlinear, dynamical network of interactions. There are a number of interesting open questions about what kind of information can be determined about the structure and dynamics of this network from limited experimental data.

Output deadbeat control in one step is considered for a class of discrete-time systems described by a nonlinear single-input/singleoutput recursive representation. Global stability conditions are established for the particular subclass of systems with one-dimensional zero dynamics. The results are illustrated with applications to polynomial and neural dynamical systems.

We propose coherence as a tool to quantify spatiotemporal dynamics, in particular, in spatially inhomogeneous dynamical systems. We demonstrate coherence to be an appropriate measure of predictability and, hence, spatial coupling in nonlinear systems, using analysis and via experimental results from a circular jet flow. Coherence measurements reveal sizable regions of strong spatial coupling in...

This paper is concerned with the robust H∞ finite-time control for discrete delayed nonlinear systems with Markovian jumps and external disturbances. It is usually assumed that the disturbance affects the system states and outputs with the same influence degree of 100%, which is not evident enough to reflect the situation where the disturbance affects these two parts by different influence degr...

A higher order sliding mode control algorithm is proposed for a class of uncertain multi-input multi-output nonlinear systems. This problem can be viewed as the finite time stabilization of a higher order input-output dynamic system with bounded uncertainties. The developed control scheme is based on geometric homogeneity and sliding mode control. The proposed procedure provides explicit condit...