Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function

Sensory adaptation: An information-theoretic viewpoint

Summary form only given. The authors examine the goals of early stages of a perceptual system, before the signal reaches the cortex, and describe its operation in information-theoretic terms. The effects of receptor adaptation, lateral inhibition, and decorrelation can all be seen as part of an optimization of information throughput, given that available resources such as average power and maximum firing rates are limited. The authors suggest a modification to Gabor functions which improves their performance as band-pass filters

Sensory adaptation: An information-theoretic viewpoint

Summary form only given. The authors examine the goals of early stages of a perceptual system, before the signal reaches the cortex, and describe its operation in information-theoretic terms. The effects of receptor adaptation, lateral inhibition, and decorrelation can all be seen as part of an optimization of information throughput, given that available resources such as average power and maximum firing rates are limited. The authors suggest a modification to Gabor functions which improves their performance as band-pass filters