Liapunov Multipliers and Decay of Correlations in Dynamical Systems

Sanger’s Type Dynamical Systems for Canonical Variate Analysis

In this paper, several dynamical systems for computing canonical correlations and canonical variates are proposed. These systems are shown to converge to the actual components rather than to a subspace spanned by these components. Using Liapunov stability theory, qualitative properties of the proposed systems are analyzed in detail including the limit of solutions as time approaches infinity.

Dynamics of a discrete-time plant-herbivore model

Dynamical Systems with Several Equilibria and Natural Liapunov Functions

Dynamical systems with several equilibria occur in various fields of science and engineering: electrical machines, chemical reactions, economics, biology, neural networks. As pointed out by many researchers, good results on qualitative behaviour of such systems may be obtained if a Liapunov function is available. Fortunately for almost all systems cited above the Liapunov function is associated...

Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems

We discuss the notion of Liapunov exponent for integrate-and-fire (IF) type dynamical systems. In contrast to smooth flows there is a contribution to the IF Liapunov exponent arising from the discontinuous nature of the firing mechanism. Introducing the notion of an IF mode-locked state we are able to show that linear stability is consistent with the requirement of a negative IF Liapunov expone...

Examples of quasi-hyperbolic dynamical systems with slow decay of correlations

We give examples of quasi-hyperbolic dynamical systems with the following properties : polynomial decay of correlations, convergence in law toward a non gaussian law of the ergodic sums (divided by n) associated to non degenerated regular functions.