Toward a new method of derivation of the invariant measures of (chaotic) dynamical systems application to living cell dynamics

摘要

In the analysis of signals from physical systems we usually assume that we are dealing with a single flow behaviour and not with the evolution of averages over an ensemble of flow. When dealing with biological systems (e.g., living cell population) the latter case has to be taken into consideration [1]. We are proposing a general method able to determine a set of invariants under the dynamics of an ensemble of systems with behaviours (flows) described by the same dynamical system, starting from different initial conditions. Unlike the classical approaches, this procedure deals with time series of averages of certain state parameters and not with time series related to a single system dynamics.