Under the acceptable hypothesis that cardiac rhythm is an approximately deterministic process with a small scale noise component, an available way is provided to construct a model that can reflect its prominent dynamics of the deterministic component. When applied to the analysis of 19 heart rate data sets, three main findings are stated. The obtained model can reflect prominent dynamics of the deterministic component of cardiac rhythm; cardiac chaos is stated in a reliable way; dynamical noise plays an important role in the generation of complex cardiac rhythm.
In this paper, we first discuss the stability of linearized error dynamics of the nonlinear observer used for time-continuous driving chaos synchronization and give the criteria on it. Then we find by theoretical analysis and numerical experiments that the observer can still synchronize with the original system under time-discrete driving provided that some conditions are met. Finally we derive the asymptotical stability criterion of the nonlinear observer used for time-discrete driving chaos synchronization. Simulations illustrate the validity of the criterion.
