Time-Varying Cardiovascular Complexity with Focus on Entropy and Lyapunov Exponents

2017 ◽  
pp. 233-256
Author(s):  
Gaetano Valenza ◽  
Luca Citi ◽  
Enzo Pasquale Scilingo ◽  
Riccardo Barbieri
Keyword(s):  
Lyapunov Exponents ◽  
Time Varying

Properties of the Lower Bohl Exponents of Diagonal Discrete Linear Time-Varying Systems

2015 ◽  
Vol 789-790 ◽  
pp. 1052-1058
Author(s):  
Michał Niezabitowski
Keyword(s):  
Dynamical Systems ◽  
Linear System ◽  
Control Theory ◽  
Lyapunov Exponents ◽  
Discrete Time ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
Time Varying Systems

The Bohl exponents, similarly as Lyapunov exponents, are one of the most important numerical characteristics of dynamical systems used in control theory. Properties of the Lyapunov characteristics are well described in the literature. Properties of the second above-mentioned exponents are much less investigated in the literature. In this paper we show an example of two-dimensional discrete time-varying linear system with bounded coefficients for which the number of lower Bohl exponents of solutions may be greater than dimension of the system.

scholarly journals On a continuity of characteristic exponents of linear discrete time-varying systems

2012 ◽  
Vol 22 (1) ◽  
pp. 17-27 ◽  
Author(s):  
Adam Czornik ◽  
Piotr Mokry ◽  
Michał Niezabitowski
Keyword(s):  
Linear System ◽  
Lyapunov Exponents ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Time Varying ◽  
Characteristic Exponents ◽  
Time Varying Systems ◽  
Time Invariant

On a continuity of characteristic exponents of linear discrete time-varying systemsIn this paper we present a sufficient condition for continuity of Lyapunov exponents of discrete time-varying linear system. Basing on this result we show that Lyapunov exponents of time-invariant systems depend continuously on the time-varying perturbations.

On new estimates for Lyapunov exponents of discrete time varying linear systems

Automatica ◽  
2010 ◽  
Vol 46 (4) ◽  
pp. 775-778 ◽  
Author(s):  
Adam Czornik ◽  
Aleksander Nawrat
Keyword(s):  
Linear Systems ◽  
Lyapunov Exponents ◽  
Discrete Time ◽  
Time Varying

scholarly journals On the Sequences Realizing Perron and Lyapunov Exponents of Discrete Linear Time-Varying Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Michał Niezabitowski
Keyword(s):  
Lyapunov Exponents ◽  
Equivalence Class ◽  
Discrete Time ◽  
Equivalence Relation ◽  
Linear Time ◽  
Time Varying ◽  
Natural Numbers ◽  
Arithmetic Sequences ◽  
Time Varying Systems ◽  
Increasing Sequences

We investigate properties of partial exponents (in particular, the Lyapunov and Perron exponents) of discrete time-varying linear systems. In the set of all increasing sequences of natural numbers, we define an equivalence relation with the property that sequences in the same equivalence class have the same partial exponent. We also define certain subclass of all increasing sequences of natural numbers, including all arithmetic sequences, such that all partial exponents are achievable on a sequence from this class. Finally, we show that the Perron and Lyapunov exponents may be approximated by partial exponents achievable on sequences in certain sense similar to geometric sequences.

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