Generalized Lyapunov functions and functional equations

1965 ◽  
Vol 69 (1) ◽  
pp. 305-320 ◽  
Author(s):  
Philip Hartman
Keyword(s):  
Lyapunov Functions ◽  
Functional Equations ◽  
Generalized Lyapunov Functions

NEW ESTIMATIONS FOR GLOBALLY ATTRACTIVE AND POSITIVE INVARIANT SET OF THE FAMILY OF THE LORENZ SYSTEMS

2006 ◽  
Vol 16 (11) ◽  
pp. 3383-3390 ◽  
Author(s):  
PEI YU ◽  
XIAOXIN LIAO
Keyword(s):  
Lyapunov Functions ◽  
Chaotic Systems ◽  
Invariant Set ◽  
The Other ◽  
Qualitative Behavior ◽  
The Family ◽  
Infinite Intervals ◽  
Globally Attractive ◽  
Generalized Lyapunov Functions ◽  
Positive Invariant Set

In this paper, we employ generalized Lyapunov functions to derive new estimations of the ultimate boundary for the trajectories of two types of Lorenz systems, one with parameters in finite intervals and the other in infinite intervals. The new estimations improve the results reported so far in the literature. In particular, for the singular cases: b → 1+ and a → 0+, we have obtained the estimations independent of a. Moreover, our method using elementary algebra greatly simplifies the proofs in the literature. This is an interesting attempt in obtaining information of the attractors which is difficult when merely based on differential equations. It indicates that Lyapunov function is still a powerful tool in the study of qualitative behavior of chaotic systems.

On some functional equations related to derivations and bicircular projections in rings

2014 ◽  
Vol 49 (2) ◽  
pp. 313-331
Author(s):  
Maja Fošner ◽  
◽  
Benjamin Marcen ◽  
Nejc Širovnik ◽  
Joso Vukman ◽  
...  
Keyword(s):  
Functional Equations

Functional equations related to weightable quasi-metrics

2015 ◽  
Vol 4 (1047) ◽  
Author(s):  
M.J. Campion ◽  
E. Indurain ◽  
G. Ochoa
Keyword(s):  
Functional Equations
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