Hybrid dynamical systems theory and nonlinear dynamical systems over finite fields

1989 ◽  
pp. 483-495 ◽  
Author(s):  
Albert Benveniste ◽  
Paul Le Guernic
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Finite Fields ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Systems Theory ◽  
Hybrid Dynamical Systems ◽  
Nonlinear Dynamical

scholarly journals Sex Differences and Heritability of Two Indices of Heart Rate Dynamics: A Twin Study

2007 ◽  
Vol 10 (2) ◽  
pp. 364-372 ◽  
Author(s):  
Harold Snieder ◽  
Lorenz J. P. van Doornen ◽  
Dorret I. Boomsma ◽  
Julian F. Thayer
Keyword(s):  
Heart Rate ◽  
Sex Differences ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Systems Theory ◽  
Sinus Arrhythmia ◽  
Nonlinear Dynamical ◽  
Heart Rate Dynamics ◽  
Two Indices

AbstractWe investigated whether women show larger heart rate variability (HRV) than men after controlling for a large number of health-related covariates, using two indices of HRV, namely respiratory sinus arrhythmia (RSA) and approximate entropy (ApEn). In a twin design, the heritability of both indices was examined. The covariation between RSA and ApEn, a measure of heart rate dynamics derived from nonlinear dynamical systems theory, was decomposed into genetic and environmental components. Subjects were 196 male and 210 female middle-aged twins. Females showed larger HRV than men before (ApEn: p < .001; RSA: p = .052) and after adjustment for covariates (ApEn: p < .001; RSA: p = .015). This sex difference was confirmed by significant intrapair differences in the opposite-sex twin pairs for both ApEn (p < .001) and RSA (p = .03). In addition to sex, only heart period and age (both p < .001) were found to be independent predictors of ApEn, whereas RSA was also influenced by respiration rate and smoking (both p < .001). Age explained 16% and 6% of the variance in RSA and ApEn, respectively. Oral contraceptive use and menopausal status had no effect on HRV. Genetic model fitting yielded moderate heritability estimates for RSA (30%) and ApEn (40%) for both males and females. The correlation between RSA and ApEn (r = .60) could be attributed to genetic factors (48%), environmental factors (36%) and age (16%). The present study found support for a gender difference in HRV with women having greater HRV than men even after controlling for a large number of potential confounders. Indices of heart rate dynamics derived from nonlinear dynamical systems theory are moderately heritable and may be more sensitive than traditional indices of HRV to reveal subtle sex differences with important implications for health and disease.

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