On exponential stability of functional differential equations with variable impulse perturbations

We consider a class of functional differential equations subject to perturbations, which vary in time, and we study the exponential stability of solutions of these equations using the theory of generalized ordinary differential equations and Lyapunov functionals. We introduce the concept of variational exponential stability for generalized ordinary differential equations and we develop the theory in this direction by establishing conditions for the trivial solutions of generalized ordinary differential equations to be exponentially stable. Then, we apply the results to get corresponding ones for impulsive functional differential equations. We also present an example of a delay differential equation with Perron integrable right-hand side where we apply our result.

Robust Switched Control Design for Nonlinear Systems Using Fuzzy Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comportamento caótico em modelos matemáticos de câncer

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Distribuição espacial, amostragem sequencial e dinâmica populacional de Leptopharsa heveae (Hemiptera: Tingidae) na cultura da seringueira

Pós-graduação em Agronomia (Produção Vegetal) - FCAV

Infiltração de água em um podzólico vermelho-escuro sob dois métodos de preparo, usando chuva simulada com duas intensidades

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A informação no contexto arquivístico: uma discussão a partir dos conceitos de informação-como-coisa e informação orgânica

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fractal scaling exponents of heart rate variability association with linear indices and Poincaré Plot

The literature indicated that the fractal analysis of heart rate variability (HRV) is related to the chaos theory. However, it is not clear if the both short and long-term fractal scaling exponents of HRV are reliable for short period analysis in women. We evaluated the association of the fractal exponents of HRV with the time and frequency domain and geometric indices of HRV. We evaluated 65 healthy women between 18 and 30 years old. HRV was analyzed with a minimal number of 256 RR intervals in the time (SDNN, RMSSD, NN50 and pNN50) and frequency (LF, HF and LF/HF ratio) domains, the geometric index were also analyzed (triangular indexRRtri, triangular interpolation of RR intervals-TINN and Poincaré plot-SD1, SD2 and SD1/SD2) as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). No significant correlation was observed for alpha-2 exponent with all indices. There was significant correlation of the alpha-1 exponent with RMSSD, pNN50, SDNN/RMSSD, LF (nu), HF (nu and ms2 ), LF/HF ratio, SD1 and SD1/SD2 ratio. Our data does not indicate the alpha-2 exponent to be used for 256 RR intervals and we support the alpha-1 exponent to be used for HRV analysis in this condition.

Fractal dynamics of heart rate variability for short term

The fractal analysis of heart rate variability (HRV) has been associated to the chaos theory. We evaluated the association of the fractal exponents of HRV with the time and frequency domain and geometric indices of HRV for short period. HRV was analyzed with a minimal number of 256 RR intervals in the time (SDNN-standard deviation of normal-to-normal R-R intervals, pNN50-percentage of adjacent RR intervals with a difference of duration greater than 50ms and RMSSD-root-mean square of differences between adjacent normal RR intervals in a time interval) and frequency (LF-low frequency, HF-high frequency and LF/HF ratio) domains. The geometric indexes were also analyzed (RRtri-triangular index, TINN-triangular interpolation of RR intervals and Poincaré plot) as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). We observed strong correlation of the alpha-1 exponent with RMSSD, pNN50, SDNN/RMSSD, LF (nu), HF (nu), LF/HF ratio, SD1 and SD1/Sd2 ratio. In conclusion, we suggest that the alpha-1 exponent could be applied for HRV analysis with a minimal number of 256 RR intervals.

Fractal correlation property of heart rate variability in response to the postural change maneuver in healthy women

Background: We evaluated the effects of the PCM on the fractal analysis of the HRV in healthy women Method: We evaluated healthy women between 18 and 30 years old. HRV was analyzed in the time (SDNN, RMSSD, NN50 and pNN50) and frequency (LF, HF and LF/HF ratio) domains as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). HRV was recorded at rest for ten minutes at seated rest and then the women quickly stood up from a seated position in up to three seconds and remained standing for 15 minutes. HRV was recorded at the following time: rest, 0–5 min, 5–10 min and 10–15 min during standing. Results: We observed decrease (p < 0.05) in the time-domain indices of HRV between seated and 10–15 minutes after the volunteer stood up. The LF (ms2) and HF (ms2) indices were also reduced (p < 0.05) at 10–15 minutes after the volunteer stood up compared to seated while the LF (nu) was increased at 5–10 min and 10–15 min (p < 0.05). The short-term alpha-1 exponent was increased (p < 0.05) at all moments investigated compared to seated. Increase in the properties of short-term fractal correlations of heart rate dynamics accompanied by a decrease in the parasympathetic modulation and global HRV was observed in response to the postural change maneuver. Conclusion: We suggest that fractal analysis of HRV is more sensitive than frequency and time-domain analysis of HRV during the postural change maneuver.

Ziembinski – o encenador dos tempos modernos: a construção de uma trajetória na crítica de Décio de Almeida Prado (1950-1959)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estudo de órbitas periódicas em equações diferenciais não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Positive Solution for a Class of Degenerate Quasilinear Elliptic Equations in R-N

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On Switched Regulator Design of Uncertain Nonlinear Systems Using Takagi-Sugeno Fuzzy Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Scaling properties and universality in a ratchet system

Critical exponents that describe a transition from unlimited to limited diffusion for a ratchet system are obtained analytically and numerically. The system is described by a two dimensional nonlinear mapping with three relevant control parameters. Two of them control the non-linearity while the third one controls the intensity of the dissipation. Chaotic attractors appear in the phase space due to the dissipation and considering large non-linearity are characterised by the use of Lyapunov exponents. The critical exponents are used to overlap different curves of average momentum (dynamical variable) onto a single plot confirming a scale invariance. The formalism used is general and the procedure can be extended to different systems.

Epidemiological Models of Directly Transmitted Diseases: An Approach via Fuzzy Sets Theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)