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Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameters identification and synchronization of uncertain chaotic delayed systems subject to time-varying delay. Firstly, a novel and systematic adaptive scheme of synchronization is proposed for delayed dynamical systems containing uncertainties based on Razumikhin condition and extended invariance principle for functional differential equations. Then, the proposed adaptive scheme is used to estimate the unknown parameters of nonlinear delayed systems from time series, and a sufficient condition is given by virtue of this scheme. The delayed system under consideration is a very generic one that includes almost all well-known delayed systems (neural network, complex networks, etc.). Two classical examples are used to demonstrate the effectiveness of the proposed adaptive scheme.
Background: The goal was to study lipid profiles (TG, TC, LDL, HDL), effects on serum leptin, and fat tissue adiponectin, and resistin as well as body weight effects of Shan He Jian Fei Granules (SHJFG) in rats on a high fat diet.
Methods: Rats were randomly divided into five groups: normal control group fed with normal fat diet, rats on high fat diet receiving low dosage, middle dosage, high dosage of Shan He Jian Fei Granules (SHJFG) as well as a high fat diet group receiving placebo. Rats were treated for 8 weeks. Body weight and naso-anal length of each rat were recorded and Lee's index was calculated. Serum TG, TC, LDL, HDL and leptin concentrations were analyzed. The gene expressions of adiponectin and resistin in adipose tissues were tested by RT-PCR.
Results: Compared to the high-fat diet group, body weights, Lee's indexes, weight of fat tissues and serum TG, TC, LDL and leptin of SHJFG groups significantly decreased (p<0.05), whereas mRNA expressions of adiponectin and resistin of SHJFG groups significantly increased (p<0.05).
Conclusions: SHJFG could significantly lower body weight and serum TG, TC, and LDL of obese rats. The effects of SHJFG in lowering leptin synthesis and raising mRNA expression of adiponectin and resistin in fat tissues may act as part of the mechanisms in lowering body weight of obese rats. Further studies are needed to demonstrate whether SHJFG may also reduce overall cardiovascular morbidity and mortality like other lipid lowering drugs.