In this letter, a very simple method to calculate the positive Largest Lyapunov Exponent (LLE) based on the concept of interval extensions and using the original equations of motion is presented. The exponent is estimated from the slope of the line derived from the lower bound error when considering two interval extensions of the original system. It is shown that the algorithm is robust, fast and easy to implement and can be considered as alternative to other algorithms available in the literature. The method has been successfully tested in five well-known systems: Logistic, Hénon, Lorenz and Rössler equations and the Mackey–Glass system.
In this paper, a new approach to analyze the asymptotic, exponential and robust stability of the master-slave synchronization for Lur'e systems using time-varying delay feedback control is proposed. The discussion is motivated by the problem of transmitting information in optical communication systems using chaotic lasers. The approach is based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz–Newton model based transformation, without including any additional dynamics. Using the problem of synchronizing coupled Chua's circuits, three examples are given to illustrate the effectiveness of the proposed methodology.
Maternal immune activation (MIA) during pregnancy in rodents increases the risk of the offspring to develop schizophrenia-related behaviors, suggesting a relationship between the immune system and the brain development. Here we tested the hypothesis that MIA induced by the viral mimetic polyinosinic-polycytidylic acid (poly I:C) in early or late gestation of mice leads to behavioral and neuroanatomical disorders in the adulthood. On gestational days (GDs) 9 or 17 pregnant dams were treated with poly I:C or saline via intravenous route and the offspring behaviors were measured during adulthood. Considering the progressive structural neuroanatomical alterations in the brain of individuals with schizophrenia, we used magnetic resonance imaging (MRI) to perform brain morphometric analysis of the offspring aged one year. MIA on GD9 or GD17 led to increased basal locomotor activity, enhanced motor responses to ketamine, a psychotomimetic drug, and reduced time spent in the center of the arena, suggesting an increased anxiety-like behavior. In addition, MIA on GD17 reduced glucose preference in the offspring. None of the treatments altered the relative volume of the lateral ventricles. However, a decrease in brain volume, especially for posterior structures, was observed for one-year-old animals treated with poly I:C compared with control groups. Thus, activation of the maternal immune system at different GDs lead to neuroanatomical and behavioral alterations possibly related to the positive and negative symptoms of schizophrenia. These results provide insights on neuroimmunonological and neurodevelopmental aspects of certain psychopathologies, such as schizophrenia.
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