Using the Routh–Hurwitz stability criterion and a systematic computer search, 23 simple chaotic flows with quadratic nonlinearities were found that have the unusual feature of having a coexisting stable equilibrium point. Such systems belong to a newly introduced category of chaotic systems with hidden attractors that are important and potentially problematic in engineering applications.

Using a systematic computer search, a simple four-dimensional chaotic flow was found that has the unusual feature of having a plane of equilibria. Such a system belongs to a newly introduced category of chaotic systems with hidden attractors that are important and potentially problematic in engineering applications.

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Not only does the modeling of dynamical systems, for instance the biological systems, play an important role in the accurate perception and analysis of these systems, but it also makes the prediction and control of their behavior straightforward. The results of multiple researches in the field of the modeling of biological systems have indicated that the chaotic behavior is a prevalent feature of most complex interactive biological systems. Our results demonstrate that the artificial neural network provides us an effective means to model the underlying dynamics of these systems. In this paper, at first, we represent the results of the use of a multilayer feed-forward neural network to model some famous chaotic systems. The specified neural network is trained with the return maps extracted from the time series. We proceed with the paper by evaluating the accuracy and robustness of our model. The ability of the select neural network to model the dynamics of chosen chaotic systems is verified, even in the presence of noise. Afterwards, we model the brain response to the flicker light. It is known that the brain response to some stimuli such as the flicker light recorded as electroretinogram is an exemplar of chaotic behavior. The need remains, however, for realistic modeling of this behavior of the brain. In this paper, we represent the results of the modeling of this chaotic response by utilizing the proposed neural network. The capability of the neural network to model this specific brain response is confirmed.

The mass of the lower extremity muscles is a clinically significant metric. Manual segmentation of these muscles is a timeconsuming task. Most of the segmentation methods for the thigh muscles are based on statistical models and atlases which need manually segmented datasets. The goal of this work is an automatic segmentation of the thigh muscles with only one initial segmented slice. A new automatic method is proposed for concurrent individual thigh muscles segmentation using a hybrid level set method and anatomical information of the muscles. In the proposed method, the muscle regions are extracted by the Fast and Robust Fuzzy C-Means Clustering (FRFCM) method, and then a contour is determined for each muscle which changes according to the muscle shape variation through its length. The anatomical information is used to control the contours variations and to refine the final boundaries. The method was validated by 22 CT datasets. The average dice similarity coefficient (DSC) of the method for individual muscle segmentation with one and two initial slices were 89.29 ± 2.59 (%) and 91.77 ± 1.87 (%), respectively. Also, the average symmetric surface distances (ASSDs) were 0.93 ± 0.29 mm and 0.64 ± 0.18 mm. Furthermore, applying to ten MRI datasets, the average DSC and ASSD for muscles were 90.9 ± 2.61 (%) and 0.71 ± 0.33 mm, respectively. The quantitative and intuitive results of the proposed method show the effectiveness of this method in segmentation of large and small muscles in CT and MR images. The consumed computation time is lower than the previous works, and this method does not need any training datasets.