Parkinson's disease is a neurodegenerative disease that causes severe movement disorders including bradykinesia, rigidity, and tremors. There is no cure for Parkinson's disease, only the symptoms can be managed. Parkinson's disease is diagnosed using the MDS-UPDRS global grading scale. In this scale, four levels including slight, mild, moderate, and severe levels are defined for the disease. Recurrence plots and RQA Features are tools for describing the behavior of Chaotic systems and revealing hidden patterns in system dynamics. In this paper, the effect of Parkinson's disease progression on RQA Chaotic Features is studied. For this purpose, the dataset of the accelerometer mounted on the hand during the finger tapping test was used, which included 67 healthy data, 54 level one data, 66 level two data, 59 level three data, and 14 level four data. After pre-processing, the recurrence plots of the data were drawn and their RQA characteristics were calculated. Patterns of recurrence plots including separate recurrence points, diagonal lines, vertical lines, black squares, and horizontal and vertical white bands were investigated. According to the obtained results, the patterns of recurrence plots had significant differences among different levels of Parkinson's disease. Therefore, RQA Features can be used to automatically determine the level of Parkinson's disease.

Fault detection of ball bearings by the complex and non-stationary vibration signals with noise is very difficult, especially at the early stages. Also, many failure mechanisms and various adverse operating conditions in ball bearings involve significant nonlinear dynamical properties. The quality of Chaotic vibration of ball bearings is studied by the reconstructed phase space. The phase space demonstrates different Chaotic vibration of ball bearing for different healthy/faulty conditions. But, to easily use of this procedure in the ball bearing fault detection, the Chaotic behavior of vibration signal is quantified by a set of new Features. The new set of Features based on Chaotic behavior, including the largest Lyapunov exponent, approximate entropy and correlation dimension are extracted to acquire more fault characteristic information. The effectiveness of the new Features based on Chaotic vibrations in the ball bearing fault detection is demonstrated by the experimental data sets. The proposed approach can reliably recognize different fault types and have more accurate results. Also, the performance of the new procedure is robust to the variation of load values and shows good generalization capability for various load values.

Increasing population and food demand, disproportionate cultivation and annual production of various agricultural products with market needs and low productivity of the agricultural sector and the loss of water and soil resources have made it necessary to determine and implement the country's optimal cropping pattern. In this study, due to the limitations and problems of classical methods in order to reduce processing time and improve the quality of solutions, the Multi-Objective Chaotic Particle Swarm Optimization was used to determine the optimal cultivation pattern of Sistan plain in optimal conditions and deficit irrigation. The results of the Multi-Objective Chaotic Particle Swarm Optimization for the dominant cultures in the region showed that the current cropping pattern of the region is not optimal and with the implementation of the proposed model, the profit per unit area under cultivation will increase. The results of application of deficit irrigation during different growing periods of wheat, barley, alfalfa, sorghum, watermelon and grapes showed that applying deficit irrigation in this plain is not a good strategy and therefore only a full irrigation strategy is recommended. The results of sensitivity analysis of the model showed that at low prices, farmers reaction is less and at higher prices more reaction to price changes and with increasing prices, the program efficiency is lower.

Sleep is a normal state in humans and the subconscious level of brain activity increases during sleep. The brain plays a prominent role during sleep, so a variety of mental and brain-related diseases can be identified through sleep analysis. A complete sleep period according to the two world standards R&K and AASM consists of seven and five steps, respectively. To diagnose diseases through sleep, it is necessary to identify different stages of sleep because the disorder at each stage indicates a certain disease. On the other hand, efficient and useful Features should be selected to increase the accuracy of sleep stage classification. In this paper, at first, different statistical, entropy, and Chaotic Features are extracted from sleep data. Afterwards, by introducing and using the Laplacian score selector, the best feature set is selected. At the end, some conventional classification algorithms such as SVM, ANN and KNN are used to classify different sleep stages. Simulation results confirms the superiority of the proposed method based on the classification results. With the proposed algorithm, 2, 3, 4, 5 and 6 stages of sleep were classified by SVM and decision tree with 98. 0%, 98. 0%, 97. 3%, 96. 6%, and 95. 0% accuracy, which are more superior to previous method’ s results.

In this paper, we introduce Chaotic measure for discrete and continuous dynamical systems and study some properties of measure Chaotic systems. Also relationship between Chaotic measure, ergodic and expansive measures is investigated. Finally, we prove a new version of variational principle for Chaotic measure.

The movements in oil prices are complex and, therefore, seem to be unpredictable. The traditional linear structural models have not been promising when applied to forecasting, particularly in the case of complex series such as oil prices. Although linear and nonlinear time series models have done much better job in forecasting oil prices, there is yet room for an improvement. If the data generating process is nonlinear, applying linear models could result in misleading forecasts. Model specification in nonlinear modeling can also be very case dependent and time-consuming. In this paper, we model and forecast daily futures oil price, listed in NYMEX, applying ARIMA, and GARCH models, for the period April June 1983 - Jan. 2003. Then, we test for chaos using BDS, Lyapunov exponent, Neural Networks, and Embedding Dimension methods. Finally, we will set up a nonlinear and flexible ANN model to forecast the series. Since the tests for chaos indicate that the oil price in futures markets is Chaotic, the ANN model should make better forecasts. The forecasts comparison among the models approves that.