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In this paper, the behavior of the double pendulums has been studied by considering the effect of initial conditions (angular displacement of the outer pendulum for four cases 12, 30, 90, and 150 degrees) and the influence of system geometry (increasing rod length and mass of the second pendulum), also. After extracting motion equations using the Lagrangian method, in order to deal with the frequency spectrum, traces of bobs, and understanding the system behavior for every case, the Fast Fourier Transform (FFT) technique and Poincare sections have been applied. The obtained results show that the consequence of the rising angular displacement the outer pendulum is to increase the energy level of the system and the change of its behavior from quasi-periodic for angular displacement is less than 90 degrees to chaotic when it is 150 degrees. Therefore, the energy level, in this case, has increased more than twice compared to the first. In addition, it seems a quasi-periodic behavior is forming at the heart of chaotic behavior. On the other hand, the results indicate a very significant effect of geometrics on a system's behavior. According to the calculations, the consequence of increasing the length of the rod of the second pendulum has only led to a different behavior from its similar case (case number 3) completely. however, their energy level is the same. Increasing the mass of the outer by twice not only to lead decrease energy level of the system by 330J but also has shown chaotic behavior (in comparison to the case3).

In this paper, a hybrid model for increasing the precision of the support vector machine classifier is proposed to detect stator windings short circuit fault detection in induction motors. The proposed method consists of three different phases, wherein the first phase the statistical features of a healthy and defective data set are extracted. The principal component analysis is used to reduce the dimensions of the obtained features. Then, different SVMs are constructed based on training data sets. To achieve a better result, the parameters of the SVM are determined by the fractionalorder chaotic particle swarm optimization algorithm. Finally, a hybrid model for combining SVMs with type-2 Fuzzy logic is implemented. The proposed approach is then applied on measured stator current data for stator winding short circuit fault detection in a three-phase induction motor with 2.2kW, 50Hz, 6 Pole. The average accuracy of 98.4% of the detection of stator winding error on laboratory data under different load conditions indicates the performance and validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This research investigated the specific patterns of dust influx into the metropolis of Tehran from 2005 to 2017. The study utilized the data on dust occurrence days and synoptic station data in Tehran. The research methodology involved employing the HYSPLIT trajectory model, as well as dust detection indices, and determining the chemical properties of dust, including main and rare elements, by using the X-Ray Fluorescence (XRF) method. The findings indicated that the primary source of dust entering Tehran originated from desert regions and vast, arid areas outside the country. External sources of dust, such as the North Arabian Sahara and the East African Sahara, have been active since ancient times and are not solely related to modern dust occurrences. The cause of their impact on Tehran could be attributed to the desiccation of internal lagoons and lakes. The changes in the frequency of fine-dust trajectories could not be solely explained by their connection with external sources. Instead, it appeared that the micro-particle movement system was striving to establish a deeper order, which was not solely influenced by changes in the origin and destination of the particles. Rather, the entry of fine particles into this movement system had undergone changes during their movement within the system. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear vibration of a Euler-Bernoulli nanobeam resting on a non-linear viscoelastic foundation is investigated. It is assumed that the nanobeam is subjected to a harmonic excitation that can be representative of an electrostatic field. The non-linear viscoelastic foundation is considered for both hardening and softening cases. By neglecting of the in-plane inertia, Eringen's nonlocal elasticity theory is used to model and derive the equation of motion of the nanobeam. Using the Galerkin method and the first mode shape, the obtained partial differential equation is reduced to the ordinary differential equation. Calculating the system's equilibrium points lead to heteroclinic bifurcation and the heteroclinic orbits are obtained. Then, using the Melnikov integral method, the chaotic motion of the system is studied analytically, and the safe region of the system is determined respect to the parametric space of the problem. When the viscoelastic foundation has a hardening characteristic, the chaotic behavior in the system does not occur. It has been observed that the use of nonlocal elasticity theory is necessary to investigate the chaotic behavior of nanobeam, and using the classical theory of elasticity may place the system in the chaotic region. [ABSTRACT FROM AUTHOR]

Introduction In today's world having multiple identities, national, local, international, religious, occupational, gender, professional, group, tribal, linguistic and so on is a part of the requirements of social life. This paper seeks to investigate the elements formulating Islamic-Iranian identity in the current period. This period has experienced strong progress in all aspects of science, art, and literature, which has in turn brought about new needs and problems. What is clear is the fact that with the advent of the twentieth century and its idiosyncrasies, human beings appear to be bewildered, frustrated, alienated from themselves. Philosophers, intellectuals and ordinary people are confronted with a state of confusion, asking themselves: Who am I? What am I? Why am I here? With an understanding of the complexity of multiple identities, the big question that remains is: What factors affect the Islamic Identity in the present period and how these elements contribute to formulation, prosperity, and decline of this identity? In reply to this question, we put this hypothesis to the test: Islamic Iranian identity under the influence of various interactive elements and numerous actors will be organized through self-organizing and its injuries are treated through self-healing. Material & Methods In this research, a comparative method is used in which political and social phenomena are compared to biological, technical and mathematical phenomena. In this paper we use the theory of chaos and complexity. Many scientists believe that twentieth century science will be known for only three theories: relativity, quantum mechanics and chaos theory, which refers to systems that, despite their irregularities, contain a latent regularity which express irregular, unpredictable, complicated and nonlinear behavior, and the system is believed to enjoy a pattern of ultimate discipline within all this chaos. Discussion of Results & Conclusions Identity making is a collective phenomenon in a way that everyone can have a role in shaping it. Community identity is like a living and dynamic system that continuously moves toward an endless excellence. We have argued in this paper that components of the Islamic-Iranian identity function not as a pyramid but rather as a unified network: 1- Self-similarity identity: Iranian identity, ranging from religion to politics and from the political parties to economic groups, is presented as a system made up of self-similarity components. Hence, our daily activities are like our identity construction. If Iranian identity structure experiences any crisis and injuries, these damages are also observed in micro and macro scales. 2- Self-Organization identity: Iranian Community regulates itself with no need for external factors. This organization is brought about as a result of the behavior of individual members and will continue to an infinite boundary. 3- The Butterfly Effect and Identity: Based on the theory of chaos and the Butterfly Effect, factors like individual behavior, individual thoughts and have a great impact on the whole structure of our identity. 4- Strange attractions and identity: Basically, identity and self-understanding is something fluid, fragmented, incomplete and changing. Because of its chaotic system, identity has nonlinear and non-repetitive behavior, and the relationships among the elements are not periodic or spot. Rather, due to the immense complexity of the next point of departure, identity behavior is not clear. 5- Iranian Islamic identity self-healing in dealing with the Western civilization: Iranian identity identifies the errors or injuries resulting from globalization and then works them out; identifies system malfunctions and initiates corrective policies and enforces them without disturbing the environment. Hence, these corrective measures may involve changes in a particular element or all the elements of identity. The remaining non-defective parts of the identity find their way to go on without the defective parts. In light of the above arguments, self-healing seems to be an important component of Islamic-Iranian identity. This identity is composed of some components which make up a unified system. Now that some elements of this identity have been challenged by other identities, its unaffected parts will remain dynamic and will go on to self-heal itself like sophisticated systems. In the new era, institutions such as universities and schools are inefficient in identity making, and scatter everyone to form a separated identity.

Introduction In today's world having multiple identities, national, local, international, religious, occupational, gender, professional, group, tribal, linguistic and so on is a part of the requirements of social life. This paper seeks to investigate the elements formulating Islamic-Iranian identity in the current period. This period has experienced strong progress in all aspects of science, art, and literature, which has in turn brought about new needs and problems. What is clear is the fact that with the advent of the twentieth century and its idiosyncrasies, human beings appear to be bewildered, frustrated, alienated from themselves. Philosophers, intellectuals and ordinary people are confronted with a state of confusion, asking themselves: Who am I? What am I? Why am I here? With an understanding of the complexity of multiple identities, the big question that remains is: What factors affect the Islamic Identity in the present period and how these elements contribute to formulation, prosperity, and decline of this identity? In reply to this question, we put this hypothesis to the test: Islamic Iranian identity under the influence of various interactive elements and numerous actors will be organized through self-organizing and its injuries are treated through self-healing. Material & Methods In this research, a comparative method is used in which political and social phenomena are compared to biological, technical and mathematical phenomena. In this paper we use the theory of chaos and complexity. Many scientists believe that twentieth century science will be known for only three theories: relativity, quantum mechanics and chaos theory, which refers to systems that, despite their irregularities, contain a latent regularity which express irregular, unpredictable, complicated and nonlinear behavior, and the system is believed to enjoy a pattern of ultimate discipline within all this chaos. Discussion of Results & Conclusions Identity making is a collective phenomenon in a way that everyone can have a role in shaping it. Community identity is like a living and dynamic system that continuously moves toward an endless excellence. We have argued in this paper that components of the Islamic-Iranian identity function not as a pyramid but rather as a unified network: 1- Self-similarity identity: Iranian identity, ranging from religion to politics and from the political parties to economic groups, is presented as a system made up of self-similarity components. Hence, our daily activities are like our identity construction. If Iranian identity structure experiences any crisis and injuries, these damages are also observed in micro and macro scales. 2- Self-Organization identity: Iranian Community regulates itself with no need for external factors. This organization is brought about as a result of the behavior of individual members and will continue to an infinite boundary. 3- The Butterfly Effect and Identity: Based on the theory of chaos and the Butterfly Effect, factors like individual behavior, individual thoughts and have a great impact on the whole structure of our identity. 4- Strange attractions and identity: Basically, identity and self-understanding is something fluid, fragmented, incomplete and changing. Because of its chaotic system, identity has nonlinear and non-repetitive behavior, and the relationships among the elements are not periodic or spot. Rather, due to the immense complexity of the next point of departure, identity behavior is not clear. 5- Iranian Islamic identity self-healing in dealing with the Western civilization: Iranian identity identifies the errors or injuries resulting from globalization and then works them out identifies system malfunctions and initiates corrective policies and enforces them without disturbing the environment. Hence, these corrective measures may involve changes in a particular element or all the elements of identity. The remaining non-defective parts of the identity find their way to go on without the defective parts. In light of the above arguments, self-healing seems to be an important component of Islamic-Iranian identity. This identity is composed of some components which make up a unified system. Now that some elements of this identity have been challenged by other identities, its unaffected parts will remain dynamic and will go on to self-heal itself like sophisticated systems. In the new era, institutions such as universities and schools are inefficient in identity making, and scatter everyone to form a separated identity.

This paper investigates the stochastic heating of electrons caused by Raman backscatter radiations during the interaction of a laser pulse with helium atoms by means of a parallel particle-in-cell (PIC) code. At different propagation times, the self-consistent laser pulse changes are investigated via the space-time Fourier transform of the transverse vector potential. It is demonstrated that, since ionization has a striking influence on the emission of Raman backscattered radiation, it also plays an important role in the threshold of electron stochastic heating. As demonstrated by the experiments, the Raman backscattered radiations are initiated by a strong initial noise when a laser pulse has a long rise time, 100 fs. Hence, the fundamental condition for the chaos threshold is satisfied sooner by examining ionization effects. In this manner, stochastic heating of the electrons is initiated more rapidly than if the laser pulse were emitted in the preplasma. Accordingly, in concurrence with the idea of chaos, the electrons acquire more energy via the stochastic mechanism in the field-ionized plasma.

In this paper a new method is introduced for studying time series of complex systems. This method is based on using the concept of entropy and Jensen-Shannon divergence. In this paper this method is applied to time series of billiard system and heart signals. By this method, we can diagnose the healthy and unhealthy heart and also chaotic billiards from non chaotic systems . The method can also be applied to other time series.

In this paper, we use the Euler method to introduce a discrete mutualism model with proportional harvesting rate and analyze its dynamics. Using the center manifold theorem, we show that the model is subjected to a period-doubling bifurcation. Also, using the Maximal Lyapunov exponent, we show that the model is chaotic and then use the feedback control method to control the chaos in this model.

The accurate and fast localization in the Internet of Things is an essential requirement in expanding the use of applications for these networks. Due to limited computing power of sensor nodes and the limited power capacity of these nodes, reducing computational complexity and reducing communication overhead in localization algorithms is critical. In this paper, a particle swarm optimization based algorithm is proposed for localization of sensor nodes in IoT. In general, trapping in local optima and the slow convergence rate are two main weaknesses of the classic PSO. In the proposed algorithm, using the chaos theory, trapping in local optima is prevented and convergence of the algorithm is improved. In addition, using the fractional derivatives, the particles convergence rate accelerates to the optimal solution. The performance evaluation of the algorithm is performed by its implementation on specific test functions. Simulation results exhibit the effectiveness of the proposed algorithm in localization of sensor nodes in IoT.

Artificial Bee Colony Algorithm(ABC) is one of the swarm intelligence optimization algorithms that is extensively used for the goals and applications static. Many practical, real-world applications, nevertheless, are dynamic. Thus we need to get used optimization algorithms that could be solved problems in dynamic environments as well. Dynamic optimization problems where change(s) may occur through the time. In this paper we proposed one approach based on chaotic ABC combined with explicit memory method, for solving dynamic optimization problems. In this proposed algorithm, we used the explicit memory for store the aging best solution for the maintaining diversity in the population. Use the aging best solution and diversity in environments helps the speed convergence in algorithm. The proposed approaches have been tested on Moving Peaks Benchmark. The Moving Peaks Benchmark is the suitable function for testing optimization algorithms in dynamic environments. The experimental study on a Moving Peaks Benchmark show that proposed approach has a superior performance in comparison with several other algorithms in dynamic environments.

This paper deals with forecasting the tax revenues of legal entities in Iran. For this purpose, the structural natures of time series of tax revenues for Iranian legal entities are detected. Based on the separation among the resources (government and NGOs), the linearity, nonlinearity, chaotic, and random behaviors are diagnosed via the Lyapunov exponential analysis. Using Box- Jenkins and Neural Networks models with different numbers of input, output, hidden layers, learning algorithm, learning rate and etc., the performance of each model are evaluated during the years of 1381- 1387. Finally, the optimal forecasting model is proposed as a multi input- multi output neural network structure with a novel algorithm. The performance of the proposed structure is evaluated during the years of 1388- 1393 in the forecasting process.

The very complex movements in the stock prices are usually taken as random or stochastic, but they may be produced by a deterministic data generating process. Chaos refers to the nonlinear dynamic deterministic process that generates a series, which appears like random, but has a long memory. In the Economics and Finance literature, stock prices are known to be random due to their complexities, and therefore being unpredictable. In this paper, we test for chaos in the stock prices using the data from the daily and weekly stock prices listed in the Tehran Exchange Market (TEPIX) in 1377-1382 (1998-2003). We apply three tests for chaos, namely; BDS, Lyaponov Exponent, and Neural Networks; to the residuals of linear (ARIMA) and nonlinear (GARCH) models. The BDS and the Neural Networks tests results show that there exists nonlinearity in the ARIMA residuals, but not in the GARCH residuals. However, the Lyaponove exponent test result is positive for all different dimensions indicating that the TEPIX is chaotic.

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.

Chaos theory is rather new in science, but, it is, in fact, rooted in ancients' perception of the world. The main idea is that although a complex system, such as world, seems to be generated by a random, and therefore, unpredictable process, it may run by a nonlinear deterministic process. Chaos theory has been applied to some Economic time series to see if they have an order, and, therefore, predictable. Some Economic time series, such as stock prices, look random, but, according to the chaos theory, they may come from a nonlinear deterministic process. If the data generating process is nonlinear, using traditional linear methods in estimation and forecasting can be misleading. Chaos theory is also applied to macroeconomic models. Some macroeconomic concepts, such as endogenous business cycles, can now be explained by the theory. In this paper, I try to review the chaos theory and its mathematical root for economists. Then, I will survey the Economic applications of the theory, and finally, will analyze different methods introduced for testing for chaos.

Evaluation Criteria for Different Versions of the Same Database the concept of information, during its development, is connected to the concept of entropy created by the 19th century termodynamics scholars. Information means, in this view point, order or negentropy. On the other hand, entropy is connected to the concepts as chaos and noise, which cause, in turn, disorder. In the present paper, the fore-told concepts and their interconnections are discussed from the different points of view.