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Biogeography-based optimization algorithm (BBO) realizes the information circulation and sharing by using the species migration among habitats and achieves the global optimization by improving habitat adaptability. Based on the population adaptive migration mechanism, a chaotic biogeography-based optimization (CBBO) algorithm is proposed by combining the chaotic mapping strategy and the BBO optimal migration model. Simulation experiments are carried out to compare the optimization performances of the typical chaotic mapping methods on the function optimization problems. The simulation results and analysis show that CBBO algorithm has good optimization performance. The combination of migration model and chaotic map close to the natural law has higher optimization precision and faster convergence velocity. [ABSTRACT FROM AUTHOR]

The artificial bee colony (ABC) algorithm is a simple and effective optimization algorithm that can be applied to solve many real-world optimization problems. In this paper, an improved artificial bee colony algorithm, named IABC, is proposed. In this algorithm, a new search equation for onlooker bees is presented, in which the optimal and sub-optimal solutions are considered in the iteration process. In addition, for enhancing the global convergence, the initial population are generated by using a chaotic system and an opposition-based method. Furthermore, for improving the global convergence speed of our algorithm, a chaotic search is adopted in the best solution of the current iteration. Experimental results tested on 20 benchmark functions show that the IABC algorithm is far better than the basic ABC algorithm and other three improved ABC algorithms on the tested problems. [ABSTRACT FROM AUTHOR]

The basic dynamic properties of a four dimensional hyperchaotic system are investigated in this paper. More precisely, the stability of equilibrium point of hyperchaotic system is studied by means of nonlinear dynamics theory. We analyses the existence and stability of Hopf bifurcation, and the formulas for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. In addition, a sliding mode controller is designed and controlled the hyperchaotic system to any fixed point to eliminate the chaotic vibration by means of sliding mode method. Finally, the numerical simulations were presented to confirm the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

Chaotic cryptography has been widely studied in the last 20 years. A common issue in the design of several proposed chaos-based cryptosystems is the use of a single chaotic map in the encoding/decoding processes, fact which leads to a low level security. We present a new symmetric keystream image encryption scheme, in which three 2D chaotic maps, recently proposed by the authors, are used instead of a single chaotic map. Those maps are derived from some plans curves equations, their trigonometric forms ensuring a large key space. The proposed scheme has a bi-modular architecture, in which the pixels are shuffled via a random permutation generated by using a new efficient algorithm, and a diffusion stage, in which the pixels' values are altered using a new XOR- scheme. In order to evaluate the security of the proposed image encryption scheme, a standard analysis was carried out. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the problem of controlling chaos in a 3D ratio-dependent food chain system. Time-delayed feedback control method is applied to suppress chaos to unstable equilibria or unstable periodic orbits. By local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Some numerical simulations are presented to support theoretical predictions. Finally, main conclusions are drawn. [ABSTRACT FROM AUTHOR]

Based on a very special property of the shift map (Theorem 1), we believe that chaos should involve not only nearby points can diverge apart but also far apart points can get close to each other and these happen infinitely often. Therefore, we propose to call a continuous map f(x) from an infinite compact metric space (G, d) (with metric d) to itself chaotic if there exists a positive number δ such that for any point x and any nonempty open set V (not necessarily an open neighborhood of x) in G there is a point y in V such that limsupn→∞ d(fn(x), fn(y)) ≥ δ and liminfn→∞ d(fn(x), fn(y)) = 0. [ABSTRACT FROM AUTHOR]

Clustering is an important analysis tool employed in data statistics. Identification of the structure of large-scale data has become an increasingly important topic in data mining problem. We propose Gauss chaotic map particle swarm optimization (GaussPSO) method for clustering, which uses a Gauss chaotic map to adopt a random sequence with a random starting point as a parameter, the method relies on this parameter to update the positions and velocities of the particles. The Gauss chaotic map provides the significant chaos distribution to balance the exploration and exploitation capability of search process. This easy and fast function generates random seed processes, and further improves the performance of PSO due to its unpredictability. In the study, eight different clustering algorithms were extensively compared on six test data sets. The results indicate that the performance of the GaussPSO method is significantly better than the performance of other algorithms for data clustering problems. [ABSTRACT FROM AUTHOR]

Researchers are finding their way to solve the chaotic and uncertain problems using the extensions of classical fuzzy model. At present Interval Type-2 Fuzzy logic Systems (IT2-FLS) are extensively used after the thriving exploitation of Type-2 FLS. Fuzzy time series models have been used for forecasting stock and FOREX indexes, enrollments, temperature, disease diagnosing and weather. In this paper an integrated fuzzy time series model based on ARIMA and IT2-FLS is presented. The propose model will use ARIMA to select appropriate coefficients from the observed dataset. IT2-FLS is utilized here for forecasting the result with more accuracy and certainty. [ABSTRACT FROM AUTHOR]

This paper presents the study of the axial dual-spin spacecraft dynamics. These spacecraft are usually called gyrostats. The gyrostat is composed of two rigid bodies: an asymmetric platform and an axisymmetric rotor aligned with the platform principal axis. The dynamics of gyrostats without external torque is considered. The dynamics is described by using ordinary differential equations with Andoyer-Deprit canonical variables. For undisturbed motion, when the internal torque is equal to zero and the moments of inertia of the gyrostat are constant, the stationary solutions are found, and their stability is studied. Also we obtain general exact analytical solutions in terms of elliptic functions. These results can be interpreted as the development of the classical Euler case for a solid with additional degree of freedom - the relative rotation of bodies. Results of the study can be useful for the analysis of dual-spin spacecraft dynamics and for studying the chaotic behavior of the spacecraft. [ABSTRACT FROM AUTHOR]

This paper proposes a robust suppression sliding mode controller design for uncertain Duffing-Holmes chaotic systems. A form of time-varying second-order differential equation is organized to describe the dynamical system. Control system performance is proved robust against parametric uncertainties and external disturbances. The control input involves a discontinuous switching control input which is used to deal with the uncertainties and disturbances. Illustrative example is given. Input chattering is remarkably eliminated and trajectory tracking is effectively achieved. [ABSTRACT FROM AUTHOR]

This paper presents the advances of a research using a combination of recurrent and feed-forward neural networks for long term prediction of chaotic time series. It is known that point-to-point, long term prediction for chaotic time series is not possible; however, in this research we are looking for ways to build dynamical systems using artificial neural network, that contain the same characteristics as the unknown systems producing a time series. The created systems should be such that they have chaotic invariants similar to the ones presented in the time series. Being able to create such system, the bounds of the predictions may be defined. We present some general concepts related to chaos, dynamical systems and artificial neural networks and present one model that, if not able to predict yet, is able to autonomously oscillate in bounded limits and in a chaotic way. Some experimental results and future work is also presented. [ABSTRACT FROM AUTHOR]

In this paper, based on genetic algorithm (GA) and steepest descent method (SDM), we proposed a hybrid algorithm for the learning of neural network to identify the chaotic systems. The chaotic systems considered in this paper are the Duffing equation. An identification scheme of neural network trained by the proposed hybrid algorithm is used to identify the Duffing equation. Simulation results show that performance of the hybrid algorithm proposed in this paper is more efficient than those of other methods. [ABSTRACT FROM AUTHOR]