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The chaotic dynamics in a commensurate fractional-order nonlinear financial system is studied from the time-domain point of view. Through obtaining and analyzing all equilibrium points of the financial system, the necessary condition for the existence of chaotic attractors in the system is derived via the stability theory of fractional-order system. It has been found that chaos is yielded with lowest order 2.55 in the fractional-order financial system. Meanwhile, a reliable binary discriminant for chaos (called "0-1" test) is utilized to detect the chaos presence in the system dynamics. The validation of theory analysis and the effectiveness of the proposed method are demonstrated by the simulation results. [ABSTRACT FROM AUTHOR]

The heating steam is an important secondary energy, so it is of great significance to predict the required steam load in the future hours, which is important for the thermal power plant to provide users with high quality heat load securely and economically. Steam load time series proves to be with chaos characteristics. According to Takens theorem, delay time and embedding dimension are calculated respectively using C-C method and Cao method, and the steam load time series is reconstructed in phase space, and then the steam load forecasting model is established using least squares support vector machine (LSSVM). A SA_WPSO algorithm (improved particle swarm optimization (PSO) with simulated annealing algorithm (SA)) is proposed to implement the optimization of LSSVM parameters. The simulation results show that the method can achieve good prediction results. [ABSTRACT FROM AUTHOR]

A chaotic time series hybrid forecasting method based on wavelet transform, least squares support vector machine (LSSVM) optimized by particle swarrn optimization (PSO) and generalized au-toregressive conditional heteroscedasticity (GARCH) is proposed. Firstly, the chaotic time series is decomposed and reconstructed into approximate series and detailed series. Secondly, the approximate series future values are predicted by PSO-LSSVM model; while the detailed series future values are forecasted by GARCH model. Finally, the sum of the approximate and detailed series future values is used as the final forecasting values. Two chaotic time series, namely, Mackey-Glass and variable-parameter Logistic, are used to evaluate the performance. The results imply that the proposed method can provide more accurate results, which demonstrates the validity of this method. [ABSTRACT FROM AUTHOR]

In order to reduce amount of computation, speed up convergence and restrain premature phenomena of quantum evolutionary algorithm, a hybrid chaotic quantum evolutionary algorithm is presented. The algorithm uses the chaotic initialization method to generate initial population that have better diversity, the simple quantum rotation gate to update non-optimal individuals of population to reduce amount of computation, and the hybrid chaotic search strategy to speed up its convergence and enhance its global search ability. A large number of tests show that the proposed algorithm has higher convergence speed and better optimizing ability than quantum evolutionary algorithm, real-coded quantum evolutionary algorithm and hybrid quantum genetic algorithm. Tests also show that when chaos is introduced to quantum evolutionary algorithm, the hybrid chaotic search strategy is superior to the carrier chaotic strategy, and has better comprehensive performance than the chaotic mutation strategy in most of cases. The proposed algorithm is the only one all of whose tests are convergent, and is easily implemented and applied in practice. It is satisfied in solving traffic signal timing optimization problem of urban road. [ABSTRACT FROM AUTHOR]

The problem of impulsive synchronous control of unified chaotic systems with parameter uncertainty and variable delays is studied. On the case that the master system's delay is different from that of the slave system, sufficient conditions for their uniform asymptotical synchronization are developed by employing the Lyapunov stability theory and matrix inquality techniques, and the impulsive controllers with respect to delays and initial value of systems are designed. Finally, the validity of the obtained results is shown by a numerical example and its simulation. [ABSTRACT FROM AUTHOR]