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A chaotic orbit generated by a nonlinear system is irregular, aperiodic, unpredictable and has sensitive dependence on initial conditions. However, the chaotic trajectory is still not well enough to be a crypto system in digital secure communication. Therefore, we propose a Modified Logistic Map (MLM) and give a theoretical proof to show that the MLM is a chaotic map according to Devaney's definition. Based on the MLMs, we establish a Modified Logistic Hyper-Chaotic System (MLHCS) and apply MLHCS to develop a symmetric cryptography algorithm, Asymptotic Synchronization of Modified Logistic Hyper-Chaotic System (ASMLHCS). [ABSTRACT FROM AUTHOR]

Performance results for finding the best genetic algorithm for the complex real problem of optimal machinery equipment operation and predictive maintenance are presented. A genetic algorithm is a stochastic computational model that seeks the optimal solution to an objective function. A methodology calculation is based on the idea of measuring the increase of fitness and fitness quality evaluation with chaos theory principles applying within genetic algorithm environment. Fuzzy neural networks principles are effectively applied in solved manufacturing problems mostly where multisensor integration, real - timeness, robustness and learning abilities are needed. A modified Mamdani neuro-fuzzy system improves the interpretability of used domain knowledge. [ABSTRACT FROM AUTHOR]