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In this paper, adaptive bacterial foraging algorithms and their application to solve real world problems is presented. The constant step size in the original bacterial foraging algorithm causes oscillation in the convergence graph where bacteria are not able to reach the optimum location with large step size, hence reducing the accuracy of the final solution. On the contrary, if a small step size is used, an optimal solution may be achieved, but at a very slow pace, thus affecting the speed of convergence. As an alternative, adaptive schemes of chemotactic step size based on individual bacterium fitness value, index of iteration and index of chemotaxis are introduced to overcome such problems. The proposed strategy enables bacteria to move with a large step size at the early stage of the search operation or during the exploration phase. At a later stage of the search operation and exploitation stage where the bacteria move towards an optimum point, the bacteria step size is kept reducing until they reach their full life cycle. The performances of the proposed algorithms are tested with various dimensions, fitness landscapes and complexities of several standard benchmark functions and they are statistically evaluated and compared with the original algorithm. Moreover, based on the statistical result, non-parametric Friedman and Wilcoxon signed rank tests and parametric t-test are performed to check the significant difference in the performance of the algorithms. The algorithms are further employed to predict a neural network dynamic model of a laboratory-scale helicopter in the hovering mode. The results show that the proposed algorithms outperform the predecessor algorithm in terms of fitness accuracy and convergence speed.