Exploring sensitive dependence and transitivity to optimize travel time in chaotic systems
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Transitivity and sensitive dependence on initial conditions are the main characteristics of chaotic behavior. The latter one can be exploited so that small controlled perturbations in system parameters may imply a faster transfer in time from a desired start point to a neighborhood of a desired final state. In this study three targeting approaches are evaluated: The first one uses a geometric approach to find the proper perturbation which allows a faster transfer between two desired points; The second, an evolutionary algorithm called GEO (Generalized External Optimization), is adapted to search for optimized orbits; The third one, uses successive perturbations along the path in order to direct the orbits to the final desired point in a short time interval. These three methods are evaluated regarding performance and implementation complexity.