We propose the use of a simple, cheap, and easy technique for the study of dynamic and synchronization of the coupled systems: effects of the magnetic coupling on the dynamics and of synchronization of two Colpitts oscillators (wireless interaction). We derive a smooth mathematical model to describe the dynamic system. The stability of the equilibrium states is investigated. The coupled system exhibits spectral characteristics such as chaos and hyperchaos in some parameter ranges of the coupling. The numerical exploration of the dynamics system reveals various bifurcations scenarios including period-doubling and interior crisis transitions to chaos. Moreover, various interesting dynamical phenomena such as transient chaos, coexistence of solution, and multistability (hysteresis) are observed when the magnetic coupling factor varies. Theoretical reasons for such phenomena are provided and experimentally confirmed with practical measurements in a wireless transfer.

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The losses in networks of Beninese Electrical Energy Company (SBEE) are very high and therefore constitute a concern for the operators. This work consisted in finding an optimal topology of a 41 nodes real network of SBEE by Modified Ant Colony Algorithms (MACA) in order to reduce the losses and ensure a continuous power supply to the customers in case of occurrence disturbances on any branch of this network. With technological breakthrough of Automation and Supervision Systems (SCADA), the operation of distribution networks can be ensured remotely in real time with the aim of minimizing losses, eliminating equipment overload and improving reliability. The criteria of technical performance improvement formulated under operating constraints are solved by Modified Ant Colony Algorithm (MACA) which is association of ant system and fuzzy logic on the Matlab platform. The best results obtained show the effectiveness and efficiency of this method. The SBEE's HVA networks can then be reconfigured automatically to significantly improve their continuity of supply and reliability. The improved results obtained after tests on a standard 33-nodes and a real 41 nodes networks show the robustness and accuracy of this MACA algorithm.