Complex Dynamics and Synchronization in a System of Magnetically Coupled Colpitts Oscillators

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.