Nonlinear dynamics of coupled oscillators: State space energy approach

The presented contribution is motivated by some fundamental questions arising in theoretical analysis of communication systems with chaotic synchronization. Knowledge of principles of nonlinear dynamics and synthesis of chaotic attractors is found to be very important also for other potential applications, such as encryption by secure communication, modeling of nonlinear phenomena in power networks, etc. This provides a strong motivation for the current research on exploiting some new chaotic attractors and their implementations. In this paper, an electronic circuit was designed and built to confirm typical behavior of a class of nonlinearly coupled chaotic oscillators. It was explained theoretically, as well as demonstrated by computer simulation combined with laboratory experiments that some typical chaotic phenomena can appear as a consequence of irregular energy exchange between two coupled oscillators. In our experiments, the system consists of a 2-nd order nonlinear antidissipative subsystem nonlinearly coupled with a linear oscillator with dissipation.