A chaotic oscillation generator based on mixed dynamics of adaptively coupled Kuramoto oscillators

Abstract

A chaotic oscillation generator based on the concept of mixed dynamics is implemented on the field programmable gate array (FPGA). This generator reproduces the dynamics of two adaptively coupled Kuramoto phase oscillators. It is experimentally shown that the generator exhibits oscillations corresponding to a chaotic attractor and a chaotic repeller (attractor in reversed time). We have shown that the chaotic attractor and the chaotic repeller intersect on a closed invariant set - a reversible core, which confirms the existence of the so-called mixed dynamics. It was found that for different values of the parameters of the generator, either ordinary dissipative chaos or mixed dynamics can be realized. It is shown that in the case of mixed dynamics the behavior of the trajectories in phase space becomes more complex and the spectral characteristics change towards a more uniform power distribution over the spectrum frequencies. The action of harmonic external force on the mixed dynamics of the generator is also investigated and it is shown that this leads to additional complexity of the dynamical behavior of the generator’s output signals.