Generation of amplitude death and rhythmogenesis in coupled hidden attractor system with experimental demonstration

Third-order nonlinear dynamical systems with attractors (one with no fixed point and the other with a stable fixed point) are conjugately coupled. It is observed that the combined system gives rise to nontrivial fixed points, and the corresponding long-time dynamics leads to amplitude death. On the other hand, if the coupled system starts from the neighborhood of these generated fixed points, there exists a very novel path to the generation of oscillations. Such a phenomenon is called rhythmogenesis. The characterization of such dynamics is done with the help of bifurcation diagrams and Lyapunov exponents. Another important outcome is an observed bifurcation with respect to the initial condition variation. This last phenomenon may be attributed to the fact that usual route to chaos is absent in the uncoupled system. In the second part of our paper, we have constructed the electronic circuit pertaining to the coupled system, collected the data via NI 6009 DAC, and have shown the existence of the amplitude death experimentally. The case of rhythmogenesis is done similarly, which only requires an extra circuit to fix the initial condition, and was devised in our earlier paper. It has been used to construct a new circuit to detect rhythmogenesis.