Multistability in a Single System with Hidden Attractors- Theory and Experiment

Existence of more than one attractor for a single nonlinear system and the corresponding generation of multistability is investigated both from the point of view of theory and experiment. The system under consideration is relatively a new one which possess a single stable fixed point but shows many characteristic features of attractors in phase space. It is shown that the change in the initial condition triggers a host of phenomena not observed before in any dynamical system. Change in the initial conditions enables a switch over from one attractor to the other. Our analysis clearly shows the changes in the Poincaré section and the mechanism of formation of unstable periodic orbits. We point out that in spite of these peculiarities, the model does not possess any standard route to bifurcation but one can visualize the change in the periodicity with respect to the parameters and its dependence on the initial conditions. In the next half of our paper we have constructed analogue electric circuit for the equation and have introduced a mechanism for the choice of initial condition with the help of relay in the circuit. These modified circuits were then used to simulate experimentally the sensitivity on the initial conditions and the transition from one to the other attractor.