Research paperDynamic bifurcation and strange nonchaos in a two-frequency parametrically driven nonlinear oscillator

- The dynamics of two frequency parametrically driven nonlinear oscillator is explored.
- A new dynamics in the slow passage effect called strange nonchaotic delay is identified.
- A hitherto unknown route for the birth of strange nonchotic attractor is identified.
- The mechanism of the new route for the birth of strange nonchaotic attractor is studied using Rational Approximation theory.

A periodically forced series LCR circuit with Chua's diode as a nonlinear element exhibits slow passage through Hopf bifurcation. This slow passage leads to a delay in the Hopf bifurcation. The delay in this bifurcation is a unique quantity and it can be predicted using various numerical analysis. We find that when an additional periodic force is added to the system, the delay in bifurcation becomes chaotic which leads to an unpredictability in bifurcation delay. Further, we study the bifurcation of the periodic delay to chaotic delay in the slow passage effect through strange nonchaotic delay. We also report the occurrence of strange nonchaotic dynamics while varying the parameter of the additional force included in the system. We observe that the system exhibits a hitherto unknown dynamical transition to a strange nonchaotic attractor. With the help of Lyapunov exponent, we explain the new transition to strange nonchaotic attractor and its mechanism is studied by making use of rational approximation theory. The birth of SNA has also been confirmed numerically, using Poincaré maps, phase sensitivity exponent, the distribution of finite-time Lyapunov exponents and singular continuous spectrum analysis.