We discuss the emergence and destruction of complex, critical and completely chaotic attractors in a nonlinear system when subjected to a small parametric perturbation in trigonometric, hyperbolic or noise function forms. For this purpose, a hybrid optical bistable system, which is a nonlinear physical system, has been chosen for investigation. We show that the emergence of new attractors is responsible for transients in many trajectories obeying power-law decay. The effect of perturbation on certain critical bifurcations such as period-2, onset of chaos, chaotic attractor with less complexity etc., has been studied and characterized using certain statistical features. Further, the effect of Gaussian noise with other types of perturbation has also been studied.

We wish to report the occurrence of vibrational resonance in certain discrete systems like sine square map and sine circle map, in a unique fashion, comprising of multiple resonant peaks which pave the way for enrichment. As the systems of our choice are capable of exhibiting vibrational resonance behaviour unlike the earlier reports, they are taken for investigation and the necessary numerical and analytical results are presented. Further, we study the effect of external forcing on various attractors of these systems with appropriate bifurcation and Lyapunov exponent diagrams.