A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection behavior.Thes
e points also show the bifurcation behavior as parameters of the system vary. These perpetual points are useful for locating the hidden oscillating attractors as well as co-existing attractors. Results show that these points are important for better understanding of transient dynamics in the phase space. The existence of these points confirms whether a system is dissipative or not. Various examples are presented, and results are discussed analytically as well as numerically.
