Discovery of Fifth Nonlinear Region i.e. Quasi–Chaos in Erbium Doped Fiber Ring Lasers and its Implications

The discovery of fifth nonlinear region of operation i.e. quasi–chaos is confirmed in this paper after its recently reported two observations in loss and pumpmodulated Erbium doped fiber ring lasers.Quasi-chaos is apparently chaos but its time and physical phase space trajectories actually converge instead of diverging, even for widely separated initial conditions once the system numerical model is subjected to different initial conditions. However, it qualifies all qualitative tests of chaos and misleads the observer to consider it a pure chaos. Quasi–chaos is an exciting new discovery which adds fifth nonlinear region of operation after a century old notion of sensitive dependence on initial conditions discovery by Poincare.With the appearance of quasi–chaos, the chaos itself gets bifurcated now into pure and pseudo or quasi–chaos. Some earlier results in literature, especially the experimental one, have to be revisited now to determine their category. Quasi–chaos is observed presently only in forced chaotic oscillators, once additional sine wave is added to lasing loop with frequency not integral multiple of modulating signal frequency. The implications of this discovery,as discussed in this paper, are expected to be far reaching in all nonlinear science and chaos theory applications.