Dynamics in an anti-phase delayed time coupled class-B laser system – Stability, bistability, bifurcation, and a route to hyperchaos

Abstract

An anti-phase delayed time coupled class-B laser system was presented to produce a nonlinear optical oscillator, or a bistable device, or a hyperchaotic transmitter. Bistability operated in the system was theoretically predicted in both mathematics and physics, and was numerically simulated to demonstrate by a typical bistable curve diagram. We investigated the stability of the equilibrium point, and bifurcation or limit cycles of the system as a function of the coupling strength and the delayed time. Our theory revealed that the switching function identified as the anti-phase mechanism guided the system from regular to complex behavior, and was numerically simulated to demonstrate by a typical switching wave diagram. We also displayed a quasi-periodic route to chaos and hyperchaos by adding the coupling strength, where hyperchaos was diagnosed by its corresponding two positive Lyapunov exponents. We carried out an analysis of the periodic oscillation frequency and bifurcation while the critical coupling strength is found. Our analysis of the Hopf bifurcation controlled by the delayed time, it was found how the different critical delayed time led to bifurcation processes. A display of dynamic behavior was carried out while the system exhibited some typical nonlinear dynamic behaviors, such as chaos, hyperchaos and quasi-period as well as coexistent scenarios. We also given a route to chaos through a quasi-period and a route to a quasi-period away from chaos. The hyperchaotic four-scroll strange attractor was illustrated to be characterized by ergodicity, complexity and randomness. The result has a reference value for an optical bistable device, a hyperchaotic emitter, laser technology, and their applications.