Bifurcation and hyperchaos from a class B tri-laser system

This paper presents a novel delayed double-ring anti-phase-coupling class B tri-laser system. Subsequently, this work creates a hyperchaotic laser transmitter, after which it provides a comprehensive analysis of its theoretical model, including six infinite-dimension rate equation sets and corresponding numeric results. We qualitatively investigate the dynamic behaviors, including the existence and stability of steady states, as well as the occurrence and suppression of bifurcation, chaos, and hyperchaos. We expound on how both delayed time and anti-phase-coupling effects influence the tri-laser system's behavior and lead to chaotic and hyperchaotic phenomena. We also analyze instability and multi-stability according to the nonlinear function in theory and find that multi-stability exists in an unstable region. The investigation of the tri-laser configuration provides insights into the tri-laser structure that plays a special role in the chaotic system. Simultaneously, our numeric simulation demonstrates the existence of instability via a typical nonlinear curve diagram and the existence of multi-stability via a set of quasiperiodic attractors. The system exhibits a rich variety of nonlinear dynamic behaviors, including hyperchaos, chaos, period 1, period 3, and coexistent scenarios, and following a route to chaos via bifurcation. The corresponding dynamics are identified and characterized using Lyapunov exponents. Chaos control is successfully achieved, yielding quasiperiods such as periods 3, 6, and 12, thereby steering the system away from chaos. The results provide valuable references for the study of chaotic transmitters, laser technology, hyperchaos, and their applications.