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We numerically investigate the dynamics of a ring consisting of three unidirectionally coupled Erbium-Doped Fiber Lasers (EDLFs) without external pump modulation. The study focuses on the system behavior as the coupling strength is varied, employing a six-dimensional mathematical model that includes three variables for laser intensities and three variables for population inversions of all lasers. Our primary objective is to understand the system evolution towards chaos from a stable equilibrium in the ring, considering the impact of increasing coupling strength. To analyze the system’s behavior, we employ various techniques such as time series analysis, power spectra, Poincaré sections, bifurcation diagrams, and Lyapunov exponents. During the transition to chaos, the system undergoes a Hopf bifurcation and a series of torus bifurcations. An essential aspect of this study is the exploration of a rotating wave propagating along the ring, where the wave nature (periodic, quasiperiodic, or chaotic) depends on the coupling strength. Additionally, we observe the coexistence of periodic and chaotic orbits within a specific range of the coupling strength. However, for very strong coupling, this bistability disappears, resulting in a monostable system with a single limit cycle. This regime exhibits potential for applications that demand short laser pulses with a substantial increase in peak power, reaching nearly 20 times higher levels compared to the continuous mode when the lasers are uncoupled. This discovery holds particular importance for optical communication systems, especially considering the attenuation optical signals experience when transmitted over long distances.

We study the synchronous dynamics of three diffusively coupled erbium-doped fiber lasers (EDLFs) in the unidirectional ring configuration without external pump modulation. The dynamical behavior of the system is analyzed using time series, Fourier spectra, Poincaré sections, bifurcation diagrams, and Lyapunov exponents for different values of the coupling strength. For weak coupling, we observe a well-known route to chaos from a stable equilibrium through a Hopf bifurcation and a series of torus bifurcations as the coupling strength is increased. An interesting result is found for large values of the coupling strength, where the phase locking is close to zero. This allows a significant increase in the peak energy of the EDFLs pulses, i.e., above the coupling strength the lasers switch to a Q-switching mode with large-amplitude short pulses. This result allows us to propose a new method for increasing the laser pulse energy based on the control of the bistability by the rotating wave in the array of three unidirectionally ring-coupled EDFLs as a function of the coupling strength. In our system, we were able to increase the peak laser power by almost 20 times more than a continuous single EDFL.