2016/01/25 by Pavel Kravetc, Kravetc, Pavel, Дмитрий Рачинский +3
Computer Science · Medicine · Physics and Astronomy · #Advanced Fiber Laser Technologies #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1601.06452
openalex publication_date 2016/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss a bifurcation scenario which creates periodic pulsating solutions in slow-fast delayed systems through a cascade of almost simultaneous Hopf bifurcations. This scenario has been previously associated with formation of pulses in a delayed model of mode-locked semiconductor lasers. In this work, through a case study of several examples, we establish that a cascade of Hopf bifurcations can produce periodic pulses, with a period close to the delay time, in population dynamics models and explore the conditions that ensure the realization of this scenario near a transcritical bifurcation threshold. We derive asymptotic approximations for the pulsating solution and consider scaling of the solution and its period with the small parameter that measures the ratio of the time scales. The role of competition for the realization of the bifurcation scenario is highlighted.