2025/03/12 by Rami Katz, Katz, Rami, Giulia Giordano +3 · 1 citation
Computer Science · Mathematics · Medicine · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.2503.09155
openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28
We consider time-invariant nonlinear n-dimensional strongly 2-cooperative systems, that is, systems that map the set of vectors with up to weak sign variation to its interior. Strongly 2-cooperative systems enjoy a strong Poincare-Bendixson property: bounded solutions that maintain a positive distance from the set of equilibria converge to a periodic solution. For strongly 2-cooperative systems whose trajectories evolve in a bounded and invariant set that contains a single unstable equilibrium, we provide a simple criterion for the existence of periodic trajectories. Moreover, we explicitly characterize a positive-measure set of initial conditions which yield solutions that asymptotically converge to a periodic trajectory. We demonstrate our theoretical results using two models from systems biology, the n-dimensional Goodwin oscillator and a 4-dimensional biomolecular oscillator with RNA-mediated regulation, and provide numerical simulations that verify the theoretical results.