Nonexistence of observable chaos and its robustness in strongly monotone dynamical systems

2022/03/06 by Wang, Yi, Yao, Jinxiang
Engineering · Mathematics · #Stability and Controllability of Differential Equations #Mathematical Dynamics and Fractals #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2203.02983

Abstract

For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent λ_max>0 holds on a shy set in the measure-theoretic sense. This exhibits that strongly monotone dynamical systems admit no observable chaos, the notion of which was formulated by L.S. Young. We further show that such phenomenon of no observable chaos is robust under the C¹-perturbation of the systems.

Related

• Decidability of chaos for some families of dynamical systems
• On the nonchaotic nature of monotone dynamical systems
• Robust chaos with prescribed natural invariant measure and Lyapunov exponent
• Inheriting of chaos in nonautonomous dynamical systems
• Stability Analysis of Monotone Systems via Max-separable Lyapunov\n Functions