2024/05/10 by Mehmet Onur Fen, Fen, Mehmet Onur, Fatma Tokmak Fen +1
Computer Science · #34C60 #39A05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Control Systems and Analysis
paper · pdf · doi:10.48550/arxiv.2405.06803
openalex publication_date 2024/05/10 · openalex created_date 2024/05/15 · openalex updated_date 2026/07/28
A novel type of trajectory on semiflows, called asymptotically unpredictable, was proposed by Fen and Tokmak Fen [15]. The presence of sensitivity, which is an indispensable feature of chaotic dynamics, is a crucial property that arises from such trajectories. In the present paper, we show the existence and uniqueness of asymptotically unpredictable solutions for quasilinear systems with delay making benefit of the contraction mapping principle. Additionally, we introduce the notion of an asymptotically unpredictable sequence. It is verified that there exist asymptotically unpredictable sequences which are not unpredictable. Discrete-time equations possessing asymptotically unpredictable orbits are also under investigation. Examples of continuous-time and discrete-time systems with asymptotically unpredictable solutions are provided.