Akademik Veri Yönetim Sistemi
Mediterranean Journal of Mathematics, cilt.22, sa.6, 2025 (SCI-Expanded)
A novel type of trajectory on semiflows, called asymptotically unpredictable, was proposed by Fen and Tokmak Fen (Commun Nonlinear Sci Numer Simul 134:108029, 2024). 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.