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Asymptotically Unpredictable Solutions of Quasilinear Impulsive Systems with Regular Discontinuity Moments
Mehmet Onur Fen, Fatma Tokmak Fen
The notion of asymptotic unpredictability was recently introduced in (Commun. Nonlinear Sci. Numer. Simul. 134, 108029, 2024) for semiflows. Likewise unpredictable trajectories, as…
Modulo periodic Poisson stable solutions of dynamic equations on a time scale
Fatma Tokmak Fen, Mehmet Onur Fen
The existence, uniqueness, and asymptotic stability of modulo periodic Poisson stable solutions of dynamic equations on a periodic time scale are investigated. The model under inve…
Unpredictability in Perturbed Quasilinear Systems with Regular Moments of Impulses
Mehmet Onur Fen, Fatma Tokmak Fen
It is rigorously proved that quasilinear impulsive systems possess unpredictable solutions when a perturbation generated by an unpredictable sequence is applied. The existence, uni…
A randomly determined unpredictable function
Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
In this paper, we construct a new unpredictable function. Our approach is based on adapting the concept of symbolic dynamics to introduce a map on the space of infinite sequences g…
Dynamics Motivated by Sierpinski Fractals
Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
Fatou-Julia iteration (FJI) is an effective instrument to construct fractals. Famous Julia and Mandelbrot sets are strong confirmations of this. In the present study, we use the pa…
Finding Dynamics for Fractals
Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
The famous Laplace's Demon is not only of strict physical determinism, but also related to the power of differential equations. When deterministically extended structures are taken…