74 citations · 195 across the 43 of their papers we have counts for
7 papers · 1 filter
Unpredictable solutions of differential equations
Marat Akhmet, Mehmet Onur Fen
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demo…
Periodic motions generated from non-autonomous grazing dynamics
Marat Akhmet, Aysegul Kivilcim
This paper examines impulsive non-autonomous systems with grazing periodic solutions. Surfaces of discontinuity and impact functions of the systems are not depending on the time va…
Poincaré chaos and unpredictable functions
Marat Akhmet, Mehmet Onur Fen
The results of this study are continuation of the research of Poincaré chaos initiated in papers (Akhmet M, Fen MO. Commun Nonlinear Sci Numer Simulat 2016;40:1-5; Akhmet M, Fen MO…
Replication of Li-Yorke Chaos Near a Homoclinic Orbit
Marat Akhmet, Michal Fečkan, Mehmet Onur Fen +1
We prove the presence of chaos near a homoclinic orbit in the modified Li-Yorke sense [10] by implementing chaotic perturbations. A Duffing oscillator is considered to show the eff…
Existence of Unpredictable Solutions and Chaos
Marat Akhmet, Mehmet Onur Fen
In paper [1] unpredictable points were introduced based on Poisson stability, and this gives rise to the existence of chaos in the quasi-minimal set. This time, an unpredictable fu…
Unpredictable Points and Chaos
Marat Akhmet, Mehmet Onur Fen
It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing defini…