14 papers
Anti-periodic Solutions of Quasilinear Impulsive Systems with Piecewise Constant Argument of Generalized Type
Fatma Tokmak Fen, Mehmet Onur Fen, Eman Bakır Ahmad Ajm
This study is devoted to anti-periodic solutions of quasilinear impulsive systems with piecewise constant argument of generalized type. We rigorously prove the existence and unique…
Homoclinic and Heteroclinic Trajectories of Differential Equations with Piecewise Constant Arguments of Generalized Type
Mehmet Onur Fen, Fatma Tokmak Fen
Quasilinear systems with piecewise constant arguments of generalized type are under investigation from the asymptotic point of view. The systems have discontinuous right-hand sides…
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…
Persistence and Doubling of Chaotic Attractors in Coupled 3-Cell Hopfield Neural Networks
Mehmet Onur Fen, Fatma Tokmak Fen
Two novel phenomena for unidirectionally coupled 3-cell Hopfield neural networks (HNNs) are investigated. The first one is the persistence of chaos, which means the permanency of s…
Period-Doubling Route to Chaos and Intermittency in a Hybrid Rössler Model
Mehmet Onur Fen, Fatma Tokmak Fen
A Rössler model perturbed with a piecewise constant function is investigated. The perturbation function used in the model is constructed by means of the logistic map. In the absenc…
Generation of Synchronous Unpredictable Oscillations by Coupled Hopfield Neural Networks
Mehmet Onur Fen, Fatma Tokmak Fen
A new criterion based on generalized synchronization is provided for the extension of unpredictable oscillations among coupled Hopfield neural networks (HNNs). It is shown that if…
A Novel Criterion for Unpredictable Motions
Fatma Tokmak Fen, Mehmet Onur Fen, Marat Akhmet
We demonstrate the extension of unpredictable motions in coupled autonomous systems with skew product structure in the case that generalized synchronization takes place. Sufficient…
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…
Unpredictable Solutions of Quasilinear Systems with Discontinuous Right-Hand Sides
Mehmet Onur Fen, Fatma Tokmak Fen
It is rigorously proved under certain assumptions that a quasilinear system with discontinuous right-hand side possesses a unique unpredictable solution. The discontinuous perturba…
Replication of Period-Doubling Route to Chaos in Coupled Systems with Delay
Mehmet Onur Fen, Fatma Tokmak Fen
In this study, replication of a period-doubling cascade in coupled systems with delay is rigorously proved under certain assumptions, which guarantee the existence of bounded solut…
Period-doubling route to chaos in driven impulsive systems
Mehmet Onur Fen, Fatma Tokmak Fen
In the present study, we investigate the dynamics of impulsive differential equations driven by a chaotic system. We rigorously prove that, likewise the drive, the response impulsi…
Homoclinical structure of SICNNs with rectangular input currents
Mehmet Onur Fen, Fatma Tokmak Fen
Shunting inhibitory cellular neural networks (SICNNs) with continuous as well as discontinuous external inputs are investigated. The descriptions of homoclinic and heteroclinic mot…
Homoclinic and Heteroclinic Motions in Hybrid Systems with Impacts
Mehmet Onur Fen, Fatma Tokmak Fen
In this paper, we present a method to generate homoclinic and heteroclinic motions in impulsive systems. We rigorously prove the presence of such motions in the case that the syste…
SICNNs with Li-Yorke Chaotic Outputs on a Time Scale
Mehmet Onur Fen, Fatma Tokmak Fen
In the present study, we investigate the existence of Li-Yorke chaos in the dynamics of shunting inhibitory cellular neural networks (SICNNs) on time scales. It is rigorously prove…