E-mail
marat@metu.edu.tr
Department
Department of Mathematics
ABSTRACT SIMILARITY, FRACTALS AND CHAOS
Akhmet, Marat; Alejaily, Ejaily Milad (2021-05-01)
A new mathematical concept of abstract similarity is introduced and is illustrated in the space of infinite strings on a finite number of symbols. The problem of chaos presence for the Sierpinski fractals, Koch curve, as w...
Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments
Akhmet, Marat; ARUĞASLAN ÇİNÇİN, Duygu; Tleubergenova, Madina; Nugayeva, Zakhira (2021-03-01)
This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant arg...
Shunting inhibitory cellular neural networks with strongly unpredictable oscillations
Akhmet, Marat; Seilova, Roza; Tleubergenova, Madina; Zhamanshin, Akylbek (Elsevier BV, 2020-10-01)
The paper considers a new type of solutions for shunting inhibitory cellular neural networks (SICNNs), strongly unpredictable oscillations. The conditions for the existence, uniqueness and stability of the solutions are de...
Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks
Akhmet, Marat; Tleubergenova, Madina; Nugayeva, Zakhira (2020-10-01)
In this paper, unpredictable oscillations in Hopfield-type neural networks is under investigation. The motion strongly relates to Poincare chaos. Thus, the importance of the dynamics is indisputable for those problems of a...
Unpredictable Solutions of Linear Impulsive Systems
Akhmet, Marat; Tleubergenova, Madina; Fen, Mehmet Onur; Nugayeva, Zakhira (2020-10-01)
We consider a new type of oscillations of discontinuous unpredictable solutions for linear impulsive nonhomogeneous systems. The models under investigation are with unpredictable perturbations. The definition of a piecewis...
Quasilinear differential equations with strongly unpredictable solutions
Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (2020-01-01)
The authors discuss the existence and uniqueness of asymptotically stable unpredictable solutions for some quasilinear differential equations. Two principal novelties are in the basis of this research. The first one is tha...
Nonautonomous Bifurcations in Nonlinear Impulsive Systems
Akhmet, Marat; Kashkynbayev, Ardak (Springer Science and Business Media LLC, 2020-01-01)
In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with num...
Domain-Structured Chaos in a Hopfield Neural Network
Akhmet, Marat; Alejaily, Ejaily Milad (World Scientific Pub Co Pte Lt, 2019-12-30)
In this paper, we provide a new method for constructing chaotic Hopfield neural networks. Our approach is based on structuring the domain to form a special set through the discrete evolution of the network state variables....
Generation of fractals as Duffing equation orbits
Akhmet, Marat; Fen, Mehmet Onur; Alejaily, Ejaily Milad (AIP Publishing, 2019-05-01)
Dynamics are constructed for fractals utilizing the motion associated with Duffing equation. Using the paradigm of Fatou-Julia iteration, we develop iterations to map fractals accompanied with a criterion to ensure that th...
Extension of sea surface temperature unpredictability
Akhmet, Marat; Fen, Mehmet Onur; Alejaily, Ejaily Milad (Springer Science and Business Media LLC, 2019-02-01)
The sea surface temperature (SST) variability is clearly affected by global climate patterns, which involve large-scale ocean-atmosphere fluctuations similar to the El Nino-Southern Oscillation (ENSO). We give mathematical...
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