Department of Mathematics
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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...
Domain Structured Dynamics: Unpredictability, chaos, randomness, fractals, differential equations and neural networks
Akhmet, Marat (Institute of Physics Publishing (IOP), 2021-03-01)
Domain structured dynamics introduces a way for analysis of chaos in fractals, neural networks and random processes. It starts with newly invented abstract similarity sets and maps, which are in the basis of the abstract s...
Discontinuity, Nonlinearity, and Complexity
Akhmet, Marat; Alejaily, Ejaily Milad (2021-01-01)
© 2021 L&H Scientific Publishing, LLC. All rights reserved.We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated ...
Bifurcation Analysis of Wilson-Cowan Model with Singular Impulses
Akhmet, Marat; Çağ, Sabahattin (2021-01-01)
© 2021 L&H Scientific Publishing, LLC. All rights reserved.The paper concerns with Wilson-Cowan neural model. The main novelty of the study is that besides the traditional singularity of the model, we consider singular imp...
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...
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...
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...
Dynamics with Chaos and Fractals
Akhmet, Marat (Springer, London/Berlin , 2020-02-01)
Stands as the first book presenting theoretical background on the unpredictable point and mapping of fractals.Introduces the concepts of unpredictable functions, abstract self-similarity, and similarity map.Discusses unpre...
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...
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