E-mail
marat@metu.edu.tr
Department
Department of Mathematics
Scopus Author ID
Web of Science Researcher ID
Dynamics of Shunting Inhibitory Cellular Neural Networks with Variable Two-Component Passive Decay Rates and Poisson Stable Inputs
Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (2022-06-01)
Shunting inhibitory cellular neural networks with continuous time-varying rates and inputs are the focus of this research. A new model is considered with compartmental passive decay rates which consist of periodic and Pois...
Unpredictability in Markov chains
Akhmet, Marat (2022-01-01)
We have formalized realizations of Markov chains as conveniently constructed sequences, and explained, why the random dynamics admits the unpredictability, the concept introduced in our papers previously. The method of the...
Unpredictable Solutions of Impulsive Quasi-Linear Systems
Akhmet, Marat; Tleubergenova, Madina; Nugayeva, Zakhira (2022-01-01)
© 2022. L&H Scientific Publishing, LLC. All Rights Reserved.The impulsive differential equations with unpredictable perturbations are under investigation. The definition of the discontinuous unpredictable function with the...
Abstract Hyperbolic Chaos
Akhmet, Marat (2022-01-01)
The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbolic dynamics paradigm is realized in a new...
Modular Chaos for Random Processes
Akhmet, Marat (2022-1-01)
In the present paper, an essential generalization of the symbolic dynamics is considered. We apply the notions of abstract self-similar sets and the similarity map for a chaos introduction, which orbits are expanded among ...
Modulo Periodic Poisson Stable Solutions of Quasilinear Differential Equations
Akhmet, Marat; Zhamanshin, Akylbek (2021-11-01)
In this paper, modulo periodic Poisson stable functions have been newly introduced. Quasilinear differential equations with modulo periodic Poisson stable coefficients are under investigation. The existence and uniqueness ...
Abstract similarity, fractals and chaos
Akhmet, Marat (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; 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
Alejaily, Ejaily Milad; Akhmet, Marat (2021-01-01)
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 through imposing conditions which govern a relation between...
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