Poincare chaos for a hyperbolic quasilinear system
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This article is published in Miskolc Mathematical Notes.The article was published on 2019-01-01 and is currently open access. It has received 11 citations till now.read more
Citations
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Journal ArticleDOI
Shunting inhibitory cellular neural networks with strongly unpredictable oscillations
TL;DR: A new type of solutions for shunting inhibitory cellular neural networks (SICNNs), strongly unpredictable oscillations, is considered and the conditions for the existence, uniqueness and stability are determined.
Journal ArticleDOI
Quasilinear differential equations with strongly unpredictable solutions
TL;DR: Tleubergenova and Zhamanshin this paper proposed a cellular neural network with continuous/discrete time and singular perturbations, which was supported by the Scientific and Technological Research Council of Turkey.
Journal ArticleDOI
Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks
TL;DR: The concept of strongly unpredictable oscillations in Hopfield-type neural networks is a significant novelty of the present research, since the presence of chaos in each coordinate of the space state provides new opportunities in applications.
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Dynamics of Shunting Inhibitory Cellular Neural Networks with Variable Two-Component Passive Decay Rates and Poisson Stable Inputs
TL;DR: In this article , a new model with compartmental passive decay rates which consist of periodic and Poisson stable components is considered, where the first component guarantees the Poisson stability of the dynamics, and the second one causes irregular oscillations.
References
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Book
Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
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An introduction to chaotic dynamical systems
TL;DR: In this article, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.
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Period Three Implies Chaos
TL;DR: In this article, a generalized logistic equation was used to model the distribution of points of impact on a spinning bit for oil well drilling, as mentioned if this distribution is helpful in predicting uneven wear of the bit.
Journal ArticleDOI
Unpredictable points and chaos
Marat Akhmet,Mehmet Onur Fen +1 more
TL;DR: It is revealed that a special kind of Poisson stable point, which the authors call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set.
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Poincaré chaos and unpredictable functions
Marat Akhmet,Mehmet Onur Fen +1 more
TL;DR: By shaping the unpredictable function as well as Poisson function, the first step in the development of the theory of unpredictable solutions for differential and discrete equations is performed.