Homoclinical structure of the chaotic attractor

In the reference [Akhmet MU. Devaney chaos of a relay system. Commun Nonlinear Sci Numer Simulat 2009:14:1486-93.], a relay system was introduced, which admits a chaotic attractor with Devaney's ingredients. Now, we prove that the attractor consists of homo-clinic solutions. A simulation of the attractor is provided for a pendulum equation. Similar results for impulsive differential equations were announced in the plenary talk [Akhmet MU. Hyperbolic sets of impact systems. Dyn Contin Discrete Impuls Syst Set A Math Anal 2008:15(Suppl. S1):1-2. Proceedings of the 5th international conference on impulsive and hybrid dynamical systems and applications, Beijin: Watan Press: 2008.].


Nonautonomous transcritical and pitchfork bifurcations in impulsive/hybrid systems
Kashkynbayev, Ardak; Akhmet, Marat; Department of Mathematics (2016)
The main purpose of this thesis is to study nonautonomous transcritical and pitchfork bifurcations in continuous and discontinuous dynamical systems. Two classes of discontinuity, impulsive differential equations and differential equations with an alternating piecewise constant argument of generalized type, are addressed. Moreover, the Bernoulli equation in impulsive as well as hybrid systems is introduced. For the former one, the corresponding jump equation is chosen so that after Bernoulli transformation ...
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Zheltukhın, Kostyantyn (Informa UK Limited, 2020-10-01)
We study the discretization of Darboux integrable systems. The discretization is done using x-, y-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.
Heterologous expression, characterization, and optimization of production of alpha-galactosidase from aspergillus fumigatus in aspergillus sojae
Gürkök, Sümeyra; Ögel, Zümrüt Begüm; Bölükbaşı, Ufuk; Department of Biotechnology (2012)
α-Galactosidase is an exo-glycosidase that hydrolyses non-reducing, α-1,6-linked α-galactose units from oligosaccharides, galactomannans, and galactolipids. α-Galactosidase activity has biotechnological, industrial, and medical importance. α-Galactosidase from A. fumigatus IMI 385708, in particular, can catalyse unique hydrolysis and transgalactosylation reactions on polymeric substrates. In this study, α-galactosidase of the human pathogen A. fumigatus IMI 385708 was first produced in a GRAS organism, Aspe...
Zheltukhın, Kostyantyn (2021-01-01)
© 2021 K. Zheltukhin N. Zheltukhina. All Rights Reserved.We consider a discretization problem for hyperbolic Darboux integrable systems. In particular, we discretize continuous systems admitting x- and y-integrals of the first and second order. Such continuous systems were classified by Zhvber and Kostrigina. In the present paper, continuous systems are discretized with respect to one of continuous variables and the resulting semi-discrete system is required to be also Darboux integrable. To obtain such a d...
Forward-backward asymmetries in Lambda(b)->Lambda l(+)l(-) decay beyond the standard model
Alıyev, Tahmasıb; Savcı, Mustafa (Elsevier BV, 2005-03-07)
We study the doubly-polarized lepton pair forward-backward asymmetries in Lambda(b) --> Lambdae(+)e(-) decay using a general, model independent form of the effective Hamiltonian. We present the general expression for nine doubly-polarized forward-backward asymmetries. It is observed that, the study of the forward-backward asymmetries of the doubly-polarized lepton pair is a very useful tool for establishing new physics beyond the standard model. Moreover, the con-elation between forward-backward asymmetry a...
Citation Formats
M. Akhmet, “Homoclinical structure of the chaotic attractor,” COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, pp. 819–822, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48504.