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1. Degenerate Hopf bifurcations and the formation mechanism of chaos in the Qi 3-D four-wing chaotic system

Creator:
Liang, Hongtao, Tang, Yanxia, Li, Li, Wei, Zhouchao, and Wang, Zhen
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
four-wing chaotic attractors, Lyapunov coefficient, degenerate Hopf bifurcations, and period-doubling cascade
Language:
English
Description:
In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras

Creator:
Kalina, Martin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
lattice effect algebra, center, atom, and Mac Neille completion
Language:
English
Description:
If element z of a lattice effect algebra (E,⊕,0,1) is central, then the interval [0,z] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕. It is a known fact that if the set C(E) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C(E) in E equals to the top element of E, then E is isomorphic to a subdirect product of irreducible effect algebras (\cite{R2}). This means that if there exists a MacNeille completion E^ of E which is its extension (i.e. E is densely embeddable into E^) then it is possible to embed E into a direct product of irreducible effect algebras. Thus E inherits some of the properties of E^. For example, the existence of a state in E^ implies the existence of a state in E. In this context, a natural question arises if the MacNeille completion of the center of E (denoted as MC(C(E))) is necessarily the same as the center of E^, i.e., if MC(C(E))=C(E^) is necessarily true. We show that the equality is not necessarily fulfilled. We find a necessary condition under which the equality may hold. Moreover, we show also that even the completeness of C(E) and its bifullness in E is not sufficient to guarantee the mentioned equality.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public