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New Types of Chaos and Non-Wandering Points in Topological Spaces
Issue:
Volume 3, Issue 6-1, December 2014
Pages:
1-6
Received:
7 July 2014
Accepted:
21 August 2014
Published:
2 September 2014
DOI:
10.11648/j.pamj.s.2014030601.11
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Abstract: In this paper, we will define a new class of chaotic maps on locally compact Hausdorff spaces called α-type chaotic maps defined by α-type transitive maps. This new definition coincides with Devaney's definition for chaos when the topological space happens to be a metric space. Furthermore, we will study new types of non-wandering points called α-type nonwandering points. We have shown that the α-type nonwandering points imply nonwandering points but not conversely. Finally, we have defined new concepts of chaotic on topological space. Relationships with some other type of chaotic maps are given.
Abstract: In this paper, we will define a new class of chaotic maps on locally compact Hausdorff spaces called α-type chaotic maps defined by α-type transitive maps. This new definition coincides with Devaney's definition for chaos when the topological space happens to be a metric space. Furthermore, we will study new types of non-wandering points called α-t...
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Two New Types of Chaotic Maps and Minimal Systems
Mohammed Nokhas Murad Kaki,
Sherko Hassan Abdurrahman
Issue:
Volume 3, Issue 6-1, December 2014
Pages:
7-12
Received:
5 September 2014
Accepted:
16 September 2014
Published:
17 September 2014
DOI:
10.11648/j.pamj.s.2014030601.12
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Abstract: In this paper, we introduce and study the relationship between two different notions of chaotic maps, namely topological α–chaotic maps, topological θ-chaotic maps and investigate some of their properties in two topological spaces (X, τα) and (X, τθ), τα denotes the α–topology(resp. τθ denotes the θ–topology) of a given topological space (X, τ). The two notions are defined by using the concepts of α-transitive map and θ-transitive map respectively Also, we define and study the relationship between two types of minimal mappings, namely, α - minimal mapping and θ-minimal mapping, The main results are the following propositions: 1). Every topologically α-chaotic map is a chaotic map which implies topologically θ- chaotic map, but the converse not necessarily true. 2). Every α-minimal map is a minimal map which implies θ- minimal map in topological spaces, but the converse not necessarily true.
Abstract: In this paper, we introduce and study the relationship between two different notions of chaotic maps, namely topological α–chaotic maps, topological θ-chaotic maps and investigate some of their properties in two topological spaces (X, τα) and (X, τθ), τα denotes the α–topology(resp. τθ denotes the θ–topology) of a given topological space (X, τ). Th...
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Uncertain Relations on a Finite Set and their Properties
Issue:
Volume 3, Issue 6-1, December 2014
Pages:
13-19
Received:
9 September 2014
Accepted:
13 October 2014
Published:
20 October 2014
DOI:
10.11648/j.pamj.s.2014030601.13
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Abstract: There exists some relationships which are difficult to be simply measured by “yes” or “no" in practice, and there must be a certain amount to indicate the extent of this relationship between the two elements. In this paper, the property of the uncertain relations is examined by the uncertainty theory. Firstly it offers the definition of uncertain relation and the concept of property index of the uncertain relation based on uncertain theory; secondly it gives the calculation method of the property index of the uncertain relation; finally, a simple example is presented to illustrate the method.
Abstract: There exists some relationships which are difficult to be simply measured by “yes” or “no" in practice, and there must be a certain amount to indicate the extent of this relationship between the two elements. In this paper, the property of the uncertain relations is examined by the uncertainty theory. Firstly it offers the definition of uncertain r...
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New Types of Chaotic Maps
Issue:
Volume 3, Issue 6-1, December 2014
Pages:
20-23
Received:
15 October 2014
Accepted:
20 October 2014
Published:
24 October 2014
DOI:
10.11648/j.pamj.s.2014030601.14
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Abstract: In this paper, we will study a new class of chaotic maps on locally compact Hausdorff spaces called Lambda -type chaotic maps and θ-type chaotic maps. The Lambda -type chaotic map implies chaotic map which implies θ-type chaotic map. Further, the definition of topological Lambda -type chaos implies John Tylar definition which implies topological θ-type chaos definition. Relationships with some other types of chaotic maps defined on topological spaces are given.
Abstract: In this paper, we will study a new class of chaotic maps on locally compact Hausdorff spaces called Lambda -type chaotic maps and θ-type chaotic maps. The Lambda -type chaotic map implies chaotic map which implies θ-type chaotic map. Further, the definition of topological Lambda -type chaos implies John Tylar definition which implies topological θ-...
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Catastrophic Types Depending on Degree of Non-Linearity
Mohammed Nokhas Murad Kaki
Issue:
Volume 3, Issue 6-1, December 2014
Pages:
24-27
Received:
2 December 2014
Accepted:
26 December 2014
Published:
27 December 2014
DOI:
10.11648/j.pamj.s.2014030601.15
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Abstract: In this paper, we present results on the projection of the folding part of the elementary catastrophe models on the control space to find stability and catastrophic phenomenon of the periodic solutions of some nonlinear differential equations (NLDE) by using methods of catastrophe theory. We have shown here, that the cusp and Butterfly types depend on the degree of nonlinear differential equations, and that the bifurcation can be classified as cusp or butterfly types catastrophe. Moreover, our aim, in this work, is to obtain periodic solutions of some nonlinear differential equation (NLDE) and to study the stability of these periodic solutions and the main result is the following proposition: The catastrophic Types depending on the degree of non-linear differential equation.
Abstract: In this paper, we present results on the projection of the folding part of the elementary catastrophe models on the control space to find stability and catastrophic phenomenon of the periodic solutions of some nonlinear differential equations (NLDE) by using methods of catastrophe theory. We have shown here, that the cusp and Butterfly types depend...
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