Dans les décennies à venir, des informations de position très précis a le potentiel de créer des applications révolutionnaires dans les domaines sociaux, médicaux, commerciaux et militaires. Ultra-Wideband (UWB) technologie est considéré comme un candidat potentiel pour permettre des capacités de localisation précises à travers le temps d'arrivée (TOA) télémétries. Au cours de la dernière décennie, les signaux chaotiques ont reçu significative d'attention en raison d'un certain nombre de caractéristiques intéressantes. Signaux chaotiques sont des signaux non périodiques, déterministes et aléatoires provenant de système dynamique non linéaire. Leur bonne auto-corrélation, faible corrélation croisée et la sensibilité aux conditions initiales rendent particulièrement adapté à des systèmes télémétries. Dans cette thèse, deux nouveaux algorithmes d'estimation multiutilisateur de TOA sont proposés avec une faible complexité et la robustesse de MUI. Le nombre d'utilisateurs pris en charge par ces deux algorithmes sont beaucoup plus grandes que les estimateurs de TOA actuelles. Cependant, l'utilisation de séquences d'étalement classique et impulsion contraignent l'amélioration des performances et la capacité du système. Pour briser la limite apportée par les signaux classiques, les signaux chaotiques sélectionnés sont utilisés comme impulsion séquences d'étalement ou impulsion à nos algorithmes proposés. Avec l'utilisation de signaux chaotiques, notre algorithme proposé non seulement obtient l'amélioration supplémentaire, mais aussi avec la capacité de soutenir plus grand nombre d'utilisateurs de comparaison avec son homologue en utilisant des signaux classiques.

This Ph.D. dissertation processes and analyzes signals from the neonatal intensive care units (NICUs) for the study of maturity, systemic infection (sepsis) and the influence of immunization in the premature newborn. A special attention is payed to the electroencephalography and the breathing signal. The former is often contaminated by several sources of noise, thus methods based on the signals decomposition and optimal noise cancellation, adapted to the characteristics of the immature EEG, were proposed and evaluated objectively on real and simulated signals. By means of the EEG and delta burst analysis, detected automatically by a proposed classifier, infant's maturation and the effects of vaccination are studied. Concerning the second signal, breathing, non-linear and fractal methods are adapted to evaluate maturity and sepsis. A robustness study of estimation methods is also conducted, showing that the Hurst exponent, estimated on respiratory variability signals, is a good detector of infection.

The introduced mineral deposit model (MDM) is the product of a trans-disciplinary study, based on Complexity and General Systems Theory. Both investigate the abstract organization of phenomena, independent of their substance, type, or spatial or temporal scale of existence. The focus of the research has been on giant, hydrothermal mineral deposits. They constitute <0.001% of the total number of deposits yet contain 70-85% of the world's metal resources. Giants are the definitive exploration targets. They are more profitable to exploit and less susceptible to fluctuations of the market. Consensus has it that the same processes that generate small deposits also form giants but those processes are simply longer, vaster, and larger. Heat is the dominant factor in the genesis of giant mineral deposits. A paleothermal map shows where the vast heat required to generate a giant has been concentrated in a large space, and even allows us to deduce the duration of the process. To generate a paleothermal map acceptable to the scientific community requires reproducibility. Experimentation with various approaches to pattern recognition of geochemical data showed that the AUTOCLUST algorithm not only gave reproducibility but also gave the most consistent, most meaningful results. It automatically extracts boundaries based on Voronoi and Delaunay tessellations. The user does not specify parameters; however, the modeller does have tools to explore the data. This approach is near ideal in that it removes much of the human-generated bias. This algorithm reveals the radial, spatial distribution, of gold deposits in the Lachlan Fold Belt of southeastern Australia at two distinct scales – repeating patterns every ~80 km and ~230 km. Both scales of patterning are reflected in the geology. The ~80 km patterns are nested within the ~230 km patterns revealing a self-similar, geometrical relationship. It is proposed that these patterns originate from Rayleigh-Bénard convection in the mantle. At the Rayleigh Number appropriate for the mantle, the stable planform is the spoke pattern, where hot mantle material is moving upward near the centre of the pattern and outward along the radial arms. Discontinuities in the mantle, Rayleigh-Bénard convection in the mantle, and the spatial distribution of giant mineral deposits, are correlative. The discontinuities in the Earth are acting as platforms from which Rayleigh-Bénard convection can originate. Shallow discontinuities give rise to plumelets, which manifest at the crust as repeating patterns ranging, from ~100 to ~1,000 km in diameter. Deeper discontinuities give rise to plumes, which become apparent at the crust as repeating patterns ranging from >1,000 to ~4,000 km in diameter. The deepest discontinuities give rise to the superplumes, which become detectable at the crust as repeating patterns ranging from >4,000 to >10,000 km in diameter. Rayleigh-Bénard convection concentrates the reservoir of heat in the mantle into specific locations in the crust; thereby providing the vast heat requirements for the processes that generate giant, hydrothermal mineral deposits. The radial spatial distribution patterns observed for gold deposits are also present for base metal deposits. At the supergiant Broken Hill deposit in far western New South Wales, Australia, the higher temperature Broken Hill-type deposits occur in a radial pattern while the lower temperature deposits occur in concentric patterns. The supergiant Broken Hill deposit occurs at the very centre of the pattern. If the supergiant Broken Hill Deposit was buried beneath alluvium, water or younger rocks, it would now be possible to predict its location with accuracy measured in tens of square kilometres. This predictive accuracy is desired by every exploration manager of every exploration company. The giant deposits at Broken Hill, Olympic Dam, and Mount Isa all occur on the edge of an annulus. There are at least two ways of creating an annulus on the Earth's surface. One is through Rayleigh-Bénard convection and the other is through meteor impact. It is likely that only 'large' meteors (those >10 km in diameter) would have any permanent impact on the mantle. Lesser meteors would leave only a superficial scar that would be eroded away. The permanent scars in the mantle act as ‘accidental templates’ consisting of concentric and possibly radial fractures that impose those structures on any rocks that were subsequently laid down or emplaced over the mantle. In southeastern Australia, the proposed Deniliquin Impact structure has been an 'accidental template' providing a 'line-of-least-resistance' for the ascent of the ~2,000 km diameter, offshore, Cape Howe Plume. The western and northwestern radial arms of this plume have created the very geometry of the Lachlan Fold Belt, as well as giving rise to the spatial distribution of the granitic rocks in that belt and ultimately to the gold deposits. The interplay between the templating of the mantle by meteor impacts and the ascent of plumelets, plumes or superplumes from various discontinuities in the mantle is quite possibly the reason that mineral deposits occur where they do.

The introduced mineral deposit model (MDM) is the product of a trans-disciplinary study, based on Complexity and General Systems Theory. Both investigate the abstract organization of phenomena, independent of their substance, type, or spatial or temporal scale of existence. The focus of the research has been on giant, hydrothermal mineral deposits. They constitute <0.001% of the total number of deposits yet contain 70-85% of the world's metal resources. Giants are the definitive exploration targets. They are more profitable to exploit and less susceptible to fluctuations of the market. Consensus has it that the same processes that generate small deposits also form giants but those processes are simply longer, vaster, and larger. Heat is the dominant factor in the genesis of giant mineral deposits. A paleothermal map shows where the vast heat required to generate a giant has been concentrated in a large space, and even allows us to deduce the duration of the process. To generate a paleothermal map acceptable to the scientific community requires reproducibility. Experimentation with various approaches to pattern recognition of geochemical data showed that the AUTOCLUST algorithm not only gave reproducibility but also gave the most consistent, most meaningful results. It automatically extracts boundaries based on Voronoi and Delaunay tessellations. The user does not specify parameters; however, the modeller does have tools to explore the data. This approach is near ideal in that it removes much of the human-generated bias. This algorithm reveals the radial, spatial distribution, of gold deposits in the Lachlan Fold Belt of southeastern Australia at two distinct scales – repeating patterns every ~80 km and ~230 km. Both scales of patterning are reflected in the geology. The ~80 km patterns are nested within the ~230 km patterns revealing a self-similar, geometrical relationship. It is proposed that these patterns originate from Rayleigh-Bénard convection in the mantle. At the Rayleigh Number appropriate for the mantle, the stable planform is the spoke pattern, where hot mantle material is moving upward near the centre of the pattern and outward along the radial arms. Discontinuities in the mantle, Rayleigh-Bénard convection in the mantle, and the spatial distribution of giant mineral deposits, are correlative. The discontinuities in the Earth are acting as platforms from which Rayleigh-Bénard convection can originate. Shallow discontinuities give rise to plumelets, which manifest at the crust as repeating patterns ranging, from ~100 to ~1,000 km in diameter. Deeper discontinuities give rise to plumes, which become apparent at the crust as repeating patterns ranging from >1,000 to ~4,000 km in diameter. The deepest discontinuities give rise to the superplumes, which become detectable at the crust as repeating patterns ranging from >4,000 to >10,000 km in diameter. Rayleigh-Bénard convection concentrates the reservoir of heat in the mantle into specific locations in the crust; thereby providing the vast heat requirements for the processes that generate giant, hydrothermal mineral deposits. The radial spatial distribution patterns observed for gold deposits are also present for base metal deposits. At the supergiant Broken Hill deposit in far western New South Wales, Australia, the higher temperature Broken Hill-type deposits occur in a radial pattern while the lower temperature deposits occur in concentric patterns. The supergiant Broken Hill deposit occurs at the very centre of the pattern. If the supergiant Broken Hill Deposit was buried beneath alluvium, water or younger rocks, it would now be possible to predict its location with accuracy measured in tens of square kilometres. This predictive accuracy is desired by every exploration manager of every exploration company. The giant deposits at Broken Hill, Olympic Dam, and Mount Isa all occur on the edge of an annulus. There are at least two ways of creating an annulus on the Earth's surface. One is through Rayleigh-Bénard convection and the other is through meteor impact. It is likely that only 'large' meteors (those >10 km in diameter) would have any permanent impact on the mantle. Lesser meteors would leave only a superficial scar that would be eroded away. The permanent scars in the mantle act as ‘accidental templates’ consisting of concentric and possibly radial fractures that impose those structures on any rocks that were subsequently laid down or emplaced over the mantle. In southeastern Australia, the proposed Deniliquin Impact structure has been an 'accidental template' providing a 'line-of-least-resistance' for the ascent of the ~2,000 km diameter, offshore, Cape Howe Plume. The western and northwestern radial arms of this plume have created the very geometry of the Lachlan Fold Belt, as well as giving rise to the spatial distribution of the granitic rocks in that belt and ultimately to the gold deposits. The interplay between the templating of the mantle by meteor impacts and the ascent of plumelets, plumes or superplumes from various discontinuities in the mantle is quite possibly the reason that mineral deposits occur where they do.

The introduced mineral deposit model (MDM) is the product of a trans-disciplinary study, based on Complexity and General Systems Theory. Both investigate the abstract organization of phenomena, independent of their substance, type, or spatial or temporal scale of existence. The focus of the research has been on giant, hydrothermal mineral deposits. They constitute <0.001% of the total number of deposits yet contain 70-85% of the world's metal resources. Giants are the definitive exploration targets. They are more profitable to exploit and less susceptible to fluctuations of the market. Consensus has it that the same processes that generate small deposits also form giants but those processes are simply longer, vaster, and larger. Heat is the dominant factor in the genesis of giant mineral deposits. A paleothermal map shows where the vast heat required to generate a giant has been concentrated in a large space, and even allows us to deduce the duration of the process. To generate a paleothermal map acceptable to the scientific community requires reproducibility. Experimentation with various approaches to pattern recognition of geochemical data showed that the AUTOCLUST algorithm not only gave reproducibility but also gave the most consistent, most meaningful results. It automatically extracts boundaries based on Voronoi and Delaunay tessellations. The user does not specify parameters; however, the modeller does have tools to explore the data. This approach is near ideal in that it removes much of the human-generated bias. This algorithm reveals the radial, spatial distribution, of gold deposits in the Lachlan Fold Belt of southeastern Australia at two distinct scales – repeating patterns every ~80 km and ~230 km. Both scales of patterning are reflected in the geology. The ~80 km patterns are nested within the ~230 km patterns revealing a self-similar, geometrical relationship. It is proposed that these patterns originate from Rayleigh-Bénard convection in the mantle. At the Rayleigh Number appropriate for the mantle, the stable planform is the spoke pattern, where hot mantle material is moving upward near the centre of the pattern and outward along the radial arms. Discontinuities in the mantle, Rayleigh-Bénard convection in the mantle, and the spatial distribution of giant mineral deposits, are correlative. The discontinuities in the Earth are acting as platforms from which Rayleigh-Bénard convection can originate. Shallow discontinuities give rise to plumelets, which manifest at the crust as repeating patterns ranging, from ~100 to ~1,000 km in diameter. Deeper discontinuities give rise to plumes, which become apparent at the crust as repeating patterns ranging from >1,000 to ~4,000 km in diameter. The deepest discontinuities give rise to the superplumes, which become detectable at the crust as repeating patterns ranging from >4,000 to >10,000 km in diameter. Rayleigh-Bénard convection concentrates the reservoir of heat in the mantle into specific locations in the crust; thereby providing the vast heat requirements for the processes that generate giant, hydrothermal mineral deposits. The radial spatial distribution patterns observed for gold deposits are also present for base metal deposits. At the supergiant Broken Hill deposit in far western New South Wales, Australia, the higher temperature Broken Hill-type deposits occur in a radial pattern while the lower temperature deposits occur in concentric patterns. The supergiant Broken Hill deposit occurs at the very centre of the pattern. If the supergiant Broken Hill Deposit was buried beneath alluvium, water or younger rocks, it would now be possible to predict its location with accuracy measured in tens of square kilometres. This predictive accuracy is desired by every exploration manager of every exploration company. The giant deposits at Broken Hill, Olympic Dam, and Mount Isa all occur on the edge of an annulus. There are at least two ways of creating an annulus on the Earth's surface. One is through Rayleigh-Bénard convection and the other is through meteor impact. It is likely that only 'large' meteors (those >10 km in diameter) would have any permanent impact on the mantle. Lesser meteors would leave only a superficial scar that would be eroded away. The permanent scars in the mantle act as ‘accidental templates’ consisting of concentric and possibly radial fractures that impose those structures on any rocks that were subsequently laid down or emplaced over the mantle. In southeastern Australia, the proposed Deniliquin Impact structure has been an 'accidental template' providing a 'line-of-least-resistance' for the ascent of the ~2,000 km diameter, offshore, Cape Howe Plume. The western and northwestern radial arms of this plume have created the very geometry of the Lachlan Fold Belt, as well as giving rise to the spatial distribution of the granitic rocks in that belt and ultimately to the gold deposits. The interplay between the templating of the mantle by meteor impacts and the ascent of plumelets, plumes or superplumes from various discontinuities in the mantle is quite possibly the reason that mineral deposits occur where they do.

Η Κβαντική Πληροφορία είναι μια ιδιότητα των κβαντικών συστημάτων που σχετίζεται με την κβαντομηχανική επαλληλία και την συσχέτιση των συστημάτων σε Ενδιαπλοκή. Λόγω της αλληλεπίδρασης με το κλασικό περιβάλλον η Ενδιαπλοκή χάνεται ταχύτατα με συνέπεια να περιορίζεται δραματικά η πρακτική της χρησιμότητα. Πραγματοποιήθηκε διερεύνηση διαφόρων διατάξεων κβαντικών συστημάτων είτε σε αλληλεπίδραση με άλλα συστήματα είτε μεμονωμένων, αλλά με την συνθήκη το αντίστοιχο κλασικό μη γραμμικό σύστημα να είναι χαοτικό ή ολοκληρώσιμο. Ερευνητικά αποτελέσματα: 1. Ο ρυθμός μεταβολής της Ενδιαπλοκής με την μεταβολή μιας παραμέτρου σύζευξης φράσσεται από την καμπυλότητα των ενεργειακών επιπέδων. Το αποτέλεσμα έχει γενική ισχύ, διότι βασίζεται σε γενικές ιδιότητες των τυχαίων πινάκων που κωδικοποιούν την χαοτική ή την κανονική συμπεριφορά των συστημάτων,2. Ο ρόλος της λεπτομερούς δομής του κλασικού χώρου των φάσεων. Ερευνήθηκε η εξάρτηση της Ενδιαπλοκής από την τιμή παραμέτρου σύζευξης σε σχέση με το διάγραμμα διακλαδώσεων του Βηματικού Στρόβου, καθώς και σε σχέση με την ύπαρξη Κβαντικών Ουλών, 3. Η μη γραμμικότητα συστημάτων σε συνδυασμό με την παρουσία εξωτερικών πεδίων μπορεί να οδηγήσει σε βέλτιστες τιμές ορισμένων παραμέτρων που ευνοούν την δημιουργία Ενδιαπλοκής θερμικά. Μελετήθηκε κατάλληλο μοντέλο, 4. Κβαντικός δίαυλος βρίσκεται σε αλληλεπίδραση με το τοπικό περιβάλλον. Οι ιδιότητες του τοπικού περιβάλλοντος (χάος ή κανονικότητα) μπορούν να επηρεάσουν τις δυνατότητες του διαύλου, 5. Ένα ανοικτό κβαντικό σύστημα αλληλεπιδρά με τοπικό κβαντικό περιβάλλον λίγων βαθμών ελευθερίας, καθώς και με ένα ολικό Μαρκοβιανό περιβάλλον και τελικά προκαλείται απώλεια κβαντικής συνάφειας. Διερευνήθηκε, αριθμητικά, ο τρόπος με τον οποίο, οι κλασικές ιδιότητες του τοπικού περιβάλλοντος επηρεάζουν τον ρυθμό απώλειας συνάφειας του συστήματος. / Quantum Information is a particular property of quantum systems which is associated with the quantum mechanical superposition principle and the correlation of the systems in the entangled states. Due to the interaction with the classical environment, this basic property of Entanglement is lost very quickly, with the result, its practical usefulness to be dramatically reduced. The present Thesis is concerned with the study of various arrangements of quantum systems either in interaction with other systems, or isolated, but with the condition that the corresponding classical non linear system is chaotic or integrable. Results presented in the thesis: 1. Τhe rate of change of entanglement of a quantum system with respect to the change of an interaction parameter is bounded by the curvature of the energy levels. This result has a general validity, because it is based on general properties of random matrices, which may encode the regular or chaotic behavior of physical systems, 2. The role of the detailed structure of the classical phase space. The dependence of entanglement on the position of a parameter of interaction in connection to the bifurcation diagram in the model of quantum kicked top was studied. An analysis was carried out for a possible impact of the existence of scars on the behavior of entanglement, 3. The non linearity of systems combined with the presence of external fields may lead to optimal values of certain parameters which favor the thermal creation of entanglement. A particular model was studied in which this behavior is observed, 4. A quantum channel is in interaction with its local environment. The question posed, is whether the properties of the local environment (chaos or integrability) may influence the capabilities of the channel, 5. An open quantum system interacts with a quantum local environment, which in general has few degrees of freedom, and a global infinite one. It was numerically investigated how the classical properties of the local environment Influence the decoherence rate of the system.

The purpose of this study is to explore the nature of dynamic relationships within families, and indicating how the decision to divorce may result from a family's difficulty in adjusting to new changes and stressors. Thus, divorce results in the redefinition of a nuclear system. This study made use of social constructionism as its epistemological framework. By means of in-depth one-on-one interviews, the researcher was able to hear the narratives of all six participants. Hermeneutics was used to analyze the data. The participants' stories were reencountered through the researcher's own frame of reference in which common themes of the divorce process were co-constructed. These themes were later elaborated on and a comparative analysis was undertaken to link them to the available literature. The information gained from the study could contribute to existing research on the impact of divorce, family reorganization following a divorce, and offer a new perspective in understanding family systems. / Clinical Psychology / M.A. (Clinical Psychology)

The purpose of this ethnographic study is to explore the following: 1. The counsellors’ experience of the process of career counselling provided to students at a distance learning institution 2. My own experiences of doing counselling with Unisa students. 3. How Holland’s career theory, the social cognitive career theory and the chaos theory of careers could shape the process of career counselling. The themes that emanated from the stories of six counsellors indicate that they view counselling as a continuous process wherein it is necessary to strike a balance through blended counselling between the needs of individuals versus helping the multitude of anonymous students. In order to facilitate counselling effectively, counsellors need resources and in order to develop these resources they use a diversity of career theories which act as a frame of reference. Attention is given to the development of career counsellors’ identity and self-confidence and how this impacts on the counsellors’ growth. The recommendations of this study hold the promise of contributing to the counselling process at the DCCD. / Psychology / D.Litt.et Phil. (Psychology)

The study examines cognitive rationality as to()l for problemsolving within the context of a movement from determinism and monolithic universal Reason towards indeterminism and plurality. It is contended that theories of literature do not provide an adequate conceptual framework, and therefore, extensive use is made of pluralist fallibilism (Popper, Helmut Spinner) and chaos theory. The philosophy of Friedrich Nietzsche is viewed as a decisive influence in the shift towards plurality and scepticism. In chapter 2, Conan Doyle's Sherlock Holmes stories, a novel by Agatha Christie and Gaston Leroux's Le mystere de Ia chambre jaune are discussed as examples of optimistic rationalism. Chapter 3 indicates that Eco's II nome della rosa emphasizes the conjectural nature of truth and objective knowledge, underpinned by a 'soft' rationalism which amounts to monopolistic pluralism. Chapter 4 analyses the defeat of cognitive rationality by the complex interaction of a multiplicity of independent causal series. The detectives' relationship with the feminine exemplifies the interpenetration of rationality and the instinctual, while the mystery of the feminine is a metaphor for impenetrable complexity. Chapter 5 shows that hypotheses concerning random complex systems remain inconclusive. However, as the trajectory of a complex system can be regulated, so reason can be viewed as the underlying regulative pattern (strange attractorl for an infinite proliferation of hypotheses. Thus, despite .shifting conceptions of rationality and order, all the detectives in the study accept objective truth as regulative principle and are involved in a search for objective knowledge / Afrikaans and Theory of Literature / D.Litt. et Phil. (Theory of literature)

O Dilema do Prisioneiro (DP) é o jogo mais proeminente da Teoria dos Jogos devido à emergência da cooperação entre jogadores egoístas. O comportamento de cada jogador depende da estratégia que ele adotada e do seu ganho, que é determinado em função dos parâmetros do DP (T, R, P e S) e do número z de vizinhos com que ele joga. Portanto, a estrutura espacial dos jogadores não é relevante. Em nosso trabalho, utilizamos um autômato celular unidimensional onde cada jogador pode cooperar ou desertar ao interagir, simetricamente, com seus z vizinhos mais próximos. O sistema proposto nos permitiu realizar um estudo exaustivo do espaço de parâmetros para as estratégias evolucionárias Darwiniana (EED) e a Pavloviana (EEP) e compara-las. A geometria unidimensional nos possibilita obter os mesmos resultados dos sistemas em dimensionalidade arbitrária d, além de apresentar várias vantagens em relação a elas. No sistema que propomos os efeitos de borda são menores, exige menos tempo para a execução das simulações numéricas, permite variar o valor de z e é fácil obter uma representação visual da evolução temporal do sistema. Tal visualização simplifica a compreensão das interações entre os jogadores, pois surgem padrões nos agrupamentos de cooperadores/desertores, semelhantes aos pertencentes às classes dos autômatos celulares elementares. O estudo destes padrões nos permite compreender simplesmente a emergência da cooperação ou deserção nos sistemas. A evolução temporal do sistema que adota a EED gera um diagrama de fases muito rico com a presença das fases cooperadora, desertora e caótica. Já para a EEP, obtivemos um novo resultado analítico para as transições de fase, que neste caso são: cooperadora e quasi-regular. O estudo numérico exaustivo determinou as regiões do espaço de parâmetros onde acontecem cada uma das fases, e os efeitos da auto-interação podendo assim validar os resultados teóricos. O estudo do caso particular T = 1, tradicionalmente considerado como trivial, mostrou que ele apresenta comportamentos inusitados. Nossa principal contribuição para o estudo do DP é a obtenção de um novo paradigma. A geometria unidimensional com interação de vizinhos simétricos permitiu a visualização da evolução de padrões de cooperadores e desertores, o cálculo analítico de Tc para a EEP e o estudo de T = 1 para tais sistemas. / The Prisoner Dilemma (PD) is the most prominent game of the Game Theory due to emergency of the cooperation between selfish players. The behavior of each player depends on his/her strategy and the payoff, which is determined in function of the PD parameters (T, R, P and S) and by the number z of neighbors with whom he/she plays. Therefore, the spatial structure of the players does not matter. In our work, we have used a one-dimensional cellular automaton where each player can cooperate or defect when interacting, symmetrically, with his/her z nearest neighbors. The considered system allowed us to carry out an exhaustive exploration of the parameters space for the Darwinian Evolutionary Strategy (EED) and Pavlovian (EEP) and compares them. One-dimensional geometry makes possible to us get the same results of the systems in arbitrary d dimensional networks, besides, it presents some advantages. For the system that we proposed compared to the others dimensional networks, the boundary effects are less present, it needs less time for run the numerical simulations, it allows to vary the z value and is easier to get the visual representation of the system temporal evolution. Such visualization simplifies the understanding of the interactions between the players, therefore patterns appear in the clusters of cooperator/defectors, and these patterns belong to the elementary cellular automata classes. The study of these patterns allows them to understand in an easy way the emergence of the cooperation or defection in the systems. The temporal evolution of the system that adopts the EED yields a very rich phases diagram with the presence of cooperative, defective and chaotic phases. By the other hand, for the EEP, we have got a new analytical result for the phase transitions that in this case are: quasi-regular and cooperative. The exhaustive exploration study determines the regions on the parameters space where happen each phases occurs, and the effect of the self-interaction and thus validate the theoretical results. The study of the particular case T = 1, traditionally considered as trivial one, showed that it presents unusual behaviors, that we will present. Our main contribution for the study of the DP is the attainment of a new paradigm. One-dimensional geometry with interaction of symmetrical neighbors allowed to visualizes the evolution of cooperators and defectors patterns, the analytical result for Tc for the EEP and the study of T = 1 for such systems.