الفهرس 
Some Basic ConceptsOnly 14 pages are availabe for public view
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Abstract
This thesis introduced some new results on : (1) differences between fractional and integer order differential equations for dynamical games. (2) Stability, Persistence and Hopf Bifurcation in Fractional Order Dynamical Systems. (3) Propounding of some mechanisms for studying cooperative behaviour in myopic society. This mechanisms enhance the cooperation in both unstructured and structured populations. In the unstructured population we used Memory effects on Iterated Prisoner’s Dilemma (IPD) game. While in the structured populations we studied Persistence of cooperators clusters on a spatial grid with non-Iterated Prisoner’s Dilemma , in addition to an effect of non-uniform interaction rates on evolutionary dynamics for non-repeated Prisoner’s Dilemma game. This thesis consists of three chapters : In chapter one, we introduce Some basics of Dynamical Systems : Local Stability of Fixed Points, Global Stability of Fixed Points and Hopf Bifurcation. Moreover, Some basics of Non-cooperative Game Theory : static games, Prisoner’s Dilemma game, Nash equilibrium theorem, dynamical games, Evolutionarily Stable Strategies (ESS), Replicator dynamics. In addition to, Some basics of Fractional calculus: Caputo and Riemann–Liouville fractional order differential equations, and The relation between them. We proved that fractional order differential equations for dynamical games differs significantly from its integer order counterpart. we introduced a preliminary study about Stability, Persistence and Hopf Bifurcation in Fractional Order Dynamical Systems . In chapter two, we propose the following mechanism for studying cooperative behaviour in myopic society. (I) Memory I.i) Iterated Prisoner’s Dilemma (IPD) game [Axelrod (1984)], [Lindgren (1991)]. I.ii) Bounded Memory game [Smale(1980)] , [Ahmed and Hegazi (2000)] . In chapter three, we propose an other mechanism for studying cooperative behaviour in myopic society. (II)Clustering II.i) Games on grids [Nowak and Sigmund (2000)]. II.ii) Non uniform interaction rates [Taylor and Nowak(2006)]. Moreover, we study Kin selection mechanism which ubiquitous in insect swarms [Hamilton (1964)]. Keywords: Prisoner’s Dilemma game- Iterated Prisoner’s Dilemma- Bounded Memory game- Games on grids- non-uniform interaction rates on evolutionary dynamics for non-repeated Prisoner’s Dilemma game- fractional and integer order differential equations for dynamical games-Kin selection.