Investigation of Chaotic Features of the Family of Generalized Tent Maps

The goal of this paper is to investigate some interesting dynamical and chaotic features of a family of tent maps.Such dynamical properties include fixed points and their stability, period orbits, visualizing the iterations using a kind of plot called a cobweb plot, and demonstrating a bifurcation diagram for .Furthermore, detecting the presence of chaos in is investigated.The Tent map family has chaotic regions for m > 1.Furthermore, the Cantor sets that occur as non-wandering sets for m > 2 are studied.Finally, we develop MATLAB computer programs that reflect the results interpreting such dynamical behavior.The bifurcation analysis is considered and the presence of chaotic behavior of the discrete dynamical system is solved by investigating the sensitive dependence on the initial condition.The most complex dynamics-chaos-occur only for large values of the parameter m; so the prediction of a chaotic time series could be demonstrated.In the case of the tent map, when m=2, it has become chaotic.