Bifurcation Diagrams of Logistic Function for Different Parameter Values

Dynamical systems concept is a branch of mathematics that attempts to understand processes in motion. For instance, the motions of the stars and galaxies in the heaven are a dynamical system. The world’s weather is another system that changes in time as is the stock market. The logistic map is a polynomial mapping of degree 2, often cited as archetypal example of how complex, chaotic behavior can arise from very simple non-linear dynamical equations. Bifurcation means a deflect, a rending aside. How and when physical, chemical and biological systems sustain sudden barters of the behavior is the appearance of bifurcation. Let us consider denote the logistic map, Where is considered as parameter. Here we observe the situations for different parameter values of . In fact, we will observe attracting and repelling fixed points together with phase portrait. Of course, bifurcation diagram to be sketched in each situation. In the case of logistic bifurcation, we are considering the limits or end behaviors of logistic systems. To comprehend bifurcation behavior, it is always conductive to look at the bifurcation diagram. Saddle-node bifurcation and period-doubling bifurcation are speculated. Animation of a point “rolling” along the logistic curve, bifurcation diagram on logistic map for several iterations are analyzed. We have conferred aggregate espials for different parameter values. Finally, we have exhibited that the schemes are chaotic and non-chaotic for detached parameter appraises.