AbstractChaotic systems are nonlinear dynamic systems that exhibit random and unpredictable behavior. The trajectories of chaotic dynamic systems are sensitive to initial conditions, in the sense that starting from slightly different initial conditions the trajectories diverge exponentially. To study chaos, the behavior of the solution of the logistic equation is considered. In this article, for different parameters, the solutions of the logistic equation are analyzed. At some point, the solution diverges towards multiple equilibrium points, the periodicities increasing as the parameter increases. To verify the analytical prediction of the mathematical-blood model, several computer experiments are performed. At a certain value of the parameter, the solution has infinite theoretical periodicities, i.e. it behaves randomly, the system has become chaotic.1 Introduction The behavior of solutions of the logistic equation for certain intervals of parameters is complex, sometimes of ®periodicity erent or aperiodic. Teaperiodic solutions are called chaotic solutions or chaotic motions. Quoting Zak[2], the descriptive definition of chaos can be given as "...one way to de¯nechaos is in behavior that is not an equilibrium, a cycle or even a quasi-periodic motion - there is more to say on chaos. Chaotic motion has some aspect that is probably as random as the tossing of a coin. Randomness arises from sensitive dependence on imperfectly known initial conditions, ".2 Mathematical Models In the analysis of population growth, the behavior of the population. can be modeled by differential equations known as . ..... half of the document ......30.40.50.60.70.80.9rhoxstarBifurcation diagramFigure 4: Bifurcation diagram5 DiscussionThe bifurcation diagram, shown in Fig.4 is obtained by obtaining the solutions of the equation for all values by ½. For ½ > 3 there are no attractive fixed points. As the row increases, the solutions of the logistic equation show increasing complexity. For a certain interval of ½, just above 3, the solution settles into a constant oscillation of period 2. Then, when ½ is further increased, periodic solutions of period 4,8,16. . . appear.For ½ > 3:57, the solution becomesaperiodic, chaotic.Works Cited[1] James Glick.,Chaos[2] Zak S.,Systems and Control,Oxford University Press.[3] Chin-Teng Lin and CSGeorge Lee, Neural Fuzzy Systems, Prentice HallInternation Inc.[4] http://hypertextbook.com/chaos[5] http://www.duke.edu/mjd/chaos/chaosp.html8