Paper Title
COMPARISON OF PERIOD DOUBLING BIFURCATION TO CHAOS OF ROSSLER MODEL USING COMPLEX NETWORK OVER MAXIMAL LYAPUNOV EXPONENT

Abstract
Complex network is a powerful tool in time series analysis. In this paper, we have constructed a complex network, using the time series data of the Rossler model with three different parameters a, b and c. Rossler model is a chaotic model which exhibits a period doubling route to chaos. This model contains only one non-linear parameter. By keeping a and b fixed and giving different values to one of the parameter, c of Rossler Model, varying from 1.7 to 5, we have analysed period doubling bifurcation to chaos. Traditionally lyapunov exponent is used to calculate the chaos in a dynamical system. In this paper we calculate the maximal lyapunov exponentseparately and is compared with the parameters of the complex network include average path length, betweeness centrality, degree centrality, eigenvector centrality, graph density and transitivity. Instead of maximal lyapunov exponent we can use the parameters of complex network to study the bifurcation of a chaotic Rossler model.