In the context of nonlinear dynamics, interesting dynamic behavior of Gumowski-Mira Map has been noted under various feasible circumstances. Evolutionary phenomena are discussed through the study of bifurcation analysis leading to period-doubling and chaos. The appearance of chaos in the method is identified by plotting Lyapunov characteristic exponents (LCE) and Topological Entropy within certain parameter range. Dynamic Lyapunov Indicator (DLI) has been procured for further identification of regular and chaotic motions of the Gumowski-Mira Map. The numerical results through the indicator DLI clearly demonstrate the behavior of our map. The correlation dimension has been calculated numerically for the dimension of the chaotic attractor.
Prasad, Sada Nand; Meena, K. R.; and Ansari, Abdullah A.
Complexity Dynamics of Gumowski-Mira Map,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
1, Article 15.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss1/15