Interesting dynamic behavior in some discrete maps

Document Type: Regular Paper


1 Mathematical Sciences Foundation, N-91, Greater Kailash I, New Delhi, India

2 Department of Mathematics, University of Delhi, Delhi-110007, India

3 Mathematics Department, Shiraz University, Shiraz, Iran


Different discrete models of population dynamics of certain insects have been investigated under various feasible conditions within the framework of nonlinear dynamics. Evolutionary phenomena are discussed through bifurcation analysis leading to chaos. Some tools of nonlinear dynamics, such as Lyapunov characteristic exponents (LCE), Lyapunov numbers, correlation dimension, etc. are calculated for numerical studies and to characterize regular and chaotic behavior. These results are produced through various graphics. Chaotic evolutions of such insect population have been discussed as the parameters attain certain set of critical values. The results obtained are informative and very significant. The correlation dimension for evolution of insect population signifies certain fractal structure.