Chaotic behavior and its control in a two parameter map with variable Jacobian

Abstract

Inthe present paper we have considered the mapwhere , are parameters. The map was originally proposed by Maynard Smith [17] for study of population growth. We have shown how chaos creep into the model. We have used the techniques of Lyapunov exponent, time series analysis, Fourier spectra, Bifurcation diagram, correlation and embedding dimension etc. to draw our conclusions. Further, we have shown how the 'periodic proportional pulse' method can be used to control the chaos generated in the system.