Dynamic behavior and chaos control in a complex Riccati-type map

Abstract

This paper is devoted to analyze the dynamic behavior of a Riccati- type map with complex variables and complex parameters. Fixed points and their asymptotic stability are studied. Lyapunov exponent is computed to indicate chaos. Bifurcation and chaos are discussed. Chaotic behavior of the map has been controlled by OGY feedback control method.

Mathematics Subject Classication (2010): 34C23, 26A18.

Key words: Complex Riccati-type map, xed points, asymptotic stability, Lyapunov exponent, bifurcation, chaos, feedback control method.