An efficient method to improve the Logistic map: Design and implementation

Abstract

In this paper, we have designed and proposed a new improved Logistic map (ILM) which enhances the performance of the standard Logistic map (SLM) in terms of higher Lyapunov exponent and steady chaotic behavior. In standard map, the control parameter is limited and should be close to 4 to exhibit chaos. Additionally, in some specific region called as islands of stability, the system behaves non-chaotic. However, for the improved one, the control parameter is not limited to a finite value for the system to be in chaos state and provides chaotic behavior all the time. Firstly, we have designed a new chaotic map and modeled it by using Xilinx block sets in Matlab/Simulink environment. Then, we have realized the ILM through hardware-co simulation on FPGA (Field programmable gate array) for practical applications.