Dynamics of the populations depend on previous two steps

The present paper is devoted to investigation of the modified case of the modified logistic mapping which depends on previous two steps. We learnt logistic mappings as a second order difference equations. We have classified all Cauchy problems whose solutions are stable, unstable, periodic and chaotic. Classification of Cauchy problems are equivalent to Julia and Fatou sets. In this paper we learnt the properties of Julia and Fatou sets for the modified logistic mappings. Julia and Fatou sets help to define asymptotical behavior of the trajectories solutions of certain mappings which is the solutions of deference equations