With The Memory Of Time Discrete And Continuous Dynamical Systems, Bifurcation Behavior

This paper shows that the bifurcation points of the parameters can be changed by importing the memory influence into both discrete dynamic systems and con-tinuous dynamical systems. In particular, this paper considers two representative models, i.e. the Logistic map and Lorenz systems, which are influenced by the mem-ory of the states. The forms of the memory influence have various types, including two-or-multiple steps of the part states for discrete system, and distributed-state-dependent memory for continuous systems. Using the typical bifurcation theory and technique, the paper theoretically and numerically presents how the dynamical behaviors and determined by the memory influence. Some new phenomena have ob-served, which have not been reported in the literature. Finally, this paper is closed with some remarks and conclusion.