Some predictability in one-dimensional chaotic dynamical systems arising in population models
Consider the iteration (discrete, one dimensional dynamical system) \(x_{n+1}=f(x_ n)\) where f is a nonnegative unimodal map. The sojourning time n(f,x) is the maximal number of iterations which don't carry the system with initial state x above the value of the unique maximal point of the system. The sojourning time corresponding to this maximal point k (f(k)\(\geq f(x))\) is denoted by N(f). According to the author the degree of chaos is measured by N(f). This is justified by the fact that the topological entropy of f is, loosely speaking, increasing with N(f). Fluctuating systems and predictability of sojourning times of fluctuating systems are studied. In some systems depending on a parameter the degree of chaos may increase while the sojourning time may become more predictable. The results may be applied, e.g., to the system \(x_{n+1}=x_ n\exp (r(1-x_ n/c)).\)
discrete, one dimensional dynamical system
scientific article; zbMATH DE number 3958303