Role of logistic and Ricker’s maps in appearance of chaos in autonomous quadratic dynamical systems

Abstract

New existence conditions of a chaotic behavior for wide class of \((n+1)\)-dimensional autonomous quadratic dynamical systems are suggested. It is shown that in all such systems the chaotic dynamics is generated by 1D discrete map by some combination of the logistic map \(f(x) = \lambda x(1 - x); \lambda > 0\) and Ricker’s map \(g(x) = x \exp (\mu - x); \mu > 0\).